1 Introduction

The South China Sea has emerged as one of the most contentious geopolitical hotspots of the 21st century, embodying a complex interplay of historical grievances, territorial disputes, and strategic competition. This semi-enclosed sea, bordered by China, Vietnam, Malaysia, Brunei, Indonesia, the Philippines, and Taiwan, is not merely a geographical space but a nexus of competing national interests, economic aspirations, and military strategies. The region’s significance stems from its role as a critical maritime crossroads, its abundant natural resources, and its position as a potential flashpoint in the evolving dynamics between major powers, particularly China and the United States.

The multifaceted nature of the South China Sea dispute presents a formidable challenge for policymakers, diplomats, and scholars seeking to understand and mitigate conflict risks. Traditional approaches to analyzing such complex geopolitical situations often struggle to capture the full spectrum of variables and their intricate interactions. In response to this challenge, our study employs an innovative Monte Carlo simulation approach to model and analyze potential conflict scenarios in the South China Sea.

This methodology allows us to account for the inherent uncertainties and complexities of international relations while providing quantitative insights into possible future trajectories of regional tensions. By incorporating key variables such as military spending, economic growth, territorial claims, and diplomatic relations, alongside novel factors inspired by world-systems theory, our model offers a comprehensive framework for assessing geopolitical risk in this strategically vital region.

Our research is guided by several key questions:

  1. What factors most significantly influence the likelihood of conflict in the South China Sea?
  2. How do changes in military spending, economic conditions, or diplomatic relations affect the stability of the region?
  3. Can we identify tipping points or thresholds that dramatically increase the risk of conflict?
  4. What are the potential long-term trajectories of tensions in the region under various scenarios?

To address these questions, we have developed a sophisticated simulation model that draws on diverse data sources, including the Stockholm International Peace Research Institute (SIPRI) Military Expenditure Database, the World Bank’s World Development Indicators, and the Correlates of War Project. Our approach combines elements of neo-realist theory with insights from world-systems analysis, allowing us to consider both immediate security concerns and broader economic and structural factors shaping regional dynamics.

The use of Monte Carlo methods in political science and international relations is not novel, but their application to the specific context of the South China Sea dispute represents an innovative approach. By running thousands of simulations with varying initial conditions and random events, we can generate a rich dataset of potential outcomes, providing a nuanced picture of conflict probabilities and key influencing factors.

This paper is structured as follows: We begin with a comprehensive review of the relevant literature on the South China Sea dispute and the application of simulation methods in international relations. We then provide a detailed description of our methodology, including data sources, model design, and simulation parameters. The results section presents our key findings, offering visualizations of conflict probabilities, sensitivity analyses of different variables, and insights into the temporal patterns of peace and tension in the region.

In our discussion, we interpret these results within the broader context of international relations theory and current geopolitical realities. We explore the implications of our findings for policymakers and diplomats working on South China Sea issues, offering insights into potential strategies for conflict prevention and de-escalation. We also critically examine the strengths and limitations of our Monte Carlo approach, comparing it with other methods of conflict prediction and analysis.

By providing a quantitative framework for assessing conflict dynamics in the South China Sea, this study aims to contribute to both the theoretical understanding of complex geopolitical disputes and the practical efforts to maintain peace and stability in this crucial region. Our findings offer a data-driven perspective on the factors driving regional tensions, the potential for conflict escalation, and the opportunities for diplomatic intervention.

As the global center of economic and strategic gravity continues to shift towards the Indo-Pacific, understanding the dynamics of the South China Sea becomes increasingly critical for international security. Through this research, we hope to provide valuable insights that can inform policy decisions, guide further academic inquiry, and ultimately contribute to the peaceful resolution of one of the world’s most pressing geopolitical challenges.

2 Literature Review

Conflict prediction in international relations has gained increasing attention due to the complex and dynamic nature of global politics. Predictive models are employed to foresee the likelihood of conflict, allowing policymakers to implement preventive measures. This review synthesizes the most recent research on the methodologies, challenges, and effectiveness of conflict prediction models, highlighting key findings and gaps in the literature.

2.1 Conflict Prediction in International Relations

Various predictive models have been developed to forecast conflicts, including statistical models, machine learning techniques, and hybrid approaches. These models range from traditional regression models to more sophisticated machine learning algorithms. For example, D’Orazio (2020) discusses how predictive models differ from inferential models, focusing on the importance of predictive performance in conflict research Conflict Forecasting and Prediction.

The effectiveness of conflict prediction models varies depending on the data and methodology used. Chadefaux (2017) explores the limitations of current conflict forecasting methods, questioning whether certain aspects of conflicts will always remain unpredictable Conflict Forecasting and Its Limits. The study highlights the need for more robust models that can account for the complexities of international conflicts.

One of the primary challenges in conflict prediction is the accuracy and reliability of the models. Predictive models often face difficulties in handling non-linear relationships and dependencies within conflict data. This issue is emphasized in studies like Chadefaux (2017), which calls for improved methodologies to enhance predictive accuracy. Moreover, the integration of machine learning into conflict prediction has introduced new challenges, such as bias and overfitting, as discussed by Rudin (2019) in the context of high-stakes decision-making Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead.

The practical applications of conflict prediction models extend beyond academic research, influencing policy decisions and preventive measures in international relations. Predictive models are used to guide policy, assess the importance of variables, and test theories in real-world scenarios. However, as D’Orazio (2020) notes, the use of these models also raises questions about their implications for policy-making, particularly in situations where predictions are uncertain or contested.

The literature reveals a range of approaches to conflict prediction, with each method offering unique insights and facing distinct challenges. Statistical models provide a foundation for understanding conflict dynamics, while machine learning approaches offer the potential for greater accuracy and adaptability. However, the integration of these methods remains a critical area for further research. Studies like those by D’Orazio (2020) and Chadefaux (2017) underscore the need for more comprehensive models that can address the inherent unpredictability of conflicts while providing actionable insights for policymakers.

2.2 Factors influencing international conflicts

Understanding the factors and variables that influence international conflict is crucial for the study of international relations and the development of effective conflict prevention strategies. Scholars have identified a range of factors, including political, economic, cultural, and social variables, that contribute to the outbreak, escalation, and resolution of conflicts between nations. This review synthesizes key findings from recent studies, providing a comprehensive overview of the various elements that play a role in international conflict.

Political variables, such as regime type, leadership transitions, and international alliances, play a significant role in influencing international conflicts. For example, Burgos et al. (2015) highlight the importance of civil-military relations and democratic governance in shaping conflict dynamics. They argue that the operationalization of these variables is crucial for understanding their impact on international conflict Civil-Military Dynamics, Democracy, and International Conflict.

Additionally, Bertoli, Dafoe, and Trager (2018) explore the role of political party dynamics, finding that right-wing leaders are more likely to engage in military conflict, particularly following close elections that bring these leaders to power Is There a War Party? Party Change, the Left–Right Divide, and International Conflict.

Economic conditions, such as resource scarcity, economic inequality, and the presence of valuable natural resources, are often linked to international conflicts. The study by Bernauer and Böhmelt (2020) examines conflicts over freshwater resources, emphasizing how economic scarcity can lead to both conflict and cooperation, depending on the international context International Conflict and Cooperation over Freshwater Resources.

Cultural and social factors, including ethnic divisions, religious differences, and social identity, also play a critical role in international conflicts. Masterson (2022) investigates how emotions such as humiliation can influence leaders’ conflict preferences, particularly in situations where status loss is perceived. This study provides experimental evidence that emotions can shrink the bargaining range, making conflicts more likely Humiliation and International Conflict Preferences.

Moreover, Shakirullah et al. (2020) discuss the deep-rooted cultural and social factors contributing to violent conflict in the North Waziristan Tribal Areas of Pakistan. Their study highlights the interplay between local socio-economic conditions and broader geopolitical dynamics in driving conflict The Underlying Causes of Violent Conflict in the North Waziristan Tribal Areas of Pakistan.

Demographic engineering, where states alter the demographic composition of certain regions, has also been identified as a significant factor in international conflicts. McNamee and Zhang (2019) explore how demographic changes in China and the former USSR were used as a tool of state policy to secure control over contested areas, thereby influencing international relations Demographic Engineering and International Conflict: Evidence from China and the Former USSR.

The literature on factors influencing international conflict reveals a complex interplay of political, economic, cultural, social, and demographic variables. Political factors such as regime type and leadership transitions are frequently cited as significant contributors to conflict, while economic factors often serve as both causes and potential points of resolution. Cultural and social variables, particularly those related to identity and emotions, are increasingly recognized for their influence on conflict dynamics. Demographic engineering represents a less explored but critical factor that can have long-lasting impacts on international relations.

2.3 Existing models and approaches for predicting conflicts

Traditional statistical models have been foundational in the field of conflict prediction. These models typically involve regression analysis, where various independent variables (such as economic indicators, political stability, and historical conflict data) are used to predict the likelihood of conflict. Bernauer and Böhmelt (2020) provide an example of such models, focusing on international conflict and cooperation over freshwater resources. Their study employs statistical techniques to forecast potential conflicts in river basins, demonstrating the applicability of these models to environmental and geopolitical issues International Conflict and Cooperation over Freshwater Resources.

Hybrid models combine elements of statistical methods and machine learning to leverage the strengths of both approaches. Häffner et al. (2023) introduce a hybrid model that uses deep learning in combination with interpretability techniques to create a domain-specific dictionary for conflict prediction. This model outperforms traditional methods while maintaining a balance between complexity and interpretability, which is crucial for practical applications in policy-making Introducing an Interpretable Deep Learning Approach to Domain-Specific Dictionary Creation: A Use Case for Conflict Prediction.

Early Warning Systems (EWS) are designed to predict the onset of conflicts by continuously monitoring risk factors and issuing alerts when the likelihood of conflict increases. Bazzi et al. (2022) explore the feasibility of violence early-warning prediction using fine-grained data from Colombia and Indonesia. Their study finds that while EWS can effectively identify persistent hotspots of violence, they struggle with predicting new outbreaks or escalations of violence The Promise and Pitfalls of Conflict Prediction: Evidence from Colombia and Indonesia.

In addition to general-purpose models, there are domain-specific approaches tailored to particular types of conflicts or regions. For example, the study by Bernauer and Böhmelt (2014) on “Basins at Risk” focuses on predicting conflicts in international river basins using environmental and geopolitical data. This approach highlights the importance of considering the unique characteristics of specific conflict scenarios when developing predictive models Basins at Risk: Predicting International River Basin Conflict and Cooperation.

3 Theoretical Framework

3.1 Neo-Realism

Neo-realism, introduced by Kenneth Waltz, emphasizes the anarchic structure of the international system, where states, as rational actors, seek survival primarily through the accumulation of power. The theory posits that the distribution of power among states, especially in the form of balance of power, critically shapes international relations and the likelihood of conflict. This review synthesizes contemporary scholarship on neo-realism, focusing on its explanatory power in international conflict.

Waltz’s seminal work laid the groundwork for understanding international politics through the lens of structure rather than human nature or domestic politics. Scholars like Daniel Bessner and Nicolas Guilhot have further explored how neo-realism diverged from classical realism by dismissing the role of state decision-making, focusing instead on systemic forces that compel states toward conflict or cooperation (Bessner and Guilhot 2015).

Neo-realism’s emphasis on the balance of power as a stabilizing force in international relations has been critically examined. For instance, Underwood and Paul (2020) highlight the historical and enduring relevance of balance of power in maintaining peace by preventing any state from becoming too powerful, which would otherwise increase the likelihood of conflict.

The simulation is grounded in a synthesis of neo-realist and world-systems theories. Neo-realism, as developed by Kenneth Waltz (1979), emphasizes the role of state power, security dilemmas, and balance of power in international relations. This perspective informs our modeling of military capabilities, territorial disputes, and inter-state tensions. Complementing this, we incorporate Immanuel Wallerstein’s (1974) world-systems analysis, which focuses on the global economic structure and core-periphery relationships. This approach allows us to consider the broader economic contexts and power dynamics that shape state behavior in the region.

The rise of China has tested the predictions of neo-realism regarding the behavior of emerging powers. Shifrinson (2018) analysis suggests that while neo-realism predicts conflict as China challenges US dominance, the reality may be more nuanced, with potential for cooperation depending on how power is perceived and balanced in the Asia-Pacific region.

The concept of the security dilemma, a core element of neo-realism, is revisited in the context of current international challenges. The work of Lachlan McNamee and Anna Zhang on demographic engineering shows how states may act preemptively to alter power dynamics within their borders, driven by fears of external threats (McNamee and Zhang 2019).

Neo-realism continues to provide a robust framework for analyzing international conflict, particularly through its focus on the systemic constraints imposed by the anarchic international order. While the theory’s predictions are not always borne out in every instance, its emphasis on the balance of power and state behavior in response to systemic pressures remains a valuable lens for understanding global conflict dynamics. Future research should continue to explore the intersections of neo-realism with technological advancements and the evolving geopolitical landscape.

3.2 World-System Analysis (WSA)

World-System Analysis (WSA), developed by Immanuel Wallerstein, offers a comprehensive framework for understanding the historical and contemporary dynamics of global capitalism. By focusing on the global economy as a single interconnected system, WSA challenges traditional nation-state-centered approaches, emphasizing the hierarchical relationships between core, semi-periphery, and periphery regions. This literature review explores the theoretical foundations of WSA and its application in various empirical contexts.

World-System Analysis (WSA) emerged as a critical approach in the social sciences, seeking to explain global inequalities through the lens of historical capitalism. WSA posits that the global economy is structured into a core-periphery hierarchy, where core nations exploit peripheral ones, leading to persistent global inequalities. This review synthesizes key theoretical advancements and empirical studies within the WSA framework.

Immanuel Wallerstein’s foundational work on WSA emphasized the importance of viewing the world as a single, interconnected system, rather than as a collection of independent nation-states. His work, particularly his book World-Systems Analysis, outlines the key characteristics of the modern world-system, including its capitalist economy, the division of labor, and the geopolitical hierarchies that sustain global inequalities (Wallerstein 2013b).

Wallerstein (2013a) also explored the notion of systemic crisis within the capitalist world-economy, arguing that the current global order is undergoing a fundamental transformation. His analysis of the structural crisis of the capitalist world-economy highlights the unsustainable nature of global capitalism and the potential for significant shifts in global power dynamics.

The concept of core-periphery relations is central to WSA. Scholars have applied this framework to analyze various global phenomena, including economic inequality, environmental degradation, and labor exploitation. For instance, Soendergaard (2018) study of the Brazilian soy expansion demonstrates how modern agribusiness practices in peripheral regions reflect the exploitative dynamics of core-periphery relations, leading to socio-economic and environmental challenges.

WSA has also been applied beyond economics and sociology, influencing the study of literature and culture. Franco Moretti’s exploration of world literature through WSA reveals how literary works reflect the global economic and cultural disparities that characterize the modern world-system (Moretti 2011).

3.3 Integrating Neo-Realism and World-System Analysis

3.3.1 Structural Power Dynamics and Global Hierarchies

Understanding modern international regional conflicts requires a multifaceted approach that accounts for both the structural dynamics of the international system and the historical-economic processes that shape global inequalities. Neo-realism and World-System Analysis (WSA) offer complementary frameworks that, when integrated, provide a robust model for simulating and analyzing these conflicts. Neo-realism focuses on the power dynamics and state behavior within an anarchic international system, while WSA emphasizes the historical evolution of the global economy and the hierarchical relationships between core, semi-periphery, and periphery regions.

By integrating these theoretical perspectives, our model aims to provide a more comprehensive understanding of both immediate security concerns and longer-term economic motivations influencing state actions in the South China Sea region.

3.3.2 Regional Conflicts as Manifestations of Global Inequalities

Neo-realism explains regional conflicts primarily through the lens of state behavior in response to threats and power imbalances. However, WSA emphasizes that these conflicts are often rooted in global inequalities and the historical exploitation of peripheral regions. By combining these perspectives, we can simulate how regional conflicts are not just about immediate power struggles but are also manifestations of deeper structural issues.

For instance, the conflict in Ukraine can be seen as a neo-realist power struggle between Russia and the West, with both sides attempting to maintain or alter the regional balance of power. WSA adds that this conflict also reflects the broader systemic pressures on peripheral and semi-peripheral states, where economic dependency and historical exploitation exacerbate tensions and lead to conflict.

3.3.3 Security Dilemmas and Economic Exploitation

Neo-realism’s concept of the security dilemma, where states’ actions to ensure their security lead to increased insecurity for others, can be enriched by WSA’s focus on economic exploitation and dependency. In regions where peripheral states are economically dependent on core states, efforts to enhance security through military alliances or economic policies can lead to conflicts that are not merely about power but also about resisting or reinforcing economic exploitation.

3.3.4 Simulating Conflict Scenarios

By integrating neo-realism and WSA, one can simulate conflict scenarios that account for both immediate power dynamics and long-term structural inequalities. Such simulations can include variables like shifts in global power (e.g., the rise of China), economic crises that impact core-periphery relations, and the strategic behavior of states in response to perceived threats. These simulations would highlight how regional conflicts are often the result of both immediate strategic concerns and deep-seated economic and historical processes.

For example, a simulation of conflict in the South China Sea would include neo-realist variables such as military capabilities, alliances, and strategic interests, while also incorporating WSA variables such as the historical economic dependencies of Southeast Asian nations and the impact of global trade routes on regional stability.

For example, in the Middle East, the security dilemmas faced by states like Iran and Saudi Arabia are not only about regional power but also about resisting the economic and political control exerted by global powers. WSA helps to explain how these security concerns are tied to the region’s historical role as a periphery in the global capitalist system, where control over resources has been a central issue.

Neo-realism posits that the distribution of power among states, particularly the balance of power, is a key determinant of international conflict. States, driven by the need to ensure their survival, engage in power-balancing strategies, which can lead to conflicts when power shifts or when states perceive threats to their security. WSA, on the other hand, situates these power dynamics within a broader historical context, where core states maintain dominance over peripheral regions through economic exploitation and political control. By integrating these frameworks, one can simulate how shifts in global power (as understood by neo-realism) are influenced by long-term economic inequalities and structural dependencies (as explained by WSA).

For example, the rise of China can be analyzed through neo-realism as a challenge to the existing balance of power, particularly in the Asia-Pacific region. However, WSA adds a layer of understanding by framing China’s rise as part of a broader shift in the global economic order, where a semi-peripheral state moves toward core status, challenging the established core-periphery relations.

3.3.5 Key Variables and Core-Periphery Dynamics

Our simulation incorporates a range of variables for each country, including traditional measures such as military spending (as a percentage of GDP), economic growth rate, territorial claims, and diplomatic relations. We also include measures of national military capability, democracy scores, trade surpluses, and surplus domestic product.

World System Variables
World System Variables

To capture world-systems dynamics, we introduce three novel variables: technological advancement, economic power, and global influence. These variables form the basis for calculating each country’s position in the core-periphery structure of the world-system.

We operationalize the core-periphery concept through two indices:

  1. Core Index: This is calculated as a weighted average of economic power (40%), technological advancement (30%), and global influence (30%).

  2. Periphery Index: Defined as 1 minus the Core Index.

These indices play a crucial role in determining the likelihood of a country initiating or being targeted by certain types of events, reflecting the asymmetric power dynamics inherent in the world-system.

3.4 The South China Sea

The South China Sea represents one of the most strategically significant maritime areas in the world. Encompassing approximately 3.5 million square kilometers, this semi-enclosed sea is bordered by China, Vietnam, Malaysia, Brunei, Indonesia, the Philippines, and Taiwan. Its importance stems from a combination of geographic, economic, and geopolitical factors that make it a focal point of regional and global interest.

3.4.1 Historical Geopolitical Significance of the South China Sea

The South China Sea has historically been a crucial maritime corridor, integral to trade and cultural exchange between East and West. In modern times, its significance has only grown, primarily due to its strategic location and abundant natural resources. The region is now “one of the busiest maritime corridors in the world,” with nearly one-third of global shipping traversing its waters, a factor that gives control over these sea lanes immense economic and strategic value​ (Hutagalung 2024).

The South China Sea is also believed to be rich in natural resources, including oil, gas, and fish, which are essential for the energy security and economic prosperity of the nations bordering it. These resources have made the region “a focal point of territorial disputes,” where various nations assert overlapping claims, most notably China with its “nine-dash line” claim that extends over much of the sea​ (cf. Hutagalung 2024; Heydarian 2024).

Map of the South China Sea
Map of the South China Sea

3.4.2 Historical Overview

The geopolitical significance of the South China Sea can be traced back to its early role in trade and as a contested space among regional powers. China has historically laid claim to much of the South China Sea, invoking ancient maps and historical usage as the basis for its sovereignty. After World War II, China sought to reclaim sovereignty over several islands in the region, including the Paracels and Spratlys, actions that were grounded in both historical claims and modern geopolitical strategy.

In the latter half of the 20th century, the South China Sea became increasingly militarized, with China and other claimant states establishing military outposts on various islands and reefs. The Cold War era further heightened the strategic importance of the region as it became a theater for the broader US-Soviet rivalry, with the US keen to contain the spread of communism in Southeast Asia​ (Konrad-Adenauer-Stiftung 2023; Hsieh 2018)​.

3.4.3 Geopolitical Dynamics

In recent decades, the South China Sea has emerged as a flashpoint for broader geopolitical conflicts, particularly between China and the United States. China’s assertion of the so-called “Nine-Dash Line”—a demarcation line used by China to outline its claims over most of the South China Sea—has been a source of significant tension. These claims are disputed by several Southeast Asian nations, including Vietnam, the Philippines, and Malaysia, each of whom assert their own territorial rights based on international law, particularly the United Nations Convention on the Law of the Sea (UNCLOS).

The strategic importance of the South China Sea is underscored by its role in global trade; it is a crucial maritime route through which approximately one-third of global maritime crude oil passes. Additionally, the sea is believed to be rich in natural resources, including oil and natural gas, making it a highly coveted region for resource exploration and exploitation​ (Roy 2024; Hsieh 2018).

3.4.4 Recent Developments and Future Outlook

In recent years, China has intensified its efforts to assert control over the South China Sea through the construction of artificial islands and the deployment of military assets. This has led to frequent confrontations with the United States, which conducts “freedom of navigation” operations to challenge China’s expansive claims. The US views China’s actions as part of a broader strategy to reshape the regional order and challenge the US-led international system.

The geopolitical role of the South China Sea is likely to remain contentious as the power dynamics in the region continue to evolve. The key issue moving forward will be whether these disputes can be managed through diplomacy and international law, or whether they will escalate into more direct military confrontations​ (Roy 2024; Hsieh 2018).

3.4.5 Current Geopolitical Dynamics

Today, the South China Sea is at the center of intense geopolitical competition, involving both regional and global powers. China remains the dominant player, with its expansive territorial claims and military buildup. Beijing has been described as pursuing “a wider strategy to achieve dominance in the area,” including the militarization of artificial islands and the deployment of naval forces to enforce its claims​ (Hutagalung 2024). This has led to frequent confrontations with other claimants, such as the Philippines and Vietnam, which are bolstering their own military capabilities in response.

The United States plays a critical role as an external power, committed to maintaining “freedom of navigation” and upholding international law. The U.S. regularly conducts Freedom of Navigation Operations (FONOPs) to challenge China’s claims and reassure its regional allies. As tensions rise, the U.S. has strengthened its alliances with countries like the Philippines and Japan, conducting joint military exercises and providing military aid​ (Gomez 2024; Harding and Stephenson 2023).

The Philippines, facing direct threats from China’s assertiveness, has taken significant steps to bolster its defense capabilities and forge stronger alliances. For example, “the Philippines has sought broader international support,” particularly from the U.S. and Japan, to counterbalance China’s actions​ (Heydarian 2024).

ASEAN, as a regional organization, continues to advocate for a peaceful resolution through diplomatic means, although its efforts are often hampered by internal divisions. While ASEAN aims to negotiate a Code of Conduct with China to manage the disputes, the varying interests of its member states—some of which are economically dependent on China—make a unified approach challenging​ (Hutagalung 2024).

3.5 Monte Carlo Simulation Approach

The choice of Monte Carlo simulation as our primary methodological approach is rooted in the complex and uncertain nature of geopolitical dynamics in the South China Sea region. This method offers several key advantages that make it particularly suitable for our research objectives.

Monte Carlo simulations are a class of computational algorithms that rely on repeated random sampling to obtain numerical results. The fundamental idea is to use randomness to solve problems that might be deterministic in principle.

Firstly, Monte Carlo simulation allows us to account for the inherent unpredictability of international relations. The South China Sea dispute involves multiple actors, each with their own interests, capabilities, and decision-making processes. Traditional deterministic models struggle to capture the full range of possible outcomes that can emerge from the interactions of these diverse factors. In contrast, Monte Carlo simulation enables us to model a wide spectrum of scenarios by running thousands of iterations, each with slightly different initial conditions and random events.

Secondly, this approach provides a robust framework for incorporating uncertainty. Many of the variables in our model, such as economic growth rates, military spending, and diplomatic relations, are subject to fluctuations and unpredictable changes. By using probability distributions derived from historical data to generate these variables in each simulation run, we can more accurately reflect the range of possible values these factors might take in the future.

Furthermore, Monte Carlo simulation is particularly adept at handling the non-linear relationships and feedback loops that characterize complex geopolitical systems. For instance, in our model, the probability of conflict is influenced by the tension index, which in turn is affected by various factors including past conflicts. This circular causality is difficult to model using more traditional, linear approaches, but is naturally accommodated within a Monte Carlo framework.

Another significant advantage of this method is its ability to generate probability distributions of outcomes rather than single-point estimates. This is crucial in the context of the South China Sea, where policymakers and researchers are often more interested in understanding the range of possible scenarios and their relative likelihoods, rather than in predicting a single, deterministic outcome.

Lastly, Monte Carlo simulation offers flexibility in model design and analysis. It allows us to easily adjust parameters, add or remove variables, and test different assumptions about the relationships between factors. This flexibility is invaluable in a research context where our understanding of the underlying dynamics may evolve as new data or theories emerge.

4 Methodology

4.1 Data Collection and Preparation

Our study’s foundation rests on a comprehensive and diverse dataset that captures the multifaceted nature of the South China Sea conflict. The data collection and preparation process was designed to ensure a robust and reliable basis for our Monte Carlo simulation.

We drew from a range of reputable international sources to compile our dataset. The Stockholm International Peace Research Institute (SIPRI) Military Expenditure Database provided crucial information on annual military spending for countries in the region. This data offers insights into the military posturing and defense priorities of the involved nations. To capture economic dynamics, we utilized the World Bank’s World Development Indicators (WDI), which furnished us with a wide array of economic metrics, including GDP growth rates and trade statistics. These economic indicators are vital for understanding the financial underpinnings of regional tensions and cooperation.

Information on territorial claims and ongoing maritime disputes, central to the South China Sea conflict, was sourced from the Correlates of War (COW) Project’s Militarized Interstate Disputes dataset. This comprehensive resource provides detailed accounts of interstate conflicts, offering a historical perspective on the evolution of territorial disputes in the region. To quantify the complex web of diplomatic relations, we turned to the Integrated Crisis Early Warning System (ICEWS) event database. This source allowed us to aggregate data on cooperative and conflictual events between states, providing a nuanced measure of diplomatic ties.

In recognition of the role that governance structures play in international relations, we incorporated democracy scores from the Varieties of Democracy (V-Dem) dataset. This addition allows our model to account for the potential impact of different political systems on conflict dynamics.

4.1.1 R Packages for Data Collection and Processing

The process of collecting and integrating this diverse data was facilitated by several R packages. The WDI package provided a seamless interface to access the World Bank’s development indicators, allowing us to efficiently retrieve and update economic data. The peacesciencer package was instrumental in accessing various peace science datasets, including the Correlates of War data, streamlining our access to critical conflict-related information.

Data preprocessing was a crucial step in ensuring the quality and consistency of our dataset. We harmonized all data to cover a uniform time period from 2000 to 2020, establishing a two-decade baseline for our analysis. This temporal alignment was essential for creating a coherent panel dataset that could capture long-term trends and short-term fluctuations in regional dynamics.

4.1.2 Data Preprocessing

We also undertook careful scaling of variables to ensure comparability across different measures. For instance, military spending was consistently represented as a percentage of GDP, allowing for meaningful comparisons between countries of varying economic sizes. This scaling process was crucial for maintaining the integrity of our analysis across diverse economic and military contexts.

The final step in our data preparation involved the integration of these various datasets. We merged the data based on country and year identifiers, creating a comprehensive panel dataset that forms the backbone of our Monte Carlo simulation. This integrated dataset provides a holistic view of each country’s military, economic, diplomatic, and governance status over time, allowing our simulation to capture the intricate interplay between these factors in shaping conflict dynamics in the South China Sea region.

4.2 Model design

4.2.1 Identification of key variables

The selection of key variables for our Monte Carlo simulation was guided by both theoretical considerations and empirical analysis of historical data. Drawing from neo-realist and world-systems theories, we identified several factors crucial to understanding conflict dynamics in the South China Sea region. Figure 3 presents an exploratory analysis of these basic variables, offering insights into their distributions and relationships. The variables examined include military spending (as a percentage of GDP), economic growth rate, territorial claims, and diplomatic relations. These factors were chosen for their theoretical importance and the availability of reliable historical data.

The exploratory data analysis revealed several noteworthy patterns. There appears to be a slight negative correlation between military spending and economic growth, suggesting that countries allocating a larger portion of their GDP to military expenditures may experience slower economic growth. This observation aligns with the “guns vs. butter” theory in economics, highlighting the potential trade-offs between defense spending and economic development.

Explorative Analysis of basic variables
Explorative Analysis of basic variables

The distribution of territorial claims is heavily right-skewed, indicating that while most countries have few claims, a small number of nations assert a disproportionately large number of claims. This pattern reflects the geopolitical reality of the South China Sea, where certain countries are more active in territorial disputes. The measure of diplomatic relations shows a wide spread, suggesting significant variation in the diplomatic ties between nations in the region. Interestingly, there doesn’t appear to be a strong correlation between diplomatic relations and other variables, underscoring the complex nature of international relations that cannot be reduced to economic or military factors alone.

The analysis of military spending distribution reveals a right-skewed pattern, indicating that while most countries in the region maintain moderate levels of military spending, a few outliers allocate significantly higher portions of their GDP to defense. This observation is particularly relevant in the context of the South China Sea, where military capabilities play a crucial role in shaping regional dynamics.

These insights from the exploratory data analysis informed our approach to modeling these variables in the Monte Carlo simulation. The observed distributions guided our choice of probability distributions for generating simulated data, ensuring that our model reflects the empirical realities of the region while allowing for the exploration of a wide range of potential future scenarios. By grounding our simulation in this empirical foundation, we aim to enhance the reliability and relevance of our projections for conflict dynamics in the South China Sea.

4.2.2 Creating Probability Distributions for Uncertain Factors

To ensure our simulation accurately reflects the underlying data, we fitted multiple probability distributions to each of our key variables and selected the best fit based on the Akaike Information Criterion (AIC). This process resulted in specific distributions for each of our primary factors.

For Military Spending, the gamma distribution provided the best fit. Economic Growth was most accurately represented by the weibull distribution, while Territorial Claims followed a nbinom distribution. Diplomatic Relations, our final key variable, was best modeled using a norm distribution.

Each of these distributions is defined by specific parameters. The Military Spending distribution is characterized by shape = 4.45 and rate = 2.05. For Economic Growth, the parameters are shape = 1.84 and scale = 4.02. The Territorial Claims distribution is defined by size = 1.48 and mu = 7.43, while the Diplomatic Relations distribution parameters are mean = 0.11 and sd = 0.26.

These fitted distributions form the cornerstone of our simulation methodology. By using them to generate data within our model, we ensure that the simulated scenarios closely align with the patterns observed in the real-world data. This approach significantly enhances the reliability and relevance of our simulation results, providing a solid foundation for our analysis of potential future developments in the South China Sea region.

4.3 Monte Carlo simulation process

The simulation process begins with the initialization of country data based on probability distributions fitted to historical data. Core and periphery indices are then calculated for each country.

Monte Carlo Simulation Design
Monte Carlo Simulation Design

For each year in the simulation, we follow a structured process:

  1. We update country-specific variables based on trends and random fluctuations, reflecting the dynamic nature of international relations.

  2. A tension index is computed, incorporating both traditional security factors and world-systems elements. This index is crucial in determining the likelihood of conflict and other significant events.

  3. Random events are generated, with probabilities influenced by the current tension level and core-periphery dynamics. These events range from diplomatic incidents to economic interventions, reflecting the diverse nature of international interactions.

  4. The impacts of these events on country variables and regional tension are calculated, allowing for complex feedback loops within the system.

  5. Finally, we determine the probability of conflict based on the tension index and historical conflict rates.

This process is repeated for each year of the simulation timeframe, typically set to 10 years to balance between short-term fluctuations and longer-term trends.

To account for the inherent uncertainty in international relations, we employ a Monte Carlo approach, running the simulation multiple times (default: 100 iterations) to generate a distribution of possible outcomes.

4.3.1 Tension Index

The core of our model is the Tension Index, a value between 0 and 1 that represents the overall level of geopolitical stress in the region. It is calculated as follows:

\[T = (w_1M + w_2E + w_3D + w_4C + w_5P + w_6S + w_7G + w_8CP + w_9GI) / K\]

Where M represents the military factor, E the economic factor, D the diplomatic factor, C the military capability factor, P the democracy factor, S the trade surplus factor, G the surplus domestic factor, CP the core-periphery factor, and GI the global influence factor. The w terms represent the respective weights for each factor, and K is a normalizing constant.

The probability of conflict (P) in a given year is modeled as:

\[P(conflict) = min(1, max(0, \alpha T + \beta X + \gamma Y + \delta H))\]

Where T is the tension index, X is a binary variable for potential military incidents, Y is a binary variable for potential diplomatic crises, and H represents the historical conflict rate. The coefficients \(\alpha\), \(\beta\), \(\gamma\), and \(\delta\) determine the impact of each factor on the overall conflict probability.

To normalize T beween 0 and 1 we use a min function, to ensure it not being higher than 1.

\[T = \min(1, \max(0, \sum_{i=1}^{n} w_i f_i))\]

where \(T\) is the Tension Index, \(w_i\) are the weights for each factor, and \(f_i\) are the individual factors.

The factors incorporated into the Tension Index calculation include the military factor (weight: 0.35), territorial factor (0.55), diplomatic factor (-0.05), military capability (0.40), democracy factor (-0.10), trade surplus factor (-0.10), and surplus domestic product factor (-0.05). Each factor is calculated based on relevant data from all countries in the simulation. For instance, the military factor is derived from the ratio of total military spending to economic growth across all countries:

\[f_{military} = \frac{\sum_{j=1}^{m} MS_j}{\sum_{j=1}^{m} EG_j}\]

where \(MS_j\) is the military spending and \(EG_j\) is the economic growth for country \(j\), and \(m\) is the number of countries.

4.3.2 Random Events

The Monte Carlo simulation incorporates a dynamic event system to model the unpredictable nature of international relations in the South China Sea region. This system is designed to introduce stochastic elements that can significantly impact the geopolitical landscape, reflecting the complex and often unexpected developments that characterize real-world international politics.

At each time step in the simulation, representing one year, there is a possibility for a random event to occur. The probability of an event happening is not fixed but rather influenced by the current tension index, calculated based on various factors such as military spending, economic growth, and diplomatic relations. This design choice reflects the observation that periods of higher tension tend to be more prone to significant events that can further alter the geopolitical dynamics.

The simulation considers six types of events: spy affairs, border conflicts, revolutions, military coups, trade agreements, and diplomatic breakthroughs. Each event type has a base probability of occurrence, which is then modulated by the current tension index. For instance, a spy affair has a base probability of 5%, while a more rare and impactful event like a revolution has a lower base probability of 1%. These probabilities increase as the tension index rises, simulating the heightened likelihood of significant events during periods of geopolitical stress.

When an event occurs, it triggers a set of predefined effects on various state variables. For example, a border conflict might increase military spending and decrease diplomatic relations, while a trade agreement could boost economic growth and improve diplomatic ties. The magnitude of these effects is calibrated based on historical data and expert knowledge to ensure realistic outcomes.

Importantly, events are not uniformly applied across all countries in the simulation. Instead, when an event occurs, it affects a randomly selected country. This approach allows for asymmetric developments in the region, mirroring the often uneven impact of international events on different nations. The event system also includes a feedback mechanism through its impact on the tension index. Events like border conflicts or spy affairs increase the tension index, potentially making future conflict-oriented events more likely. Conversely, positive events such as diplomatic breakthroughs or trade agreements decrease the tension index, simulating periods of détente.

This event mechanic adds a layer of unpredictability and dynamism to the simulation, preventing it from becoming overly deterministic. It allows for the emergence of complex scenarios that can significantly alter the trajectory of international relations in the simulated South China Sea region, much like how unexpected events in the real world can rapidly change the course of geopolitics.

By incorporating this stochastic event system, the simulation aims to capture the inherent uncertainty in international relations while still maintaining a foundation in data-driven probabilities and effects. This balance between deterministic trends and random events provides a more nuanced and realistic model of the complex dynamics at play in the South China Sea region.

4.3.3 Conflict Probability

The probability of a conflict occurring in a given year is calculated based on the Tension Index and historical conflict rate:

\[P(conflict) = \min(1, \max(0, 0.1T + 0.1X + 0.05Y + 0.2H))\]

In this equation, \(T\) represents the Tension Index, \(X\) is a binary variable for a potential military incident, \(Y\) is a binary variable for a potential diplomatic crisis, and \(H\) is the historical conflict rate from previous years. The probabilities of \(X\) and \(Y\) occurring are themselves functions of the Tension Index, adding an additional layer of complexity to the model.

4.4 Assumptions and Limitations

While our model strives for comprehensiveness, it is important to acknowledge its assumptions and limitations. The model assumes largely linear relationships between variables, which may not fully capture complex real-world dynamics. Our focus on a 10-year timeframe, while allowing for meaningful analysis, potentially overlooks longer-term cyclical patterns in the world-system.

The use of yearly time steps in our simulation may miss short-term fluctuations and rapid escalations that can be critical in international crises. Additionally, we assume a relatively stable core-periphery structure over the simulation period, which may not always hold true in rapidly changing global dynamics.

Our model primarily focuses on state actors, potentially underestimating the role of non-state actors and international organizations in shaping regional dynamics. This state-centric approach, while aligned with neo-realist theory, may overlook some nuances of modern international relations.

4.5 Validation

To ensure the reliability of our simulation, we validate the model’s outputs against historical data and expert assessments of regional dynamics. However, given the complex and often unpredictable nature of international relations, we emphasize that the simulation results should be interpreted as explorations of potential scenarios rather than precise predictions.

This approach allows us to gain insights into possible future trajectories of conflict and cooperation in the South China Sea, while maintaining a critical awareness of the model’s limitations.

5 Results and Analysis

The Monte Carlo simulation, conducted over 1000 iterations with each simulation spanning a 10-year period, yielded several significant insights into potential conflict dynamics in the South China Sea region. Table 1 provides a summary of key metrics from the simulation, while Figure 4 offers a visual representation of the tension index over time.

As shown in Table 1, the average probability of conflict across all simulations was 11.2%. This relatively low figure suggests that while tensions in the region are significant, outright conflict remains a relatively infrequent outcome in our model. However, this average masks important variations over time and across different scenarios. The maximum tension index reached 1.00, indicating that there were instances in the simulation where regional tensions peaked at their highest possible level. In contrast, the average tension index of 0.75 suggests that the region generally maintains a high but not extreme level of geopolitical stress.

The simulation results indicate that the likelihood of conflict is not uniform across the 10-year period. The year with the highest conflict probability was year 6, with a peak probability of 12.7%. This temporal variation in conflict risk highlights the dynamic nature of geopolitical tensions in the region and suggests that the risk of conflict may evolve in non-linear ways over time.

Interestingly, 39.2% of the simulations resulted in no conflict over the entire 10-year period. This finding underscores the potential for sustained peace in the region, even in the face of ongoing tensions. The average peace duration was infinite, driven by these conflict-free simulations, while the median peace duration was 7 years. This disparity between mean and median peace durations reflects the bimodal nature of the outcomes: many simulations saw extended periods of peace, while others experienced conflict onset within the simulation timeframe.

5.1 Overall probability of conflict in the next decade

Figure 4 provides a visual representation of how the tension index evolved over the 10-year simulation period. The graph shows a gradual increase in tension over time, with the median tension level rising from approximately 0.6 in the first year to about 0.8 by year 10. This upward trend suggests that, on average, our model predicts an intensification of regional tensions over the coming decade.

Simulation Tension Results
Simulation Tension Results

However, the wide range of the tension index values, as indicated by the shaded area in Figure 4, underscores the high degree of uncertainty in these projections. In some scenarios, tensions remained relatively low throughout the simulation, while in others, they rapidly escalated to near-maximum levels. This variability highlights the complex and unpredictable nature of geopolitical dynamics in the South China Sea region.

5.2 Factors with the highest impact on conflict probability

To elucidate the influence of individual variables on the simulation outcomes, we employed a multi-faceted approach combining machine learning techniques with interpretability methods. First, we aggregated the simulation data to create a dataset where each row represents a single simulation run, with the outcome being the occurrence of conflict and the predictors being the average values of key variables over the simulation period. We then trained a Random Forest model on this data, leveraging its ability to capture complex, non-linear relationships. To interpret this model, we utilized Partial Dependence Plots (PDPs), which illustrate the marginal effect of each variable on the probability of conflict.

Figure 5 presents Partial Dependence Plots (PDPs) derived from our Random Forest model, offering crucial insights into how key variables influence the probability of conflict in the South China Sea region. These plots illustrate the marginal effect of each variable on conflict probability while averaging out the effects of other variables, thereby providing a nuanced understanding of each factor’s impact.

The PDP for military spending reveals a non-linear relationship with conflict probability. Initially, as military spending increases, the likelihood of conflict rises sharply. However, this effect plateaus at higher levels of spending, suggesting a diminishing returns effect. This pattern aligns with deterrence theory, indicating that while military buildup may initially heighten tensions, extremely high levels of military preparedness might actually deter open conflict.

Partial Dependence Plot
Partial Dependence Plot

The impact of territorial claims on conflict probability is particularly striking. The plot shows a sharp increase in conflict probability as the number of territorial claims rises, with the effect being most pronounced for the first few claims. This underscores the critical role that territorial disputes play in the region’s stability, suggesting that even a small number of unresolved claims can significantly elevate the risk of conflict.

Diplomatic relations exhibit a complex relationship with conflict probability. Initially, improved diplomatic ties correspond with a decrease in conflict likelihood. However, beyond a certain point, further improvements in diplomatic relations appear to have diminishing returns in terms of conflict prevention. This nuanced relationship highlights the importance of diplomacy in maintaining regional stability, while also suggesting that other factors come into play at high levels of diplomatic engagement.

The PDP for the tension index shows a strong positive correlation with conflict probability. As the average tension index increases, the likelihood of conflict rises sharply, especially beyond a certain threshold. This reinforces the central role of overall regional tensions in determining conflict outcomes and validates the use of the tension index as a key metric in our model.

Interestingly, the plots for technological advancement, economic power, and global influence reveal more subtle effects on conflict probability. While these world-system variables do show some impact, their influence appears less pronounced compared to traditional factors like military spending and territorial claims. This suggests that while core-periphery dynamics play a role in shaping regional tensions, immediate security concerns and territorial issues remain the primary drivers of conflict risk in the South China Sea.

5.3 Temporal patterns in conflict probability

Our Monte Carlo simulation provides valuable insights into the temporal dynamics of peace and conflict in the South China Sea region over a projected 10-year period. The analysis of peace duration reveals several key findings with significant implications for understanding regional stability and informing diplomatic strategies.

Firstly, our model suggests that despite ongoing tensions, there is a substantial probability of sustained peace in the region. The majority of simulation runs indicate that peace can be maintained throughout the entire decade, even in the face of various risk factors and potential flashpoints. This finding underscores the resilience of regional stability and the effectiveness of existing conflict prevention mechanisms.

However, the simulation also highlights that the risk of conflict is not constant over time. The early years of the projected period show a higher probability of conflict onset compared to later years. This suggests that the immediate future may be a critical time for conflict prevention efforts. If tensions can be successfully managed in the near term, the likelihood of sustained long-term peace increases significantly.

Interestingly, our model indicates a kind of ‘peace dividend’ effect. Scenarios that maintain peace in the initial years tend to have an increased likelihood of continued peace. This could reflect the development of diplomatic norms, the strengthening of economic ties, or the establishment of effective communication channels between parties over time.

It’s crucial to note that while our simulation provides a general picture of peace duration, it does not account for the intensity of potential conflicts or the possibility of conflict resolution within the simulated timeframe. Real-world events may unfold in more complex ways than our model can capture.

The peace duration analysis also reveals increasing uncertainty in long-term projections. While near-term estimates of peace probability are relatively consistent across simulations, the range of potential outcomes widens as we look further into the future. This growing uncertainty emphasizes the challenges in making long-term predictions in complex geopolitical environments and the need for adaptive strategies.

Figure 6 visually represents these findings, showing the estimated probability of sustained peace over the simulation period. The graph’s relatively gentle downward slope and the high probability of peace remaining at the end of the 10-year period provide a visual confirmation of the generally optimistic outlook suggested by our model.

These results have important implications for policymakers and diplomats. They suggest that while the risk of conflict in the South China Sea is real, there are substantial opportunities for maintaining peace, especially if tensions can be effectively managed in the near term. The findings also highlight the potential long-term benefits of early successful conflict prevention efforts.

Moreover, the increasing uncertainty in long-term projections underscores the importance of flexible, adaptive approaches to regional diplomacy. Policymakers should be prepared to adjust strategies as new information becomes available and circumstances evolve.

5.4 Event Evaluation

Our Monte Carlo simulations not only project overall conflict probabilities but also provide insights into the frequency, impact, and patterns of various events that shape the geopolitical landscape of the South China Sea region. This event-based analysis offers a nuanced understanding of the factors that influence regional stability and the potential trajectories of interstate relations.

5.4.1 Event Frequency

The simulation results reveal a diverse range of events occurring with varying frequencies. Diplomatic and economic events, such as trade agreements and diplomatic breakthroughs, tend to occur more frequently than more extreme events like military coups or revolutions. This distribution reflects the complex nature of international relations, where day-to-day diplomatic and economic interactions form the bulk of interstate activities, while more dramatic events remain relatively rare.

Event Frequency
Event Frequency

However, the frequency of events related to territorial disputes and military posturing is notably high, underscoring the persistent tensions in the South China Sea region. These events, while not necessarily leading directly to conflict, contribute significantly to the overall tension index and shape the long-term dynamics of regional relations.

5.4.2 Tension Impact

Different types of events have varying impacts on the regional tension index. Unsurprisingly, events such as border conflicts and spy affairs tend to increase tensions substantially. Conversely, diplomatic breakthroughs and trade agreements generally reduce tensions, albeit often to a lesser degree than the increase caused by negative events.

This asymmetry in impact suggests a challenging environment for peace-building, where positive developments must be frequent and substantial to counteract the tension-increasing effects of negative events. It also highlights the importance of proactive diplomacy and economic cooperation in maintaining regional stability.

5.4.3 Events Over Time

The occurrence of events shows distinct temporal patterns over the simulated period. While some event types remain relatively constant in frequency, others show clear trends or cyclical patterns. For instance, the simulation suggests an increasing frequency of economic interventions and technology transfers over time, possibly reflecting growing economic interdependence and technological competition in the region.

Event Occurences Over Time
Event Occurences Over Time

Interestingly, the frequency of certain tension-increasing events, such as territorial disputes, tends to decrease in scenarios where early years are marked by successful diplomatic efforts. This suggests a potential virtuous cycle where early positive interactions can lead to a more stable long-term outlook.

5.4.4 Event Conflict Rate

The analysis reveals complex relationships between specific event types and the probability of conflict. Some events, particularly those related to territorial disputes and military activities, show a strong positive correlation with conflict probability. However, the relationship is not always straightforward. For example, increased frequency of trade agreements generally correlates with lower conflict probability, but extremely high levels of economic interdependence can sometimes be associated with increased tensions, possibly due to concerns over economic leverage and dependency.

Event Conflict Rate
Event Conflict Rate

Implications: This event-based analysis offers several key implications for understanding and managing regional dynamics in the South China Sea:

  1. The importance of ongoing, positive diplomatic and economic interactions in counterbalancing the tension-increasing effects of negative events.

  2. The potential for early positive engagements to set a trajectory for long-term stability.

  3. The need for nuanced approaches to economic cooperation that promote stability without creating perceived vulnerabilities.

  4. The critical role of managing territorial disputes and military posturing in preventing escalation to conflict.

  5. The long-term significance of technological and economic power dynamics in shaping regional relations.

Figures 7-10 provide visual representations of these findings, illustrating the frequency distribution of events, their impact on regional tension, temporal patterns of event occurrences, and the relationship between event types and conflict probability. These visualizations support the complex and multifaceted nature of event dynamics in the South China Sea region, as captured by our simulation model.

6 Discussion

6.1 Interpretation of the results

The Monte Carlo simulation of conflict dynamics in the South China Sea over a projected 10-year period yields several significant insights into potential future scenarios for this strategically crucial region. Perhaps most notably, the average probability of conflict across all simulations was 11.2%, suggesting that while tensions in the region are significant, outright conflict remains a relatively infrequent outcome. This finding aligns with the current state of affairs in the South China Sea, where tensions are high but have not yet escalated to full-scale military conflict. It provides a quantitative basis for cautious optimism about the region’s stability, while also underscoring the very real risks that exist.

The simulation reveals a gradual increase in the tension index over the 10-year period, with the median level rising from approximately 0.6 to 0.8. This trend suggests a potential for escalating geopolitical stress in the region if current trajectories continue unchecked. Such a finding highlights the importance of proactive measures to mitigate rising tensions and prevent the situation from deteriorating over time.

Interestingly, the results demonstrate considerable variability in outcomes, with 39.2% of simulations resulting in no conflict at all. This variability underscores the uncertainty inherent in geopolitical forecasting and suggests that while conflict is a real possibility, it is far from inevitable. The divergence in outcomes points to the potential for effective diplomacy and conflict prevention measures to significantly influence the region’s trajectory.

The Partial Dependence Plots derived from our analysis reveal that military spending, territorial claims, and the overall tension index have the strongest influence on conflict probability. Notably, these relationships are often non-linear. For instance, military spending shows diminishing returns in terms of conflict prevention at higher levels, suggesting that excessive military buildup may not necessarily enhance security and could potentially escalate tensions. Similarly, the complex relationship between diplomatic relations and conflict probability highlights the nuanced nature of international relations in the region.

Temporal patterns in the simulation results indicate that maintaining peace in the early years of the period increases the likelihood of long-term stability. This finding emphasizes the critical nature of current and near-future diplomatic efforts, suggesting there may be a window of opportunity to establish a trajectory of lasting peace in the region.

The analysis of event frequencies and impacts provides further nuance to our understanding of regional dynamics. It highlights the destabilizing potential of territorial disputes and military posturing, while also showing the stabilizing effects of positive diplomatic and economic interactions. This interplay of different types of events demonstrates the complex, multifaceted nature of geopolitical relations in the South China Sea.

6.2 Implications for policy makers and international relations

These results have several important implications for policymakers and diplomats engaged with the South China Sea region. First and foremost, the strong impact of territorial claims on conflict probability suggests that prioritizing the peaceful resolution of these disputes should be a key focus of diplomatic efforts. Creative solutions that address the concerns of all parties involved may be necessary to reduce this significant driver of potential conflict.

The observed relationship between military spending and conflict probability calls for a balanced approach to defense policies. While maintaining military preparedness is important, our results suggest that there may be a point of diminishing returns beyond which further military buildup does not significantly enhance security and may even be counterproductive. Policymakers should therefore carefully consider the potential ramifications of their defense spending decisions.

The stabilizing effects of trade agreements and diplomatic breakthroughs highlighted in our event analysis underscore the importance of continuous positive engagement among nations in the region. Efforts to increase economic interdependence and improve diplomatic ties could play a crucial role in maintaining regional stability. However, policymakers should also be mindful of potential tensions arising from perceived economic leverage or dependency, suggesting the need for balanced and mutually beneficial economic relationships.

Our findings regarding the increased effectiveness of early peacekeeping efforts suggest that there may be a critical window of opportunity in the near term to establish lasting stability. This implies that current diplomatic initiatives and peacekeeping efforts could have outsized impacts on long-term regional stability, emphasizing the importance of immediate and sustained engagement in the region.

Given the increasing uncertainty in long-term projections revealed by our simulation, policymakers should develop flexible, adaptive approaches to regional diplomacy. Strategies should be regularly reassessed and adjusted based on evolving circumstances, emerging threats, and new opportunities for cooperation.

6.3 Strengths and limitations of the Monte Carlo approach

The Monte Carlo simulation approach employed in this study offers several key strengths in modeling the complex dynamics of the South China Sea. It effectively captures the multifaceted nature of geopolitical interactions, incorporating a wide range of variables from military and economic factors to diplomatic relations and random events. By running multiple simulations with varying parameters, the method provides a robust representation of the range of possible outcomes, explicitly incorporating the uncertainty inherent in international relations.

The inclusion of dynamic event modeling adds an important element of realism and unpredictability to the simulation, mirroring the often unexpected nature of international relations. This feature allows for the emergence of complex scenarios that might be missed by more static modeling approaches.

However, it’s important to acknowledge the limitations of this approach. The model’s outcomes are heavily dependent on initial assumptions and probability distributions, which may not perfectly reflect real-world dynamics. There’s always a risk that important factors or relationships may be oversimplified or overlooked. The focus on state actors, while aligned with traditional international relations theory, may underestimate the role of non-state actors and international organizations in shaping regional dynamics.

The use of yearly time steps in the simulation, while allowing for long-term projections, may miss short-term fluctuations and rapid escalations that can be critical in international crises. Real-world conflicts often evolve on much shorter timescales, and important nuances may be lost in this annual aggregation.

7 Conclusion

The South China Sea stands as one of the most strategically significant and contested maritime regions in the world. This study employs an innovative Monte Carlo simulation approach to model and analyze potential conflict scenarios in this crucial area over a projected 10-year period. By integrating neo-realist and world-systems theoretical frameworks, our research offers a nuanced understanding of the complex dynamics shaping regional tensions and the likelihood of conflict.

7.1 Key Findings

Our simulations, run over 1000 iterations, reveal an average conflict probability of 11.2% across all scenarios. This relatively low figure suggests that while tensions in the region are significant, outright conflict remains a relatively infrequent outcome. However, the gradual increase in the median tension index from 0.6 to 0.8 over the simulated decade indicates a potential for escalating geopolitical stress if current trajectories continue unchecked.

Notably, 39.2% of simulations resulted in no conflict over the entire period, highlighting the potential for sustained peace even in the face of ongoing tensions. The median peace duration of 7 years further underscores this possibility while also pointing to the critical nature of the initial years in shaping long-term regional stability.

7.2 Influential Factors

Through Partial Dependence Plot analysis, we identified military spending, territorial claims, and the overall tension index as the most significant factors influencing conflict probability. The relationships between these variables and conflict likelihood are often non-linear, revealing complex dynamics at play. For instance, military spending shows diminishing returns in terms of conflict prevention at higher levels, suggesting that excessive military buildup may not necessarily enhance security and could potentially escalate tensions.

7.3 Event Dynamics

Our event-based analysis provides further nuance to understanding regional dynamics. Diplomatic and economic events, such as trade agreements and diplomatic breakthroughs, occur more frequently than extreme events like military coups or revolutions. However, the high frequency of events related to territorial disputes and military posturing underscores the persistent tensions in the region. The asymmetry in impact between positive and negative events highlights the challenges in peace-building, where positive developments must be frequent and substantial to counteract the tension-increasing effects of negative events.

7.4 Theoretical Implications

The integration of neo-realist and world-systems perspectives in our model provides a comprehensive framework for understanding both immediate security concerns and longer-term economic motivations influencing state actions. This approach allows for a more nuanced analysis of how shifts in global power dynamics and economic structures influence regional stability.

7.5 Policy Implications

For policymakers and diplomats, our findings emphasize several key points:

  1. The critical importance of resolving territorial disputes peacefully, given their strong influence on conflict probability.

  2. The need for a balanced approach to defense policies, recognizing the potential counterproductive effects of excessive military buildup.

  3. The value of continuous positive engagement through trade agreements and diplomatic initiatives in maintaining regional stability.

  4. The potential for early peacekeeping efforts to have outsized impacts on long-term regional stability, suggesting a critical window of opportunity in the near term.

  5. The necessity of flexible, adaptive approaches to regional diplomacy in light of the increasing uncertainty in long-term projections.

7.6 Methodological Reflections

While the Monte Carlo simulation approach offers significant strengths in modeling complex geopolitical dynamics, it’s important to acknowledge its limitations. The model’s outcomes are heavily dependent on initial assumptions and probability distributions, which may not perfectly reflect real-world dynamics. The focus on state actors and annual time steps may overlook the role of non-state actors and short-term fluctuations in shaping regional dynamics.

7.7 Future Research Directions

Building on this work, future research could explore more granular time scales, expand the role of non-state actors, and investigate the potential impacts of global events on regional dynamics. Additionally, incorporating machine learning techniques for pattern recognition and prediction could further enhance the model’s predictive capabilities.

In conclusion, this study provides a quantitative framework for assessing conflict dynamics in the South China Sea, offering valuable insights for both theoretical understanding and practical policy-making. As the global center of economic and strategic gravity continues to shift towards the Indo-Pacific, the insights gained from this simulation can serve as a valuable tool for informed decision-making and strategic planning. By understanding the complex interplay of factors influencing regional stability, stakeholders can work towards fostering a more secure and cooperative future for this critically important region.

Appendix

Tension Index Calculation

\[T = \frac{1}{2.2}(0.2\frac{\sum M}{\sum G} + 0.2\frac{\sum C}{19} + \] \[0.1(1-\min(D)) + 0.2\frac{\bar{N}}{0.2} + 0.1(1-\frac{\bar{S}+0.5}{2.8}) + \] \[0.1(1-\frac{\bar{B}+747895.7}{945587.2}) + \] \[0.1(1-\frac{\bar{P}-24.20}{6.32}) + 0.1\cdot 2\sigma(I) + \] \[0.1\cdot 0.5\max(F))\] Where:

\(M\): Military spending

\(G\): Economic growth

\(C\): Territorial claims

\(D\): Diplomatic relations

\(N\): National military capability

\(S\): Democracy score

\(B\): Trade surplus

\(P\): Surplus domestic product

\(I\): Core index

\(F\): Global influence

Conflict Probability

\[P(conflict) = \min(1, \max(0, 0.1T + 0.1X_1 + 0.05X_2 + 0.2H))\] Where:

\(T\): Tension index

\(X_1 \sim Bernoulli(0.1 + 0.1T)\)

\(X_2 \sim Bernoulli(0.05 + 0.05T)\)

\(H\): Historical conflict rate

Variable Updates: For each variable \(V\) in the set of country attributes: \[V_{t+1} = \min(V_{max}, \max(V_{min}, V_t + \epsilon))\] Where \(\epsilon\) is normally distributed with mean 0 and a variable-specific standard deviation. World-System Indices: \[I_{raw} = 0.3E + 0.3A + 0.4F\] \[I_{transformed} = (I_{raw})^2\] \[I_{logistic} = \frac{1}{1 + e^{-12(I_{normalized} - 0.5)}}\] Where:

\(E\): Normalized economic power

\(A\): Normalized technological advancement

\(F\): Normalized global influence

\(I_{normalized}\) is the normalized version of \(I_{transformed}\)

7.8 Weights and Constants

Weights and constants used in simulation
Parameter Symbol Value Description
Military Weight w₁ 0.2 Weight for military spending factor
Territorial Weight w₂ 0.2 Weight for territorial claims factor
Diplomatic Weight w₃ 0.1 Weight for diplomatic relations factor
Military Capability Weight w₄ 0.2 Weight for national military capability factor
Democracy Weight w₅ 0.1 Weight for democracy score factor
Trade Surplus Weight w₆ 0.1 Weight for trade surplus factor
Surplus Domestic Weight w₇ 0.1 Weight for surplus domestic product factor
Core-Periphery Weight w₈ 0.1 Weight for core-periphery factor
Global Influence Weight w₉ 0.1 Weight for global influence factor
Tension Impact α 0.1 Impact of tension index on conflict probability
Military Incident Impact β 0.1 Impact of potential military incident on conflict probability
Diplomatic Crisis Impact γ 0.05 Impact of potential diplomatic crisis on conflict probability
Historical Conflict Impact δ 0.2 Impact of historical conflict rate on conflict probability
Normalization Constant K 2.2 Constant used to normalize the tension index

References

Bazzi, Samuel, Robert A. Blair, Christopher Blattman, Oeindrila Dube, Matthew Gudgeon, and Richard Peck. 2022. “The Promise and Pitfalls of Conflict Prediction: Evidence from Colombia and Indonesia.” The Review of Economics and Statistics 104 (4): 764–79. https://doi.org/10.1162/rest_a_01016.
Bernauer, Thomas, and Tobias Böhmelt. 2014. “Basins at Risk: Predicting International River Basin Conflict and Cooperation.” Global Environmental Politics 14 (4): 116–38. https://doi.org/10.1162/glep_a_00260.
———. 2020. “International Conflict and Cooperation over Freshwater Resources.” Nature Sustainability 3 (5): 350–56. https://doi.org/10.1038/s41893-020-0479-8.
Bertoli, Andrew, Allan Dafoe, and Robert F. Trager. 2018. “Is There a War Party? Party Change, the LeftRight Divide, and International Conflict.” Journal of Conflict Resolution 63 (4): 950–75. https://doi.org/10.1177/0022002718772352.
Bessner, Daniel, and Nicolas Guilhot. 2015. “How Realism Waltzed Off: Liberalism and Decisionmaking in Kenneth Waltz’s Neorealism.” International Security 40 (2): 87–118. https://doi.org/10.1162/isec_a_00217.
Burgos, Russell A., Seung-Whan Choi, Patrick Macgill James, and Palgrave Macmillan. 2015. “Civil-Military Dynamics, Democracy, and International Conflict: A New Quest for Inter-.” In. https://api.semanticscholar.org/CorpusID:147956366.
Chadefaux, Thomas. 2017. “Conflict Forecasting and Its Limits.” SSRN Electronic Journal. https://doi.org/10.2139/ssrn.2920514.
D’Orazio, Vito. 2020. “Conflict Forecasting and Prediction,” July. https://doi.org/10.1093/acrefore/9780190846626.013.514.
Gomez, Jim. 2024. “US, Australia, Canada, Philippines Stage Naval and Air Force Maneuvers in Disputed South China Sea.” The Diplomat. https://thediplomat.com.
Häffner, Sonja, Martin Hofer, Maximilian Nagl, and Julian Walterskirchen. 2023. “Introducing an Interpretable Deep Learning Approach to Domain-Specific Dictionary Creation: A Use Case for Conflict Prediction.” Political Analysis 31 (4): 481–99. https://doi.org/10.1017/pan.2023.7.
Harding, Brian, and Alex Stephenson. 2023. “South China Sea: Crisis Communication Is Crucial to de-Escalate Geopolitical Tensions.” United States Institute of Peace. https://www.usip.org.
Heydarian, Richard Javad. 2024. “Philippines Roping in More Allies in South China Sea Fight.” Asia Times. https://asiatimes.com.
Hsieh, Tsu-Sung, ed. 2018. The South China Sea Disputes: Historical, Geopolitical and Legal Studies. Singapore: World Scientific. https://asianreviewofbooks.com/content/the-south-china-sea-disputes-historical-geopolitical-and-legal-studies/.
Hutagalung, Simon. 2024. “South China Sea: Rising Tensions and the Quest for Peace.” Eurasia Review. https://www.eurasiareview.com.
Konrad-Adenauer-Stiftung. 2023. “Geopolitics in the South China Sea.” https://www.kas.de/documents/252038/22161843/Geopolitics+in+the+South+China+Sea.pdf/f1f15511-78cd-43ea-c733-d2b2af1d4b01?t=1692348833404.
Masterson, Michael. 2022. “Humiliation and International Conflict Preferences.” The Journal of Politics 84 (2): 874–88. https://doi.org/10.1086/715591.
McNamee, Lachlan, and Anna Zhang. 2019. “Demographic Engineering and International Conflict: Evidence from China and the Former USSR.” International Organization 73 (02): 291–327. https://doi.org/10.1017/s0020818319000067.
Moretti, Franco. 2011. “World-Systems Analysis, Evolutionary Theory, Weltliteratur.” In, 67–77. Duke University Press. https://doi.org/10.1215/9780822393344-004.
Roy, Nalanda. 2024. “Revisiting Geopolitics in the South China Sea.” In The Palgrave Handbook of Contemporary Geopolitics, edited by Zak Cope, 1–14. Cham: Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-25399-7_19-1.
Rudin, Cynthia. 2019. “Stop Explaining Black Box Machine Learning Models for High Stakes Decisions and Use Interpretable Models Instead.” Nature Machine Intelligence 1 (5): 206–15. https://doi.org/10.1038/s42256-019-0048-x.
Shakirullah, Bahadar Nawab, Ingrid Nyborg, and Noor Elahi. 2020. “The Underlying Causes of Violent Conflict in the North Waziristan Tribal Areas of Pakistan.” Civil Wars 22 (1): 114–36. https://doi.org/10.1080/13698249.2020.1730632.
Shifrinson, Joshua. 2018. “The Rise of China, Balance of Power Theory and US National Security: Reasons for Optimism?” Journal of Strategic Studies 43 (2): 175–216. https://doi.org/10.1080/01402390.2018.1558056.
Soendergaard, Niels. 2018. “Modern Monoculture and Periphery Processes: A World Systems Analysis of the Brazilian Soy Expansion from 2000-2012.” Revista de Economia e Sociologia Rural 56 (1): 69–90. https://doi.org/10.1590/1234-56781806-94790560105.
Underwood, Erik, and T. V. Paul. 2020. “Balance of Power,” January. https://doi.org/10.1093/obo/9780199796953-0202.
Wallerstein, Immanuel. 2013a. “Tout Se Transforme. Vraiment Tout.” In. https://api.semanticscholar.org/CorpusID:128387242.
———. 2013b. “World-Systems Analysis.” Sociopedia. https://doi.org/10.1177/2056846013114.