(a) Modeling the Competition Between Microsoft (GPT Chat) and Google Using the Polya Urn Model

Google’s reaction to the success of GPT chat may seem surprising, but it makes sense when you consider their knowledge of past events in the tech industry, like the browser wars between Netscape and Microsoft. The issue isn’t just about competing search engines. Instead, Google is concerned because Microsoft has a history of using its control over platforms like Windows to push out competitors. Microsoft didn’t win by creating better products but by using strategies like bundling Internet Explorer (IE) with Windows, making it the default browser.

Back in the 1990s, Netscape Navigator was the top browser with a 90% market share. Even though it was technically better than IE, Microsoft’s strategy to bundle IE with Windows and strike deals with PC manufacturers and internet providers gave it a huge advantage. Over time, Netscape lost users and market share until it was eventually out of the competition. Legal actions were later introduced to prevent these practices, which is one reason Microsoft Edge hasn’t become dominant today.

Now, Google worries that Microsoft might use a similar approach by integrating GPT into the Windows operating system. If this happens, it could hurt Google’s search engine traffic, giving Microsoft a significant edge in AI services.

Overview of the Polya Urn Model

The Polya urn model is a way to explain how “success leads to more success.” Imagine an urn with balls of different colors. Each color stands for a competitor, like Microsoft and Google. Every time you draw a ball, you add another of the same color to the urn. This makes it more likely to draw that color again. Over time, the winning color keeps getting stronger because of this positive feedback. In this example:

  • Microsoft’s color (e.g., blue) grows if GPT’s integration with Windows gives it an early boost.
  • Google’s color (e.g., red) can stay strong or even grow if Google keeps attracting users through new features.

Applying the Model to the AI Chat Competition

Microsoft and Google are engaged in a competition between two different approaches: Microsoft’s integration of OpenAI’s ChatGPT into Windows and Google’s dominant search engine. In this competition, we can represent these two entities using the Polya urn model, where each urn tracks user adoption. One urn represents GPT adoption through Windows integration, while the other tracks Google Search adoption through its established dominance.

Initially, Google has a strong lead in search, similar to how it currently dominates the search engine market. Microsoft, however, is actively working to close the gap by integrating ChatGPT across multiple platforms like Windows Terminal, PowerToys, and Copilot. This seamless integration provides users with AI-driven responses directly within their workflow. For example, developers who might typically search Google for coding help, such as commands for Stack Overflow, may now use ChatGPT in Windows Terminal for quick assistance, bypassing traditional search engines entirely.

Graph Explanation

This simulation models a scenario where Microsoft’s GPT gains a significant edge over Google Search due to increased integration within Windows:The competition can be understood in two distinct phases, illustrated by a graph that shows how market shares evolve over time:

  • Period 1 (Google’s strong lead): At the start, Microsoft’s GPT has a very small share (4%), while Google controls most of the market with 85%. Google’s large user base and strong network effects help it stay on top, and GPT’s share grows slowly. There isn’t much competition at this stage because Google is clearly in the lead.

  • Period 2 (Microsoft’s rapid rise): Once GPT is fully integrated into Windows, its market share rises quickly. The vertical gray line on the graph shows the moment when things start to change. After this point, GPT adoption speeds up, and eventually, GPT overtakes Google. Google’s market share steadily drops as Microsoft’s integration strategy and network effects push GPT to the top.

Model and Formula Explanation

The dynamics of this competition can be modeled with the following probability function:

\[ f(x) = \frac{p(x) + \lambda z}{c + i} \]

Where:

  • \(p(x)\): Current market share of the technology.

  • \(\lambda\): Strength of the network effect, representing how integration affects adoption.

  • \(z\): Installed user base for the platform.

  • \(c, i\): Pecuniary (monetary) and non-pecuniary (e.g., time, effort) switching costs.

This formula shows how integration boosts GPT’s chances of adoption by leveraging both the network effect and the size of Windows’ installed user base. As the integration strengthens, Microsoft’s GPT gains a competitive edge, just as Internet Explorer did during the browser wars.

Simulation Steps

The model simulates each time period as a moment when users decide between GPT and Google Search. The probability of choosing either option depends on factors like: - The current market share (path dependence). - Platform integration (Windows vs. Google services). - External factors such as updates or legal restrictions.

Microsoft’s integration advantage could replicate past successes if GPT adoption increases, while Google may maintain its dominance by continuously enhancing its search and AI services.

Behavior and Market Impact

The simulation results emphasize that network effects and installed user bases are key to shaping outcomes. For instance, users are more likely to adopt GPT because it’s built into Windows and easy to access. This reduces reliance on traditional search engines. However, Google can still defend its market position by delivering innovative, high-quality search experiences with AI integration.

In both cases, multiple simulations reveal how Microsoft’s strategy may either replicate its previous success or face resistance from Google’s loyal users.

Internal and External Validity

For the model to be valid, it should reflect real-world behavior and competition dynamics:

  • Internal validity: The model should accurately capture user adoption, market competition, and feedback loops.

  • External validity: The simulation results should align with historical patterns, such as Microsoft’s integration of Internet Explorer, which successfully disrupted Netscape’s dominance.



(b) not listed here



(c) Applying Arthur’s Theory of Increasing Returns to Microsoft vs. Google

In Increasing Returns and the New World of Business, W. Brian Arthur explains how industries like technology behave differently from traditional industries like manufacturing. In traditional industries, companies face diminishing returns—as production increases, costs go up due to resource limitations. However, in technology-driven industries, increasing returns often occur. This means early success leads to even more success, creating a growth cycle where small initial advantages can expand quickly.

The current competition between Microsoft and Google in AI services is a good example of increasing returns. Microsoft has integrated GPT into Windows through tools like Copilot and Windows Terminal. As a result, users find it easier and more convenient to use GPT because it is built into their operating system. As more users adopt GPT, this influences others to adopt it too, creating a strong network effect. This could help Microsoft gain a larger market share, even though Google is still the dominant player in search.

The current competition between Microsoft and Google in AI services is a good example of increasing returns. Microsoft has integrated GPT into Windows through tools like Copilot and Windows Terminal. (Source: Reddit.com) As a result, users find it easier and more convenient to use GPT because it is built into their operating system. As more users adopt GPT, this influences others to adopt it too, creating a strong network effect. (Source: WindowsLatest)

This could help Microsoft gain a larger market share, even though Google is still the dominant player in search (Source: Investopedia).

As we can see in the first graph below, Google currently holds 89.98% of the global search engine market share, while Microsoft’s Bing only has 3.94%. (Source: Oberlo)

Search Engine Market Share in 2024
Search Engine Market Share in 2024

On the other hand, the second graph shows that Windows has a significant 70%+ share in the desktop operating system market. (Source: Statista)

Desktop Operating System Market Share
Desktop Operating System Market Share



Since Microsoft controls the platform that many people use every day, it has the potential to change how users interact with search and AI services. For example, users might stop relying on Google Search for tasks like coding help or quick information queries if GPT can provide those answers directly within Windows.

Arthur points out that in increasing returns markets, success is often unpredictable and does not always go to the best product. In the past, Microsoft became dominant with DOS despite it being technically inferior to other options. This happened because Microsoft controlled the platform. Similarly, GPT could succeed, not necessarily because it is better than Google’s AI, but because of how easily accessible it is through Windows. Over time, if GPT becomes the default AI interface, Microsoft’s share in AI-driven services could increase and start reducing Google’s dominance.

Arthur also describes these markets as non-ergodic, which means that early actions or events can have long-term effects. By integrating GPT early into Windows, Microsoft could gain an enduring advantage. However, Google can still defend its position by continuing to innovate and improve its search experience to keep users loyal.

In conclusion, this competition shows how technology industries work under the concept of increasing returns. Success doesn’t just depend on having the best product. It also relies on controlling key platforms, utilizing network effects, and being able to adapt quickly—concepts central to Arthur’s theory. As Microsoft strengthens its AI integration in Windows, it has the potential to disrupt Google’s current dominance in search. The graphs provide a clear view of how Microsoft’s control over the desktop OS market can play a crucial role in changing search engine market dynamics.



(d) Report Applying Biological Competition Models to Analyze Economic Rent-Seeking

1. Introduction

This project uses ideas from biology to understand competition between companies. It focuses on rent-seeking, which means companies stay on top by blocking competitors instead of creating new things. They do this by controlling important resources or influencing laws to their advantage.

Biological competition models, like the Lotka-Volterra equations, show how companies can either compete fairly or dominate by taking control of key resources. This report reviews how these models work and looks at other ways to study rent-seeking in technology markets

2. Biological Competition Models

Lotka-Volterra model: The Lotka-Volterra model compares how two species (or companies) compete for resources. One may survive by innovation or monopolizing resources, while the other declines

The Lotka-Volterra model is often used to study how animals or plants compete for food, space, or water. In business, it can help explain how companies compete for market share and users.

The model shows two possible results:

  • Coexistence: Companies survive together by offering different products or services (e.g., Microsoft focuses on Windows, while Google focuses on search).

  • Monopolization: One company takes control of the market by gaining more resources and users (e.g., Microsoft growing GPT’s share by integrating it with Windows).

In Lecture 14, this model is used to show how market shares change over time. If Microsoft integrates GPT early, its adoption may grow quickly, creating a cycle where more users attract even more users. Google, on the other hand, risks losing users unless it keeps improving.

The Lotka-Volterra Competition Model: Understanding α
The Lotka-Volterra Competition Model: Understanding α

Lotka-Volterra Competition Model

The following equations describe the interaction between two competing species (or companies in economic competition):

Species 1:
\[ \frac{dN_1}{dt} = r_1 N_1 \left(1 - \frac{\alpha_{1 \leftarrow 1} N_1 + \alpha_{1 \leftarrow 2} N_2}{K_1} \right) \]

Species 2:
\[ \frac{dN_2}{dt} = r_2 N_2 \left(1 - \frac{\alpha_{2 \leftarrow 2} N_2 + \alpha_{2 \leftarrow 1} N_1}{K_2} \right) \]

Explanation of Terms

  • \(N_1, N_2\): Population sizes or market shares of competing entities (e.g., companies).
  • \(r_1, r_2\): Growth rates of each species or company.
  • \(K_1, K_2\): Carrying capacities or maximum market sizes for each competitor.
  • \(\alpha_{i \leftarrow i}\): Intraspecific competition coefficient, showing how a species’ own population limits its growth.
  • \(\alpha_{i \leftarrow j}\): Interspecific competition coefficient, showing how one species affects the growth of the other by competing for resources.

These equations demonstrate how both internal and external competition can influence the growth or decline of entities in a shared environment, whether in nature or in markets.

This model helps explain how companies compete for resources and market share over time. One company may dominate, leading to a decline in the other’s share, or both may coexist through niche differentiation.

3. Rent-Seeking by Big Tech Companies

In technology, rent-seeking is common. Companies like Microsoft, Google, and Amazon started by offering new and innovative products. Over time, they shifted to using their existing platforms to block competitors.

For example, Microsoft integrates GPT into Windows, making AI services like Copilot and Windows Terminal part of everyday tasks. This makes it harder for other platforms to compete because users no longer need to leave the Windows system. Google uses similar tactics by embedding its search engine in products like Chrome and Android.

This is similar to how dominant species in nature control resources to limit competition and maintain their position.

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Formula:
\[ f(x) = \frac{p(x) + \lambda z}{c + i} \]

Explanation:
- \(p(x)\): Current market share.
- \(\lambda\): Strength of network effects.
- \(z\): Installed user base (current users of the platform).
- \(c, i\): Costs of switching or adopting a new service.

This formula shows how a company can maintain or grow its market dominance by leveraging network effects and reducing user incentives to switch to competitors.

4. Other Ways to Study Rent-Seeking

In addition to using biological models, there are other approaches to understanding rent-seeking in technology markets. These methods offer different perspectives on how companies maintain control and block competitors, often by leveraging their platforms and networks.

a) Agent-Based SimulationsOe useful approach is agent-based simulations. These simulations track how both users and companies behave over time. For instance, users may choose between Microsoft GPT and Google Search depending on which service offers better integration and convenience. The simulation can reveal how these individual decisions influence market competition as a whole. It can also help predict adoption patterns based on changing user preferences and platform advantages. Example Rule:
\[ P_{GPT}(t+1) = \frac{P_{GPT}(t) + \Delta_{integration}}{1 + P_{Google}(t)} \]

Explanation:
- \(P_{GPT}(t)\): Market share of GPT at time \(t\).
- \(\Delta_{integration}\): Boost in adoption due to platform integration (e.g., embedding GPT into Windows).

Agent-based models simulate interactions between users and platforms, showing how adoption patterns evolve based on factors like convenience and accessibility.

  • b) Network Analysis-Another approach is network analysis. This method looks at how platforms like Windows and Google Search create complex networks of users and services. By focusing on key nodes—such as major platforms or services—researchers can understand how companies sustain their dominance. For example, if Windows controls a large part of the desktop ecosystem, it can reduce users’ reliance on competing services by offering built-in AI tools. Network analysis helps identify how this interconnected structure amplifies control over resources and limits opportunities for rivals.

  • c) Case Studies-Finally, case studies provide insights based on historical events. By examining regulatory interventions, such as Microsoft’s antitrust case in the 1990s or Google’s ongoing investigations, researchers can better understand how policies affect market dynamics. These cases illustrate how monopolistic behavior is challenged and sometimes curtailed by legal actions, which in turn create opportunities for fairer competition.

Together, these methods provide a more complete understanding of rent-seeking. They show how companies use strategies like integration and network control to maintain market power, while also highlighting the role of regulations in promoting innovation and reducing monopolistic practices.

5. Strengthening the Model

The biological model works well but can be improved in two key areas:

a) Feedback Loops Early competitive moves often have long-term effects. For example, if Microsoft integrates GPT early into its Windows platform, it could secure lasting market dominance through network effects. By adding feedback loops to the model, we can better simulate how early adoption and strategic moves influence long-term market trends.

b) Policy Scenarios The model could also incorporate the impact of policies and regulations on competition. For instance, policies designed to prevent platform monopolies could limit rent-seeking behavior and encourage innovation by promoting fair competition. Modeling these scenarios can help predict how regulatory changes affect market dynamics.

These improvements will enhance the model’s ability to forecast how competition evolves over time.

5. Conclusion

This research bridges biological and economic models to explain modern competition. Understanding these strategies can inform law makers and researchers about how to regulate and promote fair competition in technology markets.