Please show your work for credit.

  1. Consider Hardin’s (1968) model of rational herders’ problem. You and your neighbors are both herders and you share a common pasture where your cattles can graze. Each of you receive a direct benefit from your animals (more you can graze them, the better it is for your personal profit), but both of you also suffer from delayed cost due to deterioration of the common pasture when yours’ or your neighbor’s cattles overgraze.

There are two strategies you and your neighbor can choose – i) “cooperate strategy” labeled as “C” (where you can your neighbor equally share resources) and ii) defect strategy “D” (This is when the player grazes as many cattle as she can for her self interest, not really caring about her neighbor).

Here is how the payoffs are designed.

If you and your neighbor both cooperate, both of you get 10 profit points. 

If one of you cooperate and the other defects, then the one who cooperates will get -1 profit point and the one who defects will get 11 profit points.

If both of you choose to defect (overgrazing), this depletes the resource quick enough such that you get a profit of 0 points.

 

  1. Based on the information above, label the braches of the tree correctly. In Figure 1, Y refers to you and N refers to your neighbor.

  2. Neatly express the mechanics of the game on a 2 by 2 matrix. Show the players, strategies, and respective outcomes as in lecture.

  3. Pick out your neighbor’s dominant strategy.

  4. What is your dominant strategy?

  5. Given that both of you play your dominant strategy (which is usally what happens under the assumption that you are solely driven by self-interest), what is the equilibrium outcome?

  6. Is the equilibrium outcome in part e pareto optimal? Explain.

 

  1. Now consider a social planner (say, the government) who is well aware of the mechanism that drives the dilemma in question 1, and the social planner can also accurately observe who is overgrazing and who is not with full information. The social planned then comes up with a “punishment” scheme such that if any player is over grazing, she is fined 2 profit points.

  1. Express Figure 1 by changing the payoffs such that the newer tree diagram accomodates the fine when invovled in over grazing.

  2. What is your dominant strategy after the fine is implemented?

  3. What is your neighbors dominant strategy once the fine is put in place?

  4. What is the new equlibrium outcome? Is the equilibrium outcome pareto optimal?

 

  1. Although solution to the dilemma as pointed out in question 1 can be theoretically solved by imposing punishment scheme as shown in part 2, it will be quite impractical to assume that the social planner can accurately monitor the quantity of overgrazing. The assumption of full information is unrealistic; there is lack of perfect information between the social planner and the grazing behavior (imperfect information). In other words, the social planner sometimes may inaccurately classify you as choosing the defect strategy, even when you are actually cooperating. This is an error from the social planner’s part.

Consider the following:

The social planner classifies you are a cooperator with a probability of 0.7, when you are actually cooperating. 

The social planner classifies you as a defector with a probability of 0.7, when you are actually defecting. 

Note that the player is still fined 2 profit points if caught overgrazing.

  1. Using the above information above, restructure the payoffs shown in Figure 1.

  2. What is the equilibrium outcome in this case?

  3. Is the equilibrium found in part b pareto optimal? Why?

 

  1. Consider the following game between Bala and Anil, where they produce rice and potatoes. This problem is extracted from section 4.13 of the Core Project book.
Figure 2.

Figure 2.

  1. What is the best response of Anil if Bala produces rice?

  2. What is the best response of Anil if Bala produces potatoes?

  3. Does Anil have a dominant strategy? Exlpain as to Why.

  4. What are the Nash equlibrium in this case?

  5. If people choose their actions (strategy) independently (without communicating or sharing informations between one another), which equilibrium outcome is more likely to occur?

  6. If people choose their actions by coordinating with one another, which equilibrium outcome is more likely to occur?

 

  1. The topic of menstruation is surrounded by social stigma in many developing countries. In countries such as Nepal, India and several South African countries, menstruation is often stigmatized. For instance, many women in Nepal are restricted from entering kitchen or visiting holy shrines during the time of menstruation and a tradition called Chaupadi confines a menstruating girl or woman in a shed (where livestocks are kept). Given such barriers created due to social norms, importance of menstrual health and hygiene (MHH) is not as publicly discussed as in developed countries. In many situations, women in developing countries (Nepal, India) still use cloths or rags during menstruation.

In such cases, adoption of technologically advanced menstrual health product such as sanitary pads presents a unique challenge – in process of purchasing sanitary pads a girl or a woman needs to interact with several members of the society, which given the restrictive norms against menstruation, might make her uncomfortable. For instance, she would need to interact with a male shopkeeper of the pharmacy. Hence, this nature of “shame” due to existing social norm creates an additional cost or hinderance in purchasing more technologically advanced menstrual health products, which we refer to as “shame cost.”

Say, there are two females (players of the game) – i) Shanti, and ii) Pooja, who are considering whether to purchase sanitary pads. They can either choose to adapt the menstrual health product by purchasing or refrain from adapting the product.

Using sanitary pads during menstruation gives an additional boost in promoting menstrual health.

However, there exists "shame cost" when purchasing sanitary pads due to social stigma. This "shame cost" is higher for Shanti than Pooja.

The "shame cost" is extremely high for the purchaser if only one player decides to purchase. 

If both players decide to purchase, players receive moral support from each other, which lowers the "shame cost."

Consider the following set up.

Figure 3.

Figure 3.

  1. What is Shanti’s dominant strategy?

  2. What is Pooja’s dominant strategy? Explain.

  3. If both Pooja and Shanti are allowed to converse, what is the likely equilibrium?

  4. Is the equilibrium from part c. pareto optimal?