THE ECONOMY: THE CORE PROJECT

UNIT 4. SOCIAL INTERACTIONS

T4.1 Prisoners’ dilemma In a simultaneous one-shot prisoners' dilemma game: Select one answer The players’ payoffs are lower in the dominant strategy equilibrium than in some other outcomes. The players will choose to cooperate to attain the socially optimal outcome. Each player’s payoff is the highest in the socially optimal outcome, which would be attained by cooperation. Each player would choose to cooperate if he or she knew that the other player would definitely also choose to cooperate. Section 4.3

ANSWER: T4.1 Prisoners’ dilemma In a simultaneous one-shot prisoners' dilemma game: Select one answer The players’ payoffs are lower in the dominant strategy equilibrium than in some other outcomes. The players will choose to cooperate to attain the socially optimal outcome. Each player’s payoff is the highest in the socially optimal outcome, which would be attained by cooperation. Each player would choose to cooperate if he or she knew that the other player would definitely also choose to cooperate. Feedback The dominant strategy equilibrium is for both players to not cooperate, which leads to lower payoffs for both players (relative to the cooperative outcome). In a one shot prisoner’s dilemma game the players have an incentive to deviate. Therefore, the socially optimal outcome will not be attained. In a prisoner’s dilemma, a player would attain a higher payoff if he deviates from the socially optimal outcome. The cooperative strategy is still dominated by the non-cooperative strategy, so a player would get a higher payoff by not cooperating even if the other player cooperates. Section 4.3

T4.2 Altruistic preferences The following diagram shows Anil’s preferences when he is either completely selfish or somewhat altruistic, when he and Bala participate in the prisoners' dilemma game with the payoffs shown below. Based on the graph, which of the following statements are correct? Select all correct answers The outcome (I, T) is attained as the dominant strategy equilibrium if Anil is completely selfish and Bala is somewhat altruistic. The outcome (I, T) is attained as the dominant strategy equilibrium if Anil is somewhat altruistic and Bala is completely selfish. The outcome (I, T) cannot be attained as the dominant strategy. The outcome (I, I) is attained as the dominant strategy equilibrium only if both Anil and Bala are somewhat altruistic. Section 4.5

ANSWER: T4.2 Altruistic preferences The following diagram shows Anil’s preferences when he is either completely selfish or somewhat altruistic, when he and Bala participate in the prisoners' dilemma game with the payoffs shown below. Based on the graph, which of the following statements are correct? Select all correct answers The outcome (I, T) is attained as the dominant strategy equilibrium if Anil is completely selfish and Bala is somewhat altruistic. The outcome (I, T) is attained as the dominant strategy equilibrium if Anil is somewhat altruistic and Bala is completely selfish. The outcome (I, T) cannot be attained as the dominant strategy. The outcome (I, I) is attained as the dominant strategy equilibrium only if both Anil and Bala are somewhat altruistic. Feedback In this case Anil’s dominant strategy is T while Bala’s dominant strategy is I. Therefore, the dominant strategy equilibrium is (T, I). When Anil is somewhat altruistic, (I, I) is on a higher indifference curve than (T, I), and (I, T) is on a higher indifference curve than (T, T). So playing I is Anil’s dominant strategy. The outcome (I, T) is attained as the dominant strategy equilibrium if Anil is somewhat altruistic and Bala is completely selfish. T is the dominant strategy for any completely selfish player. Therefore, to get both players to play I, they both need to be somewhat altruistic. Section 4.5

T4.3 Public goods game Bruce owns a cooperative project with two other members. Any member that chooses to put in a full day of work faces a cost of £50 but produces a total income of £120, which is shared amongst the three. So, for example, if Bruce and one other member do a full day of work, then the income per member is (£120 x 2)/3 = £80, leaving Bruce with a net income of £80 - £50 = £30. Assume that a member must either put in a full day of work or none at all. Based on this information, we can conclude that: Select all correct answers The socially optimal outcome (one with the highest total net income) is when all work. The dominant strategy equilibrium of this public goods game is when no one works. Bruce is better off not working, irrespective of the actions of the other members. Bruce’s net income when all three members work is £80. Section 4.6

ANSWER: T4.3 Public goods game Bruce owns a cooperative project with two other members. Any member that chooses to put in a full day of work faces a cost of £50 but produces a total income of £120, which is shared amongst the three. So, for example, if Bruce and one other member do a full day of work, then the income per member is (£120 x 2)/3 = £80, leaving Bruce with a net income of £80 - £50 = £30. Assume that a member must either put in a full day of work or none at all. Based on this information, we can conclude that: Feedback When all members work, the total net income is (£120 x 3) – (£50 x 3) = £210, compared when two members work (£140) or if only one member works (£70). It is a dominant strategy for a player not to work, because he earns more by not working compared to working, regardless of what the other members do (£0 compared to -£10 if the other two do not work, £40 compared to £30 if one of the other members work, and £80 compared to £70 if the other two members both work). Therefore the dominant strategy equilibrium is when nobody works. It is a dominant strategy for a player not to work, because he earns more by not working compared to working, regardless of what the other members do (£0 compared to -£10 if the other two do not work, £40 compared to £30 if one of the other members work, and £80 compared to £70 if the other two members both work). When all three members work, Bruce’s net income is (£120 x 3)/3 – £50 = £70. Select all correct answers The socially optimal outcome (one with the highest total net income) is when all work. The dominant strategy equilibrium of this public goods game is when no one works. Bruce is better off not working, irrespective of the actions of the other members. Bruce’s net income when all three members work is £80. Section 4.6

T4.4 Ultimatum game You are the Responder in an ultimatum game. The social norm is a (100 - x*) : x* split, meaning the Proposer keeps 100 - x* and the Responder receives x*. Let R represent the strength of your private reciprocity motive. Based on this information, we can conclude that: Select one answer A higher R implies that you are less likely to accept a particular offer. If R = 1, then you would reject any offers of less than x*. If R = 1, then you would reject any offers of less than half of x*. If R = 0, then you would reject all offers of less than 100. Section 4.10

ANSWERS: T4.4 Ultimatum game You are the Responder in an ultimatum game. The social norm is a (100 - x*) : x* split, meaning the Proposer keeps 100 - x* and the Responder receives x*. Let R represent the strength of your private reciprocity motive. Based on this information, we can conclude that: Feedback The more that you care about reciprocity, the higher the Proposer’s offer has to be, because you gain satisfaction from rejecting low offers (which may outweigh the monetary gain from accepting the offer). If you are offered y, then you would reject the offer when y < R(x*-y). This implies that y < Rx*/(1+R). So when R = 1, you would reject if y < x*/2 (not if y < x*). If you are offered y, then you would reject the offer when y < R(x*-y). This implies that y < Rx*/(1+R). So when R = 1, you would reject if y < x*/2. If R = 0, then you don’t care about reciprocity but only about the actual offer. Since your reservation option is zero, you would gain by accepting any positive offer. Select one answer A higher R implies that you are less likely to accept a particular offer. If R = 1, then you would reject any offers of less than x*. If R = 1, then you would reject any offers of less than half of x*. If R = 0, then you would reject all offers of less than 100. Section 4.10

T4.5 Multiple equilibria The following game represents the interaction between two software engineers, Astrid and Bettina, who are working together to write code as a part of a project. Astrid is better at writing Java code, while Bettina prefers C++. The numbers represent the pay in thousands of dollars for completion of the project. Based on this information, which of the following are true? Select all correct answers There are two Nash equilibria: (Java, Java) and (C++, C++). If Astrid can choose the format first and commit to it, then (Java, Java) will be chosen. If the two can make an agreement beforehand, including a transfer of $500 from Bettina to Astrid, then (C++, C++) will be chosen. If the two cannot make an agreement beforehand, then they may end up with the (Java, C++) outcome. Section 4.13

ANSWER: T4.5 Multiple equilibria The following game represents the interaction between two software engineers, Astrid and Bettina, who are working together to write code as a part of a project. Astrid is better at writing Java code, while Bettina prefers C++. The numbers represent the pay in thousands of dollars for completion of the project. Based on this information, which of the following are true? Feedback At either of these outcomes, no player can be better off by changing their strategy, given what the other player does. If Astrid chooses Java, then Bettina makes $3,000 by choosing Java but only $2,000 by choosing C++. Therefore the outcome will be (Java, Java). A transfer of $500 will result in the payoffs (3,500, 5,500) for the (C++, C++) outcome. Astrid will then still have an incentive to reach the (Java, Java) outcome. The transfer amount needs to be between 1,000 and 3,000 for both to prefer (C++, C++). Non-Nash equilibrium outcomes will not occur, as the choices are not mutual best responses. Select all correct answers There are two Nash equilibria: (Java, Java) and (C++, C++). If Astrid can choose the format first and commit to it, then (Java, Java) will be chosen. If the two can make an agreement beforehand, including a transfer of $500 from Bettina to Astrid, then (C++, C++) will be chosen. If the two cannot make an agreement beforehand, then they may end up with the (Java, C++) outcome. Section 4.13