ECON30019 Assignment 5
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ECON30019 Assignment 5
Due at 11:59 pm on Oct 19, 2023
Question 1. (50 Points)
Consider the following game. Two students, Amy and Ben, need to work together on a group assignment. Both of them must choose between two actions: “Work” and “Shirk”. If a student chooses to work, he/she incurs a cost of c. If a student chooses to shirk, she does not incur any cost. The beneits of the actions depend on the decisions of both students. If both of them work, the assignment receives a high mark and each student receives h. If only one of them work, the assignment receives a low mark and each student receives l. If neither of them work, they fail to complete the assignment and each student receives 0.
1. Suppose both students only care about their own payofs. Amy has the utility function uA (xA ) = xA and Ben has the utility function uB (xB ) = xB , where xA refers to the payof of Amy and xB refers to the payof of Ben. Assume h > c > l.
(a) (5 Points) Write down the payof matrix of this game.
(b) (15 Points) Analyze the strategies of each player and ind the pure-strategy Nash equilibrium (or equilibria). Discuss how the equilibrium prediction could change depending on values of the parameters.
2. Now suppose that Ben still only cares about his own payofs: uB (xB ) = xB , but Amy exhibits simple altruism and has the utility function uA (xA , xB ) = xA + ϕxB , where ϕ > 0. Assume h = 8, l = 3, c = 6.
(a) (10 Points) Write down the payof matrix of this game.
(b) (20 Points) Analyze the strategies of each player and ind the pure-strategy Nash equilibrium (or equilibria). Discuss how the equilibrium prediction could change depending on values of the parameters.
Question 2. (50 Points)
Consider the following 3-player public goods game. Players 1, 2, and 3 have the same initial endowment y and simultaneously choose to contribute to a public good. If player 1 contributes c1 , player 2 contributes c2 , and player 3 contributes c3 , then player i’s monetary payof is
where 1 < m < 3.
1. (15 Points) Suppose that each player i is only concerned about his own material payofs with ui(xi) = xi. Derive the Nash equilibrium of the game.
2. (35 Points) Suppose that players 2 and 3 are only concerned about their own material payofs, and player 1 exhibits inequity aversion as speciied in the model of Fehr and Schmidt (1999):
where 0 β1 < 1 and α1 ≥ β1 . Suppose these preferences are commonly known to all players. Is it a Nash equilibrium for player 1 to contribute his entire endowment (c1 = y) while players 2 and 3 both contribute nothing (c2 = c3 = 0)? (Hint: you can answer this question by checking each player’s incentive to deviate.)
2023-10-20