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There are two players. Each player is given an unmarked envelope and asked to put in it either nothing or 300 of his own money or 600 of his own money. A referee collects the envelopes, opens them, gathers all the money, then adds 50% of that amount (using his own money) and divides the total into two equal parts which he then distributes to the players. (a) Suppose that Player 1 has some animosity towards the referee and ranks the outcomes in terms of how much money the referee loses (the more, the better), while Player 2 is selfish and greedy and ranks the outcomes in terms of her own net gain. (For example, if player 1 selects 0 and player 2 selects 300, then player 1's pay-off is 150 and player 2's payoff is -75.) Describe this game in a matrix. (b) What is the best response correspondence for the above game? (c) Find the Nash equilibria of the above game.

There are two players. Each player is given an unmarked envelope and asked to put in it either nothing or 300 of his own money or 600 of his own money. A referee collects the envelopes, opens them, gathers all the money, then adds 50% of that amount (using his own money) and divides the total into two equal parts which he then distributes to the players. (a) Suppose that Player 1 has some animosity towards the referee and ranks the outcomes in terms of how much money the referee loses (the more, the better), while Player 2 is selfish and greedy and ranks the outcomes in terms of her own net gain. (For example, if player 1 selects 0 and player 2 selects 300, then player 1's pay-off is 150 and player 2's payoff is -75.) Describe this game in a matrix. (b) What is the best response correspondence for the above game? (c) Find the Nash equilibria of the above game.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter13: best-practice Tactics: Game Theory
Section: Chapter Questions
Problem 5E
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There are two players. Each player is given an unmarked envelope and asked to put in it either nothing or 300 of his own money or 600 of his own money. A referee collects the envelopes, opens them, gathers all the money, then adds 50% of that amount (using his own money) and divides the total into two equal parts which he then distributes to the players. (a) Suppose that Player 1 has some animosity towards the referee and ranks the outcomes in terms of how much money the referee loses (the more, the better), while Player 2 is selfish and greedy and ranks the outcomes in terms of her own net gain. (For example, if player 1 selects 0 and player 2 selects 300, then player 1's pay-off is 150 and player 2's payoff is -75.) Describe this game in a matrix. (b) What is the best response correspondence for the above game? (c) Find the Nash equilibria of the above game.
Transcribed Image Text:There are two players. Each player is given an unmarked envelope and asked to put in it either nothing or 300 of his own money or 600 of his own money. A referee collects the envelopes, opens them, gathers all the money, then adds 50% of that amount (using his own money) and divides the total into two equal parts which he then distributes to the players. (a) Suppose that Player 1 has some animosity towards the referee and ranks the outcomes in terms of how much money the referee loses (the more, the better), while Player 2 is selfish and greedy and ranks the outcomes in terms of her own net gain. (For example, if player 1 selects 0 and player 2 selects 300, then player 1's pay-off is 150 and player 2's payoff is -75.) Describe this game in a matrix. (b) What is the best response correspondence for the above game? (c) Find the Nash equilibria of the above game.
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