There are two players in a game. In each round of the game, one player has to trust the other for a particular task. In the first round, Player 1 has to decide whether she will trust Player 2. If she does not trust Player 2, she will get one-third of the prize money, while Player 2 will get the rest of the prize money. If she trusts Player 2, Player 2 can either cooperate with her or defect. If Player 2 defects, Player 1 will earn $0, while Player 2 will get the entire prize money. If Player 2 cooperates, each of them will get half the prize money. What will the equilibrium outcome of this game be if Player 1 can impose a guilt penalty of two-thirds of the prize money and is known to be a vengeful player?

Question

Quizplus · Accepted Answer

The Answer is If there is no guilt penalty, in equilibrium, Player 1 will not trust Player 2. She will make this decision using backward induction. If she trusts Player 2, Player 2 is likely to defect, because he will earn the entire prize money in that case, while he will earn only half of the money by cooperating. Given this information, Player 1 will not trust him, as she will not earn any money if she trusts him, while she will earn one-third of the money if she does not trust him. However, if there is a guilt penalty of two-thirds of the prize money, Player 2 will choose to cooperate, because he will earn a lower payoff by defecting. Given this information, Player 1 will trust him, and each of them will get half of the money.

There Are Two Players in a Game