Question

Two people, Baker and Cutler, play a game in which they choose and divide a prize. Baker decides how large the total prize should be; she can choose either $10 or $100. Cutler chooses how to divide the prize chosen by Baker; Cutler can choose either an equal division or a split where he gets 90% and Baker gets 10%. Write down a payoff table of the game and find equilibria for the following situations and answer the final question about whether this is a Prisoner's Dilemma.

(a) When the moves are simultaneous

(b) When Baker moves first

(c) When Cutler moves first

(d) Is this game a Prisoner's Dilemma? Why or Why not?

Answer 1

a) the payoff table:

		Cutler
		Equal	unequal
Baker	10	5. 5	1, 9
100	50, 50	10, 90

b) When Baker moves first:

If Baker were to move first, she would know that Cutler would choose unequal for sure (higher payoff for Cutler). So she chooses 100. Because 100 would give her a payoff of 10 against 1 from selection of 10. So the equilibrium is (100, unequal)

c) When Cutler moves first:

If Cutler were to move first, he would know that Baker would select 100 (higher payoff than 10). So he would choose unequal so that she would get 90 (comapred to 50 if she chose equal.) So the equilibrium is (100, unequal)

d) This game is not like prisoner's dilemma. reason: In prisoner's dilemma, the players have dominated strategies, but it brings a lower outcome than dominated strategy. So the equilibrium is the second best outcome. In this game, Cutler has a dominatted strategy, and he plays it.