Recall the Trust Game Reported in the Evidence-Based Economics Element

Essay

Recall the trust game reported in the Evidence-Based Economics element in section 13.5.Consider the game where the trust game is played twice in succession.

Payoffs are the sum of payoff in each round.For example,suppose you choose Trust and Bernie chooses Cheat in the first round,then you choose Don't Trust in the second round (Bernie could choose either,because it does not get to his turn anyway).Then you earn $0 and Bernie earns $30 in the first round,and you earn $10 and Bernie earns $10 in the second round,so that your total payoff is $10 and Bernie's is $40.
a)Apply backward induction to this game.How do you and Bernie behave in the two-round version?
b)What would be the backward induction solution if the trust game is repeated three times? Four times? Twenty thousand times? Does this agree with what you read in the Evidence-Based Economics element in section 13.5?