Question

Game Theory Activity Let there be a dilemma facing you. You have been caught by police and can either confess or not confess. Your partner in crime faces the same options in another room. Payoffs are as follows-in years in jail. You Don't Confess Confess Don't Confess Them Confess 10 Payoffs in Years in Jail a) Identify the equilibrium, it one exists. Explain your reasoning. b) Identify the equilibrium that would obtain if the game was played repeatedly for an indeterminate number of times.

Please show how to solve this problem by hand and show all work. Thank you!

Answer 1

a) THe equilibrium if the game is played only one is confess, confess, and the payoff will be 10 each. Starting from the point where none of the players are confessing and getting 4 each the one who confess will get only 2 and other will get 20, so thinking of a better payoff they both will confess and get 10 each.

b) IF the game was played continuously, then none of them will confess and the nash equilibrium will be at don't confess, don't confess each and the pay off will be 4 each, because then in that case they will use tit for tat strategy and thing of trusting the other player for better payoff.