Question

Problem Set #2: Due Tuesday, October 29 in class Problem #1: A three-player game (4 pts) Consider a variation on the three-player Prisoner's Dilemma shown in the slides from lecture 3. This variation is identical to that game, excent that the police need two of the criminals to testly in order to convict the third. This changes the sentencing rules in two ways indicated in bold below): • If all three keep quiet, then all three get short sentences. • If only one criminal testifies, all three still get short sentences. • If two criminals testify, then they get set free, and the third gets a long sentence. • If all three testify, then all three get medium sentences. a) Construct a game table for this game. (Hint: Consult the game in the slides to see what it should look like, only the payoffs should differ.) b) Is (Quict, Quiet, Quiet) a Nash Equilibrium of this game?

Answer 1

Answer a :-

PLANERS a &3 pa ut Pa ut Paorjai Paerfeu PAAMER P3QustP3Coa PaQt Pacoes PLAYERI Shout PI Shost Fue Shout quict Shont Long pa Fe madu Shoaut Shont Pa Long P3 Fe PI Short Canfeus Shont midun PIF PI F LAUCR -

Where ,

P1 = Player 1

P2 = Player 2

P3 = Player 3

Answer b :-

Silent,Silent and Silent is the most pareto-optimal situation in this Prisoner's dilemma game .Yes it is one of the Nash equilibrium of this game ,however this game Matrix has multiple Nash equilibrium.