Consider the following prisoner’s dilemma Player 1 Share Fight Share 15,15 5,18 Player 2 Fight 18,5 7,7 a. Identify each players Nash strategies. b. Does this game have a Nash equilibrium? If yes what is it? c. Does this game have dominant strategy equilibrium? If yes what is it? d What makes it a Prisoner’s dilemma? e. What is the incentive to cheat? f. What is the social cost of cheating? g. In a repeated game what is the value of the reputation?
a) The game is represented in the following table: Share Fight Share 15,15 5,18 Fight 18,5 7,7 Player 1's dominant strategy is to Fight as his payoffs from fighting are strictly greater than his payoffs from Sharing. Similarly, for player 2, his dominant strategy is also to Fight because of the strictly greater payoffs. b) From the table above, it can be observed that the Nash Equilibrium of this game is when both players choose to fight and earn a payoff of 7 each. This game has a dominant strategy equilibrium, which is the game's Nash Equilibrium, as both players play their dominant strategy. d) This is a Prisoner's Dilemma because if both players could collude, they would choose to Share and earn a strictly higher payoff of 15 each. Since they cannot collude, they end up with a Nash Equilibrium which offers them a lower payoff of 7 each.
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