Question

on and Vlad are two players in an indefinitely repeated Prisoners Dilemma Game. Let the

probability that the game continues one more round be “q”. Assume both players are risk neutral

and have a common per-period discount rate of “d”.

1. From this information alone, what must be true about the range of possible values for d and q?

2. Is mutual defection a Nash Equilibrium (NE)? If so, under what conditions is mutual

defection a NE? (HINT: Consider Don’s best response when Vlad’s strategy is “always defect”).

3. Identify the mathematical conditions under which mutual cooperation is a NE. State this

condition in an intuitive and easy to understand sentence. (HINT: assume both players use the

“Grim Trigger” strategy).

Answer 1

2. Nash Equilibrium is one of the most important concepts of game theory developed by John Nash which was an American mathematician. It is an important concept within game theory where optimum consequence of a game is there when no incentive to depart from their preliminary strategy.

Mutual defection is a Nash Equilibrium of Prisoner's Dilemma which is a common situation analyzed in game theory.

In Prisoner's Dilemma game two players (as criminals) are arrested and each prisoner get a chance to either betray the other by appearing that the other committed the crime or collaborate by remaining silent. If both prisoners betray each other then they get five years in prison. In the mentioned question if Don and Vlad betray each other then it can be claimed Mutual Defection as Nash Equilibrium.