1) A one-shot prisoners' dilemma pays $500 to each player for cooperation, $200 to each player...

1) A one-shot prisoners' dilemma pays $500 to each player for cooperation, $200 to each player for a double defection, and $878 to a player who defects when the other player cooperates. Assume the game is repeated indefinitely, players play a GRIM strategy, and the time discount factor is 0.56. Calculate the present value of defection.

2) The cooperative payoffs in a prisoners' dilemma are $890 for each player, while the defection payoff is $1,498. The game is repeated indefinitely, players follow a Tit-for-Tat strategy, and the time discount factor is 0.5. Calculate the present value of cooperation.

Expert Solution

Q1) present value of defection = 878+200d + 200d^2 + 200*d^3 + ....

Vd = 878 + 200d/(1-d)

d = .56

So, Vd = 878 + 200*.56/(1-.56)

= 878 + 200*.56/.44

= 1132.545

.

Q2) present value of Cooperation = 890+ 890d + 890d^2 + ..

= 890/(1-d)

= 890/.5

= 1780

Rahul Sunny answered 2 years ago

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