Economic and Game Theory
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If this game is only played once there are two pure strategy NE: (C,N) and (N,C) and
mixed strategy NE: (1/2C+1/2N, 1/2C+1/2N).
If this game is played infinitely there may be much more possible outcomes. For example
(C,C) may be an outcome in equilibrium. How? Imaging that the players play (C,C) from
the beginning, if one deviates, he/she is punished by reverting to the static NE that is worse
for him/her. Then, in analyzing if deviating or not, the players should do the following
U(C)=3 and U(N)=4(1-d)+d
where d is the discount factor.
U(C)>U(N) if d>1/3.
Then, if d is greater or equal to 1/3, playing (C,C) in every period is an equilibrium outcome.
A good reference for repeated games theory is "Game
Theory", Ch.5, Fudenberg and