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Hi everyone,I've been stuck with a problem on mathing pennies. The payoffs for the game are as follows: H T H 1,-1 -1,1 T -1,1 1,-1If you graph the payoffs, you get a line joining (-1,1) and (1,-1).In repeated games, this line represents the set(its just a line unlike other games) of feasible payoffs when delta is close to 1.My question is what would the set of rational payoffs be for repated games? Intuitively I think it will be (0,0), because at that point no player has an advantage over the other. But I cannot prove it mathematically. This strategy is also the Nash equilibrium using mixed strategy. Now this game does not have an NE using pure strategy. Using mixed strategy, we get an NE by playing H and T with probability (1/2,1/2). Will there be a NE for repeated games? I know all games must have a NE using mixed strategy, but should all games have a NE when repeating?Any comments would be grealty appreciated.thanks!

I believe that you can prove your claim by applying a 'folk theorem' for repeated games. You can find a statement of a simple folk theorem in Rubinstein's book and also, I think, in Gibbon.

EDIT: double post

Didn't I answer this already in the student forum?This doesn't really qualify as a brainteaser.