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In 1980 Steven Smale introduced a class of strategies for the IteratedPrisoner's Dilemma which used as data the running average of the previouspayoff pairs. This approach is quite different from the Markov chain approach,common before and since, which used as data the outcome of the just previousplay, the memory-one strategies. Our purpose here is to compare these twoapproaches focusing upon good strategies which, when used by a player, assurethat the only way an opponent can obtain at least the cooperative payoff is tobehave so that both players receive the cooperative payoff. In addition, weprove a version for the Smale approach of the so-called Folk Theorem concerningthe existence of Nash equilibria in repeated play. We also consider thedynamics when certain simple Smale strategies are played against one another.

Good Strategies for the Iterated Prisoner's Dilemma : Smale vs. Markov