Suppose that in the twice-repeated prisoners’ dilemma of Exercise S3, a fourth possible type (type..

Suppose that in the twice-repeated prisoners’ dilemma of
Exercise S3, a fourth possible type (type S) also can exist in the population.
This type does not confess on the first play and confesses on the second play
of each episode of two successive plays against the same opponent.

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(a) Draw the four-by-four fitness table for the game.

(b) Can the newly conceived type S be an ESS of this
game?

(c) In the three-types game of Exercise S3, A and T were
both ESS, but T was only neutrally stable because a small proportion of N
mutants could coexist. Show that in the four-types game here, T cannot be ESS.

 

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