How to Make Cooperation the Optimizing Strategy in a Two-Person Game

Bernard Grofman

Jonathan Robert Pool

Published in Journal of Mathematical Sociology, 5 (1977), 173–186.

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This paper demonstrates the existence of a partial tit-for-tat (matching) strategy which, when used by one player in an iterated “Prisoner’s Dilemma” game, will induce a response of pure cooperation in the other player if that player behaves optimally. The minimum matching frequency of such a strategy is shown to be monotonically related to the Rapoport-Chammah “Cooperation Index”.

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