Jonathan A. K. Cave

In this note, we shall argue that mutual appreciation of human fallibility can resolve the Prisoner's Dilemma that so starkly describes many conflict situations. To do so, we shall suggest a new interpretation of an old idea: successive elimination of dominated strategies. We shall compare it to other solutions which reflect individual recognition of human fallibility, such as perfect and sequential equilibrium. Then we shall apply it to a repeated Prisoners' Dilemma in which players are allowed to base their actions only on the outcome of the previous round of play. While the results depend on whether players are allowed to react to their own previous moves or not, we shall find that the stubbornly noncooperative behavior that characterizes the one shot game is ruled out by the solution we propose. Most resolutions of Prisoners' Dilemma either include such noncooperative behavior as one of the possible outcomes, or are able to ensure cooperation only by the use of ad hoc beliefs or adjustment mechanisms specifically designed to favor cooperation. The wide equilibrium concept we shall propose is largely free of arbitrary specifications. There are two fundamental ideas behind our proposal. The first is the individual recognition of human fallibility, and the second is that this fallibility will not only be recognized, but will become common knowledge.

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