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On some variants of prisoner’s dilemma dynamics. (English) Zbl 1116.91015

Summary: Two variants of Prisoner’s dilemma game are given. The first one is related to spite. Spite is the willingness to harm oneself in order to cause more harm to another. An extreme case is when one goes as far as killing himself to harm his enemy. This behavior sometimes occurs in humans. To model it, the standard replicator dynamics is replaced by imitation dynamics. We study the spite replicator dynamics for the prisoner’s dilemma game and derive a case where cooperation may arise. The second variant is the prisoner’s dilemma loner game. Smale’s memory formulation for game is used to study it.

MSC:

91A22 Evolutionary games
37N40 Dynamical systems in optimization and economics
91A25 Dynamic games
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References:

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