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Preference-based Cooperation in a Prisoner's Dilemma Game: Whole Population Cooperation without Information Flow across Matches

Jung, Hanjoon Michael (2007): Preference-based Cooperation in a Prisoner's Dilemma Game: Whole Population Cooperation without Information Flow across Matches.

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Abstract

This paper studies the possibility of cooperation based on players' preferences. Consider the following infinitely repeated game, similar to Ghosh and Ray (1996). At each stage, uncountable numbers of players are randomly matched without information about their partners' past actions and play a prisoner's dilemma game. The players have the option to continue their relationship, and they all have the same discount factor. Also, they have two possible types: high ability player (H) or low ability player (L). H can produce better outcomes for its partner as well as for itself than L can. I look for an equilibrium that is robust against both pair-wise deviation and individual deviation and call such equilibrium a social equilibrium. I show that in this setting, long term cooperative behavior can arise in a social equilibrium. H wants to match and play only with another H because an HH match produces better outcomes for H than an HL match. So H would break a match with L to increase the possibility of meeting another H, and thus H would not play any cooperative action with L. L knows this intention of H and realizes that L can only cooperate with another L. Consequently, both HH and LL matches are endowed with a scarcity value. This scarcity value is utilized by players to sustain cooperative relationships. Therefore, in a social equilibrium, whole players can play long term cooperative actions because of their preferences for their partners' types.

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