Cooperation in Games with Forgetfulness

Authors:
Raphael Thomadsen;Pradeep Bhardwaj
Affiliations:
UCLA Anderson School of Management, University of California, Los Angeles, Los Angeles, California 90095;Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
Venue:
Management Science
Year:
2011

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Abstract

Companies and managers are apt to forget information, yet classic game theory analysis assumes that all players have perfect recall. This paper expands the literature by examining how introducing forgetfulness into a multiplayer game-theoretic framework can help or hinder cooperative behavior. We find that forgetfulness impacts the ability of firms to cooperate in countervailing directions. On one hand, forgetfulness can diminish the ability to punish deviators, making cooperation more difficult. On the other hand, under some conditions forgetfulness can make meting out severe punishments---even below-(stage) minimax punishments---credible and decrease the ability for players to effectively deviate, facilitating cooperation even in circumstances where cooperation cannot be sustained under perfect recall. We apply our model to a number of strategic games that commonly appear in the literature. This paper was accepted by Preyas Desai, marketing.