The Repentance Strategy

• Autores: Miguel Angel Aramendía Ruiz
• Localización: Abstracts of the Fifth Spanish Meeting on Game Theory and Applications / coord. por Jesús Mario Bilbao Arrese, Francisco Ramón Fernández García, 2002, ISBN 84-472-0733-1, pág. 70
• Idioma: inglés
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• Resumen

  • It is well known that repeating a game may lead to the emergence of new noncooperative equilibriums. In his seminal paper on trigger strategies, Friedman (1971) showed that cooperative outcomes could be sustained by these strategies as subgame perfect equilibrium provided that the players are sufficiently patient. Friedman�s strategy prescribes cooperating to begin with and as long as the others cooperate; if any of the others deviates it recommends switching to the one-shot equilibrium strategy and playing it forever. Its main drawbacks are that any deviation precludes cooperation forever in the future and all the players suffer equally.

    In a large class of infinitely repeated Cournot duopoly games with discounting and perfect monitoring, Segerstrom (1988) defined the repentance strategies and showed that the symmetric monopoly payoff (cartel benefits) could be sustained by these strategies as subgame perfect equilibrium for the same range of discount factors as the trigger strategy does. In these repentance strategies, the nondeviating player forgives the deviating player and both revert back to collusive behavior after the cheater repents paying a punishment in several periods.

    During the repentance phase, the punisher receives an entire payoff that is higher than the payoff of the punished player.

    The context of our work is the repeated Cournot oligopoly model with discounting and perfect monitoring. We define repentance strategies that keeps all the properties mentioned above and also has a special feature: during the repentance phase, each of the nondeviating players is playing his best response to the output specified to the other players. In other words, each of the punishers does not have any incentive to deviate during the repentance phase. We believe that this repentance strategy could have some applications in the field of industrial organization. With the Segerstrom�s assumptions, we show that the symmetric monopoly payoff could be sustained by these strategies as subgame perfect equilibrium for at least the same range of discount factors as the trigger strategy does.