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The effectiveness of punishment that a player pays certain costs and punishes an uncooperative player is currently discussed in the field of the study of cooperation under non-kin relationships. The discussions of the effectiveness of punishment are based on either negative or positive point of view. Contrary to these previous discussions, this study proposes a novel model introducing an alternative notion of punishment “sanction with jealousy”. The degree of sanction is proportional to the payoff of the sanctioning player. The condition for sanction to occur reflects jealousy in that each player sanctions their neighbor players when their payoff is smaller than the payoff of their neighbor players. Utilizing this model, the author investigates whether the introduction of the sanction with jealousy improves both the number of players having the strategy of cooperation and the average payoff of all players or not. In addition, the author organizes the new findings from this investigation in comparison with these previous discussions.

Study of the Evolution of Cooperation Based on an Alternative Notion of Punishment “Sanction with Jealousy”