Abstract
Intensive studies on indirect reciprocity have explored rational assessment rules for maintaining cooperation and several have demonstrated the effects of the stern-judging rule. Uchida and Sasaki demonstrated that the stern-judging rule is not suitable for maintaining cooperative regimes in private assessment conditions while a public assessment system has been assumed in most studies. Although both assessment systems are oversimplified and society is most accurately represented by a mixture of these systems, little analysis has been reported on their mixture. Here, we investigated how much weight on the use of information originating from a public source is needed to maintain cooperative regimes for players adopting the stern-judging rule when players get information from both public and private sources. We did this by considering a hybrid-assessment scheme in which players use both assessment systems and by using evolutionary game theory. We calculated replicator equations using the expected payoffs of three strategies: unconditional cooperation, unconditional defection, and stern-judging rule adoption. Our analysis shows that the use of the rule helps to maintain cooperation if reputation information from a unique public notice board is used with more than a threshold probability. This hybrid-assessment scheme can be applied to other rules, including the simple-standing rule and the staying rule.
Highlights
Indirect reciprocity [1,2,3,4,5] is a well known mechanism for maintaining cooperation among unrelated players, in which cooperators request information about potential recipients. This reciprocity-based cooperation mechanism prevents free-riders, i.e., players who do not cooperate but receive benefits from naive cooperators, from invading the population of players. It does this by imposing a discrimination that allows players to cooperate only with players with a good reputation, i.e., a good image
Along with the many empirical studies that have been done on indirect reciprocity over several decades [6,7,8,9,10], there have been a number of intensive theoretical studies
We analyzed our model theoretically to explore the effects of hybrid assessment under the stern-judging rule on indirect reciprocity using replicator dynamics
Summary
Indirect reciprocity [1,2,3,4,5] is a well known mechanism for maintaining cooperation among unrelated players, in which cooperators request information about potential recipients. We considered a hybrid-assessment scheme based on the stern-judging rule in indirect reciprocity because this rule works completely differently for the two extreme schemes (i.e., public and private). It helps to maintain cooperative regimes in the public scheme [26,33,34] but not in the private scheme [17,35]. Using a typical theoretical approach, we considered the effect of the stern-judging strategy for a population including both naive strategies
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