Indirect Reciprocity under Incomplete Observation

Indirect reciprocity, in which individuals help others with a good reputation but not those with a bad reputation, is a mechanism for cooperation in social dilemma situations when individuals do not repeatedly interact with the same partners. In a relatively large society where indirect reciprocity is relevant, individuals may not know each other's reputation even indirectly. Previous studies investigated the situations where individuals playing the game have to determine the action possibly without knowing others' reputations. Nevertheless, the possibility that observers of the game, who generate the reputation of the interacting players, assign reputations without complete information about them has been neglected. Because an individual acts as an interacting player and as an observer on different occasions if indirect reciprocity is endogenously sustained in a society, the incompleteness of information may affect either role. We examine the game of indirect reciprocity when the reputations of players are not necessarily known to observers and to interacting players. We find that the trustful discriminator, which cooperates with good and unknown players and defects against bad players, realizes cooperative societies under seven social norms. Among the seven social norms, three of the four suspicious norms under which cooperation (defection) to unknown players leads to a good (bad) reputation enable cooperation down to a relatively small observation probability. In contrast, the three trustful norms under which both cooperation and defection to unknown players lead to a good reputation are relatively efficient. Author Summary: Humans and other animals often help others even when the helping behavior is costly. Several mechanisms can explain the emergence and maintenance of cooperation. In one such mechanism called indirect reciprocity, individuals are rated according to their past behavior toward others. Individuals help others with a good reputation but not those with a bad reputation. Indirect reciprocity is relevant in relatively large societies where individuals do not meet each other repeatedly. Then, unless an authority maintains the reputation of individuals, individuals would not know information about some others even indirectly via gossip. We investigated a model in which both individuals playing the game (acting players) and observers of the game, who evaluate acting players and start gossiping, incompletely perceive others. In the unique viable and cooperative strategy, one cooperates with good and unknown peers and defects against bad peers. Populations of suspicious observers under which cooperation (defection) to unknown peers is regarded to be good (bad) enable cooperation in relatively wide parameter regions. In contrast, populations of trustful observers under which both cooperation and defection to unknown peers are regarded to be good are relatively efficient.