title: Indirect reciprocity with trinary reputations.
abstract: Indirect reciprocity is a reputation-based mechanism for cooperation in social dilemma situations when individuals do not repeatedly meet. The conditions under which cooperation based on indirect reciprocity occurs have been examined in great details. Most previous theoretical analysis assumed for mathematical tractability that an individual possesses a binary reputation value, i.e., good or bad, which depends on their past actions and other factors. However, in real situations, reputations of individuals may be multiple valued. Another puzzling discrepancy between the theory and experiments is the status of the so-called image scoring, in which cooperation and defection are judged to be good and bad, respectively, independent of other factors. Such an assessment rule is found in behavioral experiments, whereas it is known to be unstable in theory. In the present study, we fill both gaps by analyzing a trinary reputation model. By an exhaustive search, we identify all the cooperative and stable equilibria composed of a homogeneous population or a heterogeneous population containing two types of players. Some results derived for the trinary reputation model are direct extensions of those for the binary model. However, we find that the trinary model allows cooperation under image scoring under some mild conditions.
authors.affiliation: Department of Mathematical Informatics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan.
authors.forename: Shoma
authors.initials: S
authors.lastname: Tanabe
authors.forename: Hideyuki
authors.initials: H
authors.lastname: Suzuki
authors.forename: Naoki
authors.initials: N
authors.lastname: Masuda
mesh_terms: D003299:Cooperative Behavior; D005716:Game Theory; D006801:Humans; D008962:Models, Theoretical