Many humans, even children, place importance on what a person has done not only to themselves but also to others. Modelling studies on indirect reciprocity have revealed that when each player refers to social reputation of his/her co-players to choose to or not to cooperate, a conditionally cooperative strategy can be evolutionarily stable even with very few number of game sessions. Recent studies have further claimed that reputation of a player should be updated according to not only the player's choice (called the first-order information) but also reputation of his/her co-player at that time (the second-order information). Especially, an uncooperative choice against a bad co-player should not be regarded as bad (the standing norm).
However, experimental studies found that participants made decisions depending only on the first-order information and not on the higher-order information.
I present an image-scoring model that considers diffusion process of social reputations. The model assumes that each game session is not observed by third party and that personal experience passes from mouth to mouth through gossip sessions, which are described as contact processes on a complete graph.
In a population purely consisting of fair gossipers, who start good/bad gossips about their co-players when the co-players choose cooperation/defection, a conditional cooperators can gradually stop cooperation with unconditional defectors by receiving bad gossips about the defectors. Then bad gossips about some conditional cooperators are started by the defectors because the defectors are also fair gossipers. According to our individual-based simulations, however, the opposite, good gossips about those conditional cooperators can maintain their social reputation and reciprocal relationship among the whole conditional cooperators lasts long even though players do not subject to the standing norm. At the same time, however, we found a new problem that a lying player can gain higher payoff than an average fairly-gossiping conditional cooperator by starting false bad gossips about others or by spreading false good gossips about themselves.
This is a joint work with Dr. Mayuko Nakamaru in Tokyo Institute of Technology.