Multi-person Game Of Indirect Reciprocity With Two-way Implementation Errors

Reciprocity theory is an important component of evolutionary games. Economists and social scientists have applied this theory in their fields respectively and achieved excellent results. For indirect reciprocity, many studies focus on the reputation dynamics and stategy dynamics in two-person games. But the studies about indirect reciprocity in the games of three or more persons are relatively few, in which many problems should be solved.For two-person games of indirect reciprocity, the selection of reputation criterions determines stability of DIS strategy. In this paper, we study indirect reciprocity in the games of three or more persons under image score criterion and standing criterion, respectively. We introduce two-way implemention errors that make our models more practical.In Chapter 1, we introduce the background of indirect reciprocity. In Chapter 2 we specifically examine three-person games with two-way implementation errors, and reveal that indirect reciprocal cooperation can be formed and maintained stable under image score. We first present the model of three-person game with two-way implementation errors. Then we investigate the evolutionary dynamics of two strategies ALLD-DIS and ALLC-DIS respectively. Finally we derive the condition under which DIS strategy can be an evolutionary stable strategy (ESS). In Chapter 3, we discuss the models of three-person games with two-way implementation errors under the more complexed reputation criterion, i.e., standing criterion. We investigate the evolutionary dynamics of two strategies, and reach the results that the DIS strategy can be stable under standing criterion. In Chaper 4 we present the models of n-person games and obtain the conditions under which the DIS can be stable.