2022/03/24 by Yuma Fujimoto, Hisashi Ohtsuki, Fujimoto, Yuma +1 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Game Theory and Applications #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Physics and Society (physics.soc-ph)
paper · pdf · doi:10.48550/arxiv.2203.12898
openalex publication_date 2022/03/24 · openalex created_date 2022/10/29 · openalex updated_date 2026/07/28
Evaluation relationships are pivotal for maintaining a cooperative society. A formation of the evaluation relationships has been discussed in terms of indirect reciprocity, by modeling dynamics of good or bad reputations among individuals. Recently, a situation that individuals independently evaluate others with errors (i.e., noisy and private reputation) is considered, where the reputation structure (from what proportion of individuals in the population each receives good reputations, defined as goodness here) becomes complex, and thus has been studied mainly with numerical simulations. The present study gives a theoretical analysis of such complex reputation structure. We formulate the time change of goodness of individuals caused by updates of reputations among individuals. By considering a large population, we derive dynamics of the frequency distribution of goodnesses. An equilibrium state of the dynamics is approximated by a summation of Gaussian functions. We demonstrate that the theoretical solution well fits the numerical calculation. From the theoretical solution, we obtain a new interpretation of the complex reputation structure. This study provides a novel mathematical basis for cutting-edge studies on indirect reciprocity.