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Evolutionary stability and resistance to cheating in an indirect reciprocity model based on reputation

Luis A. Martinez-Vaquero1 and José A. Cuesta1,2,*

  • 1Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain
  • 2Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, 50009 Zaragoza, Spain

  • *cuesta@math.uc3m.es
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Phys. Rev. E 87, 052810 – Published 24 May, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.052810

Abstract

Indirect reciprocity is one of the main mechanisms to explain the emergence and sustainment of altruism in societies. The standard approach to indirect reciprocity is reputation models. These are games in which players base their decisions on their opponent's reputation gained in past interactions with other players (moral assessment). The combination of actions and moral assessment leads to a large diversity of strategies; thus determining the stability of any of them against invasions by all the others is a difficult task. We use a variant of a previously introduced reputation-based model that let us systematically analyze all these invasions and determine which ones are successful. Accordingly, we are able to identify the third-order strategies (those which, apart from the action, judge considering both the reputation of the donor and that of the recipient) that are evolutionarily stable. Our results reveal that if a strategy resists the invasion of any other one sharing its same moral assessment, it can resist the invasion of any other strategy. However, if actions are not always witnessed, cheaters (i.e., individuals with a probability of defecting regardless of the opponent's reputation) have a chance to defeat the stable strategies for some choices of the probabilities of cheating and of being witnessed. Remarkably, by analyzing this issue with adaptive dynamics we find that whether an honest population resists the invasion of cheaters is determined by a Hamilton-like rule, with the probability that the cheat is discovered playing the role of the relatedness parameter.

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Phys. Rev. E 87, 052810– Published 24 May, 2013
  • Received 6 February 2013

©2013 American Physical Society

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