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Evolutionary stability and resistance to cheating in an indirect reciprocity model based on reputation
Luis A Martinez-Vaquero1, José A Cuesta
1Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain.
Summary
This study identifies evolutionarily stable strategies for indirect reciprocity, crucial for understanding altruism. Honest strategies can be invaded by cheaters if actions aren't always observed, with discovery probability acting like relatedness.
Area of Science:
- Evolutionary Game Theory
- Social Behavior
- Behavioral Economics
Background:
- Indirect reciprocity is key to understanding altruism in societies.
- Reputation models, where decisions are based on past interactions, are standard for studying indirect reciprocity.
- Analyzing strategy stability against invasions is complex due to diverse strategies.
Purpose of the Study:
- To systematically analyze strategy invasions in indirect reciprocity models.
- To identify evolutionarily stable third-order strategies.
- To investigate conditions under which honest strategies can resist invasion by cheaters.
Main Methods:
- Utilized a variant of a previously introduced reputation-based model.
- Performed systematic analysis of strategy invasions.
- Employed adaptive dynamics to analyze the invasion of honest populations by cheaters.
Main Results:
- Strategies resisting invasion by others with the same moral assessment are broadly stable.
- Cheaters can defeat stable strategies if actions are not always witnessed.
- A Hamilton-like rule determines resistance to cheater invasion, with discovery probability analogous to relatedness.
Conclusions:
- Identified specific third-order strategies that are evolutionarily stable in indirect reciprocity.
- Highlighted the importance of action observability for maintaining honest strategies.
- Established a quantitative framework, akin to kin selection, for understanding the evolution of cooperation.
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