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arXiv · 2308.12725

Second-order effects of mutation in continuous indirect reciprocity

Youngsuk Mun·Seung ki Baek
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Abstract

We have developed a continuous model of indirect reciprocity and thereby investigated effects of mutation in assessment rules. Within this continuous framework, the difference between the resident and mutant norms is treated as a small parameter for perturbative expansion. Unfortunately, the linear-order expansion leads to singularity when applied to the leading eight, the cooperative norms that resist invasion of another norm having a different behavioral rule. For this reason, this study aims at a second-order analysis for the effects of mutation when the resident norm is one of the leading eight. We approximately solve a set of coupled nonlinear equations using Newton's method, and the solution is compared with Monte Carlo calculations. The solution indicates how the characteristics of a social norm can shape the response to its close variants appearing through mutation. Specifically, it shows that the resident norm should allow one to refuse to cooperate toward the ill-reputed, while regarding cooperation between two ill-reputed players as good, so as to reduce the impact of mutation.This study enhances our analytic understanding on the organizing principles of successful social norms.

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Youngsuk Mun, Seung ki Baek. 2023-08-24. Second-order effects of mutation in continuous indirect reciprocity. https://doi.org/10.1140/epjs%2Fs11734-023-00948-9

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