Second-order effects of mutation in continuous indirect reciprocity
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913434805731328 |
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| author | Mun, Youngsuk Baek, Seung ki |
| author_facet | Mun, Youngsuk Baek, Seung ki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12725 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Second-order effects of mutation in continuous indirect reciprocity Mun, Youngsuk Baek, Seung ki Physics and Society 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. |
| title | Second-order effects of mutation in continuous indirect reciprocity |
| topic | Physics and Society |
| url | https://arxiv.org/abs/2308.12725 |