Evolutionarily Stable Preferences Against Multiple Mutations in Multi-player Games

TL;DR

This paper investigates the conditions under which preferences in multi-player games remain stable against multiple mutations, revealing links between stability order and efficiency in evolutionary game theory.

Contribution

It introduces necessary and sufficient conditions for multi-mutation stability of preferences in multi-player games using the indirect evolutionary approach.

Findings

Established conditions for multi-mutation stability.

Linked stability levels to efficiency.

Analyzed single- and multi-population settings.

Abstract

We use the indirect evolutionary approach to study evolutionarily stable preferences against multiple mutations in single- and multi-population matching settings, respectively. Players choose strategies to maximize their subjective preferences, which may be inconsistent with the material payoff function giving them the actual fitness values. In each of the two settings, $n$-player games are played, and we provide necessary and sufficient conditions for multi-mutation stability. These results definitely reveal the connection between the order of stability and the level of efficiency.