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The Stabilisation of Equilibria in Evolutionary Game Dynamics through Mutation: Mutation Limits in Evolutionary Games

Bauer, J., Broom, M. ORCID: 0000-0002-1698-5495 and Alonso, E. ORCID: 0000-0002-3306-695X (2019). The Stabilisation of Equilibria in Evolutionary Game Dynamics through Mutation: Mutation Limits in Evolutionary Games. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2231), doi: 10.1098/rspa.2019.0355

Abstract

The multi-population replicator dynamics (RD) isa dynamic approach to coevolving populationsand multi-player games, and is related to Cross’learning. In general, not every equilibrium is aNash equilibrium (NE) of the underlying game,and convergence is not guaranteed. In particular,no interior equilibrium can be asymptotically stablein the multi-population RD, resulting, e.g., in cyclicorbits around a single interior NE. We introducea new notion of equilibria of RD, called mutationlimits, based on a naturally arising, simple formof mutation, which is invariant under the specificchoice of mutation parameters. We prove the existenceof mutation limits for a large class of games, andconsider a particularly interesting subclass, calledattracting mutation limits. Attracting mutation limitsare approximated in every (mutation-)perturbed RD,hence, offering approximate dynamic solution of theunderlying game, even if the original dynamic is notconvergent. Thus, mutation stabilises the system incertain cases and makes attracting mutation limitsnear-attainable. Hence, attracting mutation limits arerelevant as a dynamic solution concept of games. Weobserve that they have some similarity to Q-learningin multi-agent reinforcement learning. Attractingmutation limits do not exist in all games, however,raising the question of their characterization.

Publication Type: Article
Publisher Keywords: replicator dynamics, evolutionarygames, mutation, multiple populations
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Computer Science
School of Mathematics, Computer Science & Engineering > Mathematics
URI: https://openaccess.city.ac.uk/id/eprint/22988
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