[Oct 23rd 2019] Stability through Mutation in Evolutionary Games and Learning Dynamics

Dr. Eduardo Alonso and Johann Bauer (University of London)

Oct 23, 2019 – 11:00 AM
DIISM, Artificial Intelligence laboratory (room 201), Siena SI

The multi-population replicator dynamics (RD) is useful both in the study of co-evolving populations as well as of learning in multi-player games, and we sketch the relation between RD and a simple reinforcement-learning rule (Cross’ learning). Not all equilibria of RD are Nash equilibria (NE) of the underlying game and convergence is not guaranteed. In fact, interior equilibria can never be asymptotically stable in RD, reducing its attractiveness as a learning rule.
We address this issue by proposing the concept of mutation limits of RD based on mutation-perturbed versions of RD, the replicator-mutator dynamics (RMD). We prove the general existence of mutation limits in a large range of games. Further, we introduce attracting mutation limits of RD as being approximated by asymptotically stable equilibria of RMD. Hence, introducing arbitrarily small mutation levels stabilizes an attracting mutation limit, making RMD a candidate for a useful learning rule. We give an example case for attracting mutation limits and present preliminary numerical results of a learning rule based on RMD. In contrast to mutation limits, attracting mutation limits need not exist in all games, and the conditions for their existence are an open question.

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