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Abstract:
Evolutionary game dynamics in finite populations assumes that all mutations are equally likely, i.e., if there are n strategies a
single mutation can result in any strategy with probability 1=n. However, in biological systems it seems natural that not all
mutations can arise from a given state. Certain mutations may be far away, or even be unreachable given the current
composition of an evolving population. These distances between strategies (or genotypes) define a topology of mutations
that so far has been neglected in evolutionary game theory. In this paper we re-evaluate classic results in the evolution of
cooperation departing from the assumption of uniform mutations. We examine two cases: the evolution of reciprocal
strategies in a repeated prisoner’s dilemma, and the evolution of altruistic punishment in a public goods game. In both
cases, alternative but reasonable mutation kernels shift known results in the direction of less cooperation. We therefore
show that assuming uniform mutations has a substantial impact on the fate of an evolving population. Our results call for a
reassessment of the ‘‘model-less’’ approach to mutations in evolutionary dynamics.
