From individual-based simulations to replicator dynamics
Abstract
Game-theoretic simulations of multi-agent systems are frequently compared to the replicator dynamics, which serves as a solvable mean-field theory. Here the limits of this comparison are analyzed. We show that the population dynamics given by the classic Moran process, which was recently transfered to a game theoretic context [Nowak {\em et al.}, Nature (London) {\bf 428}, 646 (2004)], can be regarded as a stochastic mean-field approximation. A deterministic replicator equation is derived from this formulation in the limit of infinite populations. In particular, we show that the adjusted replicator dynamics is the correct approximation in this limit, solving the long standing problem of the appropriate evolutionary dynamics for multipopulation interactions.Keywords
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