Fluctuations in Coevolutionary Dynamics and Implications for Multi-Agent Models

Abstract: Companies and customers as well as competing species in biologies are widely modeled by multi-agent systems, both investigated in simulations and in analytical models. Analytical approaches allow to combine computational models for one level of description with analytical approximations for annother level. One particular issue in this context is the proper description of noise, both of external and of internal noise. In the context of evolutionary game theory, which accounts for stategic and conflict situations in biological as well as in social and economic dynamics, coevolutionary dynamics traditionally is described by deterministic repli-cator dynamics assuming implicitly infinite population sizes. The explicit stochastic dynamics in finite populations however is more difficult to tackle but currently gains more and more attention. Recently we have noted that even simple coevolutionary dynamics of 2x2 games in finite populations can lead to unexpected stationary distributions of strategies significantly de-viating from the Gaussian. The relationship between deterministic and stochastic approaches can be addressed systematically by explicitely considering the limit of infinite populations. In particular, different microscopic stochastic processes lead to different replicator equations. Moreover, differences on the individual level can lead to qualitatively different dynamics i