Stochastic sampling of interaction partners versus deterministic payoff assignment

Benno Woelfing (1) , Arne Traulsen (1)

1 Max Planck Institute for Evolutionary Biology

Evolutionary game dynamics describes how successful strategies spread in a population. In well mixed-populations, the usual assumption, e.g. underlying the replicator dynamics, is that individuals obtain a payoff from interactions with a representative sample of the population. This determines their fitness. Here, we analyze a situation in which payoffs are obtained through a single interaction, so that individuals of the same type can have different payoffs. We show analytically that for weak selection, this scenario is identical to the usual approach in which an individual interacts with the whole population. For strong selection, however, differences arise that are reflected in the fixation probabilities and lead to deviating evolutionary dynamics.

Mots clés: Evolutionary game theory; Frequency dependent selection; Payoff assignment; Deterministic versus stochastic payoffs; Evolutionary dynamics

Benno Woelfing, Arne Traulsen. Stochastic sampling of interaction partners versus deterministic payoff assignment. Journal of Theoretical Biology, 2009, 257 (4), pp.689. ⟨10.1016/j.jtbi.2008.12.025⟩. ⟨hal-00554555⟩