Article

# Evolutionary game dynamics with non-uniform interaction rates.

Program for Evolutionary Dynamics, Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA.
Theoretical Population Biology (impact factor: 1.65). 06/2006; 69(3):243-52. DOI:10.1016/j.tpb.2005.06.009 pp.243-52
Source: PubMed

ABSTRACT The classical setting of evolutionary game theory, the replicator equation, assumes uniform interaction rates. The rate at which individuals meet and interact is independent of their strategies. Here we extend this framework by allowing the interaction rates to depend on the strategies. This extension leads to non-linear fitness functions. We show that a strict Nash equilibrium remains uninvadable for non-uniform interaction rates, but the conditions for evolutionary stability need to be modified. We analyze all games between two strategies. If the two strategies coexist or exclude each other, then the evolutionary dynamics do not change qualitatively, only the location of the equilibrium point changes. If, however, one strategy dominates the other in the classical setting, then the introduction of non-uniform interaction rates can lead to a pair of interior equilibria. For the Prisoner's Dilemma, non-uniform interaction rates allow the coexistence between cooperators and defectors. For the snowdrift game, non-uniform interaction rates change the equilibrium frequency of cooperators.

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### Keywords

coexistence

equilibrium frequency

equilibrium point changes

evolutionary dynamics

evolutionary game theory

evolutionary stability

interaction rates

interior equilibria

non-linear fitness functions

non-uniform interaction rates

Prisoner's Dilemma

replicator equation

snowdrift game

strict Nash equilibrium

two strategies coexist

uniform interaction rates