Journal
THEORETICAL POPULATION BIOLOGY
Volume 69, Issue 3, Pages 243-252Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.tpb.2005.06.009
Keywords
evolutionary game dynamics; replicator dynamics; non-uniform interaction rates; Prisoner's Dilemma; snowdrift game; kin selection; evolutionary stability
Funding
- NIGMS NIH HHS [R01 GM078986, R01 GM078986-01] Funding Source: Medline
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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. (c) 2005 Elsevier Inc. All rights reserved.
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