TY - JOUR
T1 - Evolutionary game dynamics with non-uniform interaction rates
AU - Taylor, Christine
AU - Nowak, Martin A.
N1 - Funding Information:
The Program for Evolutionary Dynamics is supported by Jeffrey Epstein. The authors would like to thank the referees for careful reading and suggestions.
PY - 2006/5
Y1 - 2006/5
N2 - 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.
AB - 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.
KW - Evolutionary game dynamics
KW - Evolutionary stability
KW - Kin selection
KW - Non-uniform interaction rates
KW - Prisoner's Dilemma
KW - Replicator dynamics
KW - Snowdrift game
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U2 - 10.1016/j.tpb.2005.06.009
DO - 10.1016/j.tpb.2005.06.009
M3 - Article
C2 - 16427669
AN - SCOPUS:33645740452
VL - 69
SP - 243
EP - 252
JO - Theoretical Population Biology
JF - Theoretical Population Biology
SN - 0040-5809
IS - 3
ER -