Stability of evolutionarily stable strategies in discrete replicator dynamics with time delay

Details Stability of evolutionarily stable strategies in discrete replicator dynamics with time delay Stability of evolutionarily stable strategies in discrete replicator dynamics with time delay

2004-09-21

arxiv.org/abs/q-bio/0409024v1

Biology

Quantitative Biology

Populations and Evolution

9 pages, to appear in J. Theor. Biology

Scientific paper

We construct two models of discrete-time replicator dynamics with time delay. In the social-type model, players imitate opponents taking into account average payoffs of games played some units of time ago. In the biological-type model, new players are born from parents who played in the past. We consider two-player games with two strategies and a unique mixed evolutionarily stable strategy. We show that in the first type of dynamics, it is asymptotically stable for small time delays and becomes unstable for big ones when the population oscillates around its stationary state. In the second type of dynamics, however, evolutionarily stable strategy is asymptotically stable for any size of a time delay.

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