Journal
JOURNAL OF THEORETICAL BIOLOGY
Volume 231, Issue 2, Pages 175-179Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jtbi.2004.06.012
Keywords
replicator dynamics; evolutionarily stable strategy; asymptotic stability; time delay
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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. (C) 2004 Elsevier Ltd. All rights reserved.
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