Evolutionary Games on Cycles

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Evolutionary Games on Cycles

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Title: Evolutionary Games on Cycles
Author: Ohtsuki, Hisashi; Nowak, Martin A.

Note: Order does not necessarily reflect citation order of authors.

Citation: Ohtsuki Hisashi, and Martin A. Nowak. 2006. Evolutionary games on cycles. Proceedings of the Royal Society B 273(1598): 2249-2256.
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Abstract: Traditional evolutionary game theory explores frequency-dependent selection in well-mixed populations without spatial or stochastic effects. But recently there has been much interest in studying the evolutionary game dynamics in spatial settings, on lattices and other graphs. Here, we present an analytic approach for the stochastic evolutionary game dynamics on the simplest possible graph, the cycle. For three different update rules, called ‘birth–death’ (BD), ‘death–birth’ (DB) and ‘imitation’ (IM), we derive exact conditions for natural selection to favour one strategy over another. As specific examples, we consider a coordination game and Prisoner's Dilemma. In the latter case, selection can favour cooperators over defectors for DB and IM updating. We also study the case where the replacement graph of evolutionary updating remains a cycle, but the interaction graph for playing the game is a complete graph. In this setting, all three update rules lead to identical conditions in the limit of weak selection, where we find the ‘1/3-law’ of well-mixed populations.
Published Version: doi:10.1098/rspb.2006.3576
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:4063697
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