Replicator dynamics of an N-player snowdrift game with delayed payoffs

Thomas A. Wettergren

Applied Mathematics and Computation, 2021, vol. 404, issue C

Abstract: We consider a version of the N-player snowdrift game in which the payoffs obtained by the players are delayed. The delay in payoffs is shown to lead to a Hopf bifurcation with an associated critical value of the time delay in the replicator dynamics. For time delays larger than the critical time delay, the replicator dynamics oscillate around the equilibrium instead of asymptotically approaching it. The dependence of this critical time delay on the parameters of the game is determined. After developing the analysis for the 2-player game, the same methodology is applied to the N-player version of the game to show how the results change as a function of N, concluding with an analysis of the limiting case of large numbers of players.

Keywords: Replicator dynamics; Evolutionary games; Snowdrift game; Delayed differential equation; Hopf bifurcation; Critical time delay (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:404:y:2021:i:c:s0096300321002940

DOI: 10.1016/j.amc.2021.126204

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