Spatial evolutionary games with weak selection [Applied Mathematics]
Recently, a rigorous mathematical theory has been developed for spatial games with weak selection, i.e., when the payoff differences
between strategies are small. The key to the analysis is that when space and time are suitably rescaled, the spatial model
converges to the solution of a partial differential equation (PDE). This approach can be used to analyze all
2×2 games, but there are a number of
3×3 games for which the behavior of the limiting PDE is not known. In this paper, we give rules for determining the behavior
of a large class of
3×3 games and check their validity using simulation. In words, the effect of space is equivalent to making changes in the payoff
matrix, and once this is done, the behavior of the spatial game can be predicted from the behavior of the replicator equation
for the modified game. We say predicted here because in some cases the behavior of the spatial game is different from that
of the replicator equation for the modified game. For example, if a rock–paper–scissors game has a replicator equation that
spirals out to the boundary, space stabilizes the system and produces an equilibrium.
Publisher URL: http://feedproxy.google.com/~r/Pnas-RssFeedOfEarlyEditionArticles/~3/P53JQgte-wQ/1620852114.short
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