Spatial evolutionary games with weak selection

Published

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Nanda, M; Durrett, R

Published Date

  • June 6, 2017

Published In

Volume / Issue

  • 114 / 23

Start / End Page

  • 6046 - 6051

Electronic International Standard Serial Number (EISSN)

  • 1091-6490

International Standard Serial Number (ISSN)

  • 0027-8424

Digital Object Identifier (DOI)

  • 10.1073/pnas.1620852114

Citation Source

  • Scopus