ArticleProceedings of the National Academy of Sciences of the United States of America2017
Spatial evolutionary games with weak selection.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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8 citing papers in PubMed.
- Cooperation, Defection, and Collapse: A Multiscale Game Theory Framework for Emphysema Progression.Cells · 2026Review
- Modeling cancer's ecological and evolutionary dynamics.Medical oncology (Northwood, London, England) · 2023Article
- The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer.Dynamic games and applications · 2022Review
- Optimal control to reach eco-evolutionary stability in metastatic castrate-resistant prostate cancer.PloS one · 2020Article
- Share, but unequally: a plausible mechanism for emergence and maintenance of intratumour heterogeneity.Journal of the Royal Society, Interface · 2019Article
- Extrapolating weak selection in evolutionary games.Journal of mathematical biology · 2019Article
- Fractionated follow-up chemotherapy delays the onset of resistance in bone metastatic prostate cancer.Games · 2018Article
- Effective games and the confusion over spatial structure.Proceedings of the National Academy of Sciences of the United States of America · 2018Article
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Abstract
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 [Formula: see text] games, but there are a number of [Formula: see text] 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 [Formula: see text] 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.
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