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Evolutionary Game Theory

  • Ross Cressman
  • Joe Apaloo
Reference work entry

Abstract

Evolutionary game theory developed as a means to predict the expected distribution of individual behaviors in a biological system with a single species that evolves under natural selection. It has long since expanded beyond its biological roots and its initial emphasis on models based on symmetric games with a finite set of pure strategies where payoffs result from random one-time interactions between pairs of individuals (i.e., on matrix games). The theory has been extended in many directions (including nonrandom, multiplayer, or asymmetric interactions and games with continuous strategy (or trait) spaces) and has become increasingly important for analyzing human and/or social behavior as well. This chapter initially summarizes features of matrix games before showing how the theory changes when the two-player game has a continuum of traits or interactions become asymmetric. Its focus is on the connection between static game-theoretic solution concepts (e.g., ESS, CSS, NIS) and stable evolutionary outcomes for deterministic evolutionary game dynamics (e.g., the replicator equation, adaptive dynamics).

Keywords

ESS CSS NIS Neighborhood superiority Evolutionary game dynamics Replicator equation Adaptive dynamics Darwinian dynamics 

Notes

Acknowledgements

The authors thank Abdel Halloway for his assistance with Fig. 10.4. This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 690817.

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Authors and Affiliations

  1. 1.Department of MathematicsWilfrid Laurier UniversityWaterlooCanada
  2. 2.Department of Mathematics, Statistics and Computer ScienceSt Francis Xavier UniversityAntigonishCanada

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