Density games Journal Article

Author(s): Novak, Sebastian; Chatterjee, Krishnendu; Nowak, Martin A
Article Title: Density games
Affiliation IST Austria
Abstract: The basic idea of evolutionary game theory is that payoff determines reproductive rate. Successful individuals have a higher payoff and produce more offspring. But in evolutionary and ecological situations there is not only reproductive rate but also carrying capacity. Individuals may differ in their exposure to density limiting effects. Here we explore an alternative approach to evolutionary game theory by assuming that the payoff from the game determines the carrying capacity of individual phenotypes. Successful strategies are less affected by density limitation (crowding) and reach higher equilibrium abundance. We demonstrate similarities and differences between our framework and the standard replicator equation. Our equation is defined on the positive orthant, instead of the simplex, but has the same equilibrium points as the replicator equation. Linear stability analysis produces the classical conditions for asymptotic stability of pure strategies, but the stability properties of internal equilibria can differ in the two frameworks. For example, in a two-strategy game with an internal equilibrium that is always stable under the replicator equation, the corresponding equilibrium can be unstable in the new framework resulting in a limit cycle.
Keywords: Evolutionary game theory; Evolutionary dynamics; Replicator equation; Carrying capacity; Mathematical biology
Journal Title: Journal of Theoretical Biology
Volume: 334
ISSN: 0022-5193
Publisher: Elsevier  
Date Published: 2013-10-07
Start Page: 26
End Page: 34
Copyright Statement: CC BY-NC-ND
DOI: 10.1016/j.jtbi.2013.05.029
Notes: The authors thank two anonymous referees for helpful comments on the paper. This work has been funded by the European Research Council (ERC) Grant no. 250152, the Austrian Science Fund (FWF) Grant no. P 23499-N23, FWF NFN Grant no. S11407-N23 (RiSE), ERC Start Grant (279307: Graph Games), and the Microsoft faculty fellows award. Support from the Templeton Foundation is gratefully acknowledged.
Open access: yes (OA journal)