Density games

Novak, Sebastian and Chatterjee, Krishnendu and Nowak, Martin A (2013) Density games. Journal of Theoretical Biology, 334. pp. 26-34. ISSN 1095-8541

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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.

Item Type: Article
DOI: 10.1016/j.jtbi.2013.05.029
Uncontrolled Keywords: Evolutionary game theory, Evolutionary dynamics, Replicator equation, Carrying capacity, Mathematical biology
Subjects: 000 Computer science, knowledge & general works > 000 Computer science, knowledge & systems
Research Group: Barton Group
Chatterjee Group
SWORD Depositor: Sword Import User
Depositing User: Sword Import User
Date Deposited: 04 Jan 2016 09:52
Last Modified: 05 Sep 2017 14:28
URI: https://repository.ist.ac.at/id/eprint/400

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