title: Evolutionary stability for matrix games under time constraints.
abstract: Game theory focuses on payoffs and typically ignores time constraints that play an important role in evolutionary processes where the repetition of games can depend on the strategies, too. We introduce a matrix game under time constraints, where each pairwise interaction has two consequences: both players receive a payoff and they cannot play the next game for a specified time duration. Thus our model is defined by two matrices: a payoff matrix and an average time duration matrix. Maynard Smith's concept of evolutionary stability is extended to this class of games. We illustrate the effect of time constraints by the well-known prisoner's dilemma game, where additional time constraints can ensure the existence of unique evolutionary stable strategies (ESS), both pure and mixed, or the coexistence of two pure ESS. Our general results may be useful in several fields of biology where evolutionary game theory is applied, principally in ecological games, where time constraints play an inevitable role.
authors.affiliation: MTA-ELTE Theoretical Biology and Evolutionary Ecology Research Group and Department of Plant Systematics, Ecology and Theoretical Biology, Eötvös Loránd University, Pázmány P. s. 1/C, H-1117 Budapest, Hungary. Electronic address: garayj@caesar.elte.hu.
authors.forename: József
authors.initials: J
authors.lastname: Garay
authors.affiliation: Department of Probability Theory and Statistics, Eötvös Loránd University, Pázmány P. s. 1/C, H-1117 Budapest, Hungary. Electronic address: villo@ludens.elte.hu.
authors.forename: Villő
authors.initials: V
authors.lastname: Csiszár
authors.affiliation: Department of Probability Theory and Statistics, Eötvös Loránd University, Pázmány P. s. 1/C, H-1117 Budapest, Hungary. Electronic address: mori@math.elte.hu.
authors.forename: Tamás F
authors.initials: TF
authors.lastname: Móri
mesh_terms: D005075:Biological Evolution; D005716:Game Theory; D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical; D013997:Time Factors
keywords: Evolutionary stability; Matrix game; Prisoner's dilemma; Sharing problem; Time constraint