Gains from switching and evolutionary stability in multi-player matrix games

JOURNAL OF THEORETICAL BIOLOGY

卷:346

Article

Pena, Jorge¹  Lehmann, Laurent²  Noeldeke, Georg¹ 

[1] Univ Basel, Fac Business & Econ, CH-4002 Basel, Switzerland

[2] Univ Lausanne, Dept Ecol & Evolut, CH-1015 Lausanne, Switzerland

关键词: Evolutionary game theory;    Replicator dynamics;    Polynomials in Bernstein form;    Public goods games;   

DOI  :  10.1016/j.jtbi.2013.12.016

来源: Elsevier

【 摘 要 】

In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric N-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other individuals in the group play a given strategy. As a consequence, the gain function determining the gradient of selection can be a polynomial of degree N - 1. In order to deal with the intricacy of the resulting evolutionary dynamics, we make use of the theory of polynomials in Bernstein form. This theory implies a tight link between the sign pattern of the gains from switching on the one hand and the number and stability of the rest points of the replicator dynamics on the other hand. While this relationship is a general one, it is most informative if gains from switching have at most two sign changes, as is the case for most multi-player matrix games considered in the literature. We demonstrate that previous results for public goods games are easily recovered and extended using this observation. Further examples illustrate how focusing on the sign pattern of the gains from switching obviates the need for a more involved analysis. (C) 2013 Elsevier Ltd. All rights reserved.

【 授权许可】

Free