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

Peña, Jorge and Lehmann, Laurent and Nöldeke, Georg. (2013) Gains from switching and evolutionary stability in multi-player matrix games. WWZ Discussion Papers, 2013 (13).

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Official URL: https://edoc.unibas.ch/61343/

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Abstract

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 properties 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 it 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.
Faculties and Departments:06 Faculty of Business and Economics > Departement Wirtschaftswissenschaften > Professuren Wirtschaftswissenschaften > Mikroökonomische Theorie (Nöldeke)
12 Special Collections > WWZ Publications > WWZ Discussion Papers and Working Papers
UniBasel Contributors:Nöldeke, Georg and Pena Suarez, Jorge Alejandro
Item Type:Working Paper
Publisher:WWZ, University of Basel
Number of Pages:35
Note:Publication type according to Uni Basel Research Database: Discussion paper / Internet publication
Language:English
Identification Number:
  • handle: RePEc:bsl:wpaper:2013/13
Last Modified:09 Mar 2018 10:53
Deposited On:08 Mar 2018 08:12

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