Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/123450
Authors: 
Peña, Jorge
Lehmann, Laurent
Nöldeke, Georg
Year of Publication: 
2013
Series/Report no.: 
WWZ Discussion Paper 2013/13
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.
Subjects: 
evolutionary game theory
multi-player matrix games
replicator dynamics
public goods games
gains from switching
polynomials in Bernstein form 2
Document Type: 
Working Paper

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