Gains from switching and evolutionary stability in multi-player matrix games
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.
|Date of creation:||2013|
|Contact details of provider:|| Postal: Peter-Merian-Weg 6, Postfach, CH-4002 Basel|
Web page: http://wwz.unibas.ch
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497190, September.
- Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, July.
- Sánchez, Angel & Lugo, Haydée & Jiménez, Raúl & Cuesta, José A., 2007. "Rewarding cooperation in social dilemmas," UC3M Working papers. Economics we075227, Universidad Carlos III de Madrid. Departamento de Economía.
- Florian Herold, 2012. "Carrot or Stick? The Evolution of Reciprocal Preferences in a Haystack Model," American Economic Review, American Economic Association, vol. 102(2), pages 914-940, April.
- Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497701, September.
- U. Dieckmann & R. Law, 1996. "The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes," Working Papers wp96001, International Institute for Applied Systems Analysis.
When requesting a correction, please mention this item's handle: RePEc:bsl:wpaper:2013/13. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (WWZ)
If references are entirely missing, you can add them using this form.