Fictitious Play in Networks

University of Zurich, Department of Economics, Working Paper No. 239, Revised version

59 Pages Posted: 8 Dec 2016 Last revised: 18 Jun 2019

See all articles by Christian Ewerhart

Christian Ewerhart

University of Zurich, Department of Economics

Kremena Valkanova

University of Zurich - Department of Economics

Date Written: June 14, 2019

Abstract

This paper studies fictitious play in networks of noncooperative two-person games. We show that continuous-time fictitious play converges to the set of Nash equilibria if the overall n-person game is zero-sum. Moreover, the rate of convergence is 1/T, regardless of the size of the network. In contrast, arbitrary n-person zero-sum games with bilinear payoff functions do not possess the continuous-time fictitious-play property. As extensions, we consider networks in which each bilateral game is either strategically zero-sum, a weighted potential game, or a two-by-two game. In those cases, convergence requires a condition on bilateral payoffs or, alternatively, that the network is acyclic. Our results hold also for the discrete-time variant of fictitious play, which implies, in particular, a generalization of Robinson's theorem to arbitrary zero-sum networks. Applications include security games, conflict networks, and decentralized wireless channel selection.

Keywords: Fictitious play, networks, zero-sum games, conflicts, potential games, Miyasawa's theorem, Robinson's theorem

JEL Classification: C72, D83, D85

Suggested Citation

Ewerhart, Christian and Valkanova, Kremena, Fictitious Play in Networks (June 14, 2019). University of Zurich, Department of Economics, Working Paper No. 239, Revised version, Available at SSRN: https://ssrn.com/abstract=2881418 or http://dx.doi.org/10.2139/ssrn.2881418

Christian Ewerhart (Contact Author)

University of Zurich, Department of Economics ( email )

Schoenberggasse 1
Zurich, CH-8001
Switzerland

Kremena Valkanova

University of Zurich - Department of Economics ( email )

Zürich
Switzerland

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
119
Abstract Views
854
Rank
422,206
PlumX Metrics