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Fictitious play in networks


Ewerhart, Christian; Valkanova, Kremena (2019). Fictitious play in networks. Working paper series / Department of Economics 239, University of Zurich.

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.

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C72, D83, D85
Uncontrolled Keywords:Fictitious play, networks, zero-sum games, conflicts, potential games, Miyasawa's theorem, Robinson's theorem, Netzwerk, Nullsummenspiel, Konflikt, Konvergenz, Nichtkooperatives Spiel, Nash-Gleichgewicht, Netzwerk
Language:English
Date:June 2019
Deposited On:06 Dec 2016 15:36
Last Modified:18 Mar 2022 09:45
Series Name:Working paper series / Department of Economics
Number of Pages:57
ISSN:1664-7041
Additional Information:Revised version
OA Status:Green
Official URL:https://www.econ.uzh.ch/static/release/workingpapers.php?id=918

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