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Fictitious play in networks


Ewerhart, Christian; Valkanova, Kremena (2016). 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-player games. We show that continuous-time fictitious play converges to Nash equilibrium provided that the overall game is zero-sum. Moreover, the rate of convergence is 1/T , regardless of the size of the network. In contrast, arbitrary n-player zero-sum games do not possess the fictitious-play property. As an extension, we consider networks in which each bilateral game is strategically zero-sum, a weighted potential game, or a two-by-two game. In those cases, convergence requires either a condition on bilateral payoffs or that the underlying network structure is acyclic. The results are shown to hold also for the discrete-time variant of fictitious play, which entails 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-player games. We show that continuous-time fictitious play converges to Nash equilibrium provided that the overall game is zero-sum. Moreover, the rate of convergence is 1/T , regardless of the size of the network. In contrast, arbitrary n-player zero-sum games do not possess the fictitious-play property. As an extension, we consider networks in which each bilateral game is strategically zero-sum, a weighted potential game, or a two-by-two game. In those cases, convergence requires either a condition on bilateral payoffs or that the underlying network structure is acyclic. The results are shown to hold also for the discrete-time variant of fictitious play, which entails 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
Language:English
Date:December 2016
Deposited On:06 Dec 2016 15:36
Last Modified:24 Sep 2018 14:49
Series Name:Working paper series / Department of Economics
Number of Pages:37
ISSN:1664-7041
OA Status:Green
Official URL:http://www.econ.uzh.ch/static/wp/econwp239.pdf
Related URLs:http://www.econ.uzh.ch/static/workingpapers.php

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