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Fictitious play in networks


Ewerhart, Christian; Valkanova, Kremena (2020). Fictitious play in networks. Games and Economic Behavior, 123:182-206.

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 , 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 , 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:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Uncontrolled Keywords:Economics and econometrics, finance, fictitious play, networks, zero-sum games, conflicts, potential games, Miyasawa's theorem, Robinson's theorem
Language:English
Date:1 September 2020
Deposited On:08 Jul 2020 13:07
Last Modified:29 Jul 2020 15:23
Publisher:Elsevier
ISSN:0899-8256
OA Status:Closed
Publisher DOI:https://doi.org/10.1016/j.geb.2020.06.006
Official URL:https://www.sciencedirect.com/science/article/abs/pii/S0899825620300919?via%3Dihub

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