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Contribution Details

Type Working Paper
Scope Discipline-based scholarship
Title Fictitious play in networks
Organization Unit
  • Christian Ewerhart
  • Kremena Valkanova
  • English
Institution University of Zurich
Series Name Working paper series / Department of Economics
Number 239
ISSN 1664-7041
Number of Pages 57
Date 2019
Abstract Text 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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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
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