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Fictitious play in networks

Christian Ewerhart () and Kremena Valkanova

No 239, ECON - Working Papers from Department of Economics - 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.

Keywords: Fictitious play; networks; zero-sum games; conflicts; potential games; Miyasawa's theorem; Robinson's theorem (search for similar items in EconPapers)
JEL-codes: C72 D83 D85 (search for similar items in EconPapers)
Date: 2016-12, Revised 2019-06
New Economics Papers: this item is included in nep-gth, nep-hpe, nep-mic and nep-net
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