Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/162442
Authors: 
Ewerhart, Christian
Valkanova, Kremena
Year of Publication: 
2016
Series/Report no.: 
Working Paper Series, University of Zurich, Department of Economics 239
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.
Subjects: 
Fictitious play
networks
zero-sum games
conflicts
potential games
Miyasawa's theorem
Robinson's theorem
JEL: 
C72
D83
D85
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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