Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/200185
Authors: 
Ewerhart, Christian
Valkanova, Kremena
Year of Publication: 
2019
Series/Report no.: 
Working Paper 239
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.
Subjects: 
fictitious play
networks
zero-sum games
conflicts
potential games
Miyasawa's theorem
Robinson's theorem
JEL: 
C72
D83
D85
Document Type: 
Working Paper
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