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| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Fictitious play in networks |
| Organization Unit | |
| Authors |
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| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
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| Journal Title | Games and Economic Behavior |
| Publisher | Elsevier |
| Geographical Reach | international |
| ISSN | 0899-8256 |
| Volume | 123 |
| Page Range | 182 - 206 |
| Date | 2020 |
| 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 , 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. |
| Official URL | https://www.sciencedirect.com/science/article/abs/pii/S0899825620300919?via%3Dihub |
| Digital Object Identifier | 10.1016/j.geb.2020.06.006 |
| Other Identification Number | merlin-id:19578 |
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| Keywords | Economics and econometrics, finance, fictitious play, networks, zero-sum games, conflicts, potential games, Miyasawa's theorem, Robinson's theorem |