Flows and Decompositions of Games: Harmonic and Potential Games
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Ozdaglar_Flows and Decom.pdf
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712.53 KB
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Author(s)
Candogan, Utku Ozan
Menache, Ishai
Ozdaglar, Asuman E.
Parrilo, Pablo A.
Date Issued
June 2011
Journal
Mathematics of Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Candogan, O. et al. “Flows and Decompositions of Games: Harmonic and Potential Games.” Mathematics of Operations Research 36.3 (2011): 474–503.
Version
Author's final manuscript
Abstract
In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic, and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the well-known potential games. We refer to the second class of games as harmonic games, and demonstrate that this new class has interesting properties which contrast with properties of potential games. Exploiting the decomposition framework, we obtain explicit expressions for the projections of games onto the subspaces of potential and harmonic games. This enables an extension of the equilibrium properties of potential and harmonic games to “nearby” games.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1287/moor.1110.0500
