Monotone Operator Methods for Nash Equilibria in Non-potential Games

Monotone Operator Methods for Nash Equilibria in Non-potential Games

We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve such problems and establish their convergence. Applications to generalized Nash equilibria, zero-sum games, and cyclic...

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Bibliographische Detailangaben
Hauptverfasser: Combettes, Patrick, Briceño-Arias, Luis
Format: Buchkapitel
Sprache:eng
Schlagworte:
47H05
49M27
Algorithms
Functional analysis & transforms
Mathematics
Monotone operator
Nash equilibrium
Number theory
Operational research
Optimization and Control
Potential game
Primary 91A05
Proximal algorithm
Secondary 90C25
Splitting method
Zero-sum game
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Beschreibung
Zusammenfassung:We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve such problems and establish their convergence. Applications to generalized Nash equilibria, zero-sum games, and cyclic proximation problems are demonstrated.
ISSN:2194-1009
2194-1017
DOI:10.1007/978-1-4614-7621-4_9