Consistent Conjectural Variations Equilibria: Characterization & Stability for a Class of Continuous Games

Consistent Conjectural Variations Equilibria: Characterization & Stability for a Class of Continuous Games

Leveraging tools from the study of linear fractional transformations and algebraic Riccati equations, a local characterization of consistent conjectural variations equilibrium is given for two player games on continuous action spaces with costs approximated by quadratic functions. A discrete time dy...

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Veröffentlicht in:IEEE control systems letters 2023-01, p.1-1
Hauptverfasser: Calderone, Daniel J., Chasnov, Benjamin J., Burden, Samuel A., Ratliff, Lillian J.
Format: Artikel
Sprache:eng
Schlagworte:
Computational modeling
Costs
Game theory
Games
Linear systems
Mathematical models
Nash equilibrium
Optimization
Riccati equations
Stability criteria
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Zusammenfassung:Leveraging tools from the study of linear fractional transformations and algebraic Riccati equations, a local characterization of consistent conjectural variations equilibrium is given for two player games on continuous action spaces with costs approximated by quadratic functions. A discrete time dynamical system in the space of conjectures is derived; a solution method for computing fixed points of these dynamics (equilibria) is given via solving an eigenvalue problem; local stability properties of the dynamics around the equilibria are characterized; and conditions are given that guarantee a unique stable equilibrium.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2023.3289473