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Consistent Conjectural Variations Equilibrium: Characterization & Stability for a Class of Continuous Games
Daniel J. Calderone, Benjamin J. Chasnov, Samuel A. Burden, Lillian J. Ratliff
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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, local stability properties of the dynamics around the equilibria are characterized, and conditions are given that guarantee a unique stable equilibrium.
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