Generalized Riccati Equations in Dynamic Games

Abstract

The discrete- and continuous-time Riccati equations, which play a prominent role in linear-quadratic control and filtering theory (as discussed extensively in other chapters of this book), appear also in discrete- and continuous-time dynamic games, albeit in more general forms. Both the existence and the characterization of nonco-operative equilibria in zero-sum and nonzero-sum linear-quadratic dynamic games, under saddle-point, Nash and Stackelberg equilibrium concepts, involve the solutions of these generalized matrix Riccati (differential or algebraic) equations.