Values and Strategies for Infinite Time Linear Quadratic Games

Authors

Eleftherios F. Mageirou

Year

1976

Journal Paper

Algorithm

Infinite-Horizon LQ Game Riccati Solution

Source

IEEE Transactions on Automatic Control

Identifiers

DOI 10.1109/TAC.1976.1101291

Abstract¶

For a class of infinite time linear quadratic games it is shown that an appropriate solution of an algebraic Riccati type equation determines the value of the game but not necessarily any equilibrium strategies. In the case of nonexistence of equilibrium strategies, ε-optimal strategies are constructed through the solutions of a differential Riccati equation.

Summary¶

Mageirou studies infinite-time linear quadratic games and shows how algebraic Riccati-type equations can determine the value even when equilibrium strategies may not exist. The paper also constructs epsilon-optimal strategies through differential Riccati equations, clarifying the gap between game value and attainable equilibria.