DOUBLE INVARIANCE: A NEW EQUILIBRIUM CONCEPT FOR TWO-PERSON DYNAMIC GAMES

Doubly Invariant Equilibrium is introduced as an alternative concept to Nash equilibrium in dynamic games doing away with the notion of a payoff function. A subset of the state space enjoys the invariance property if the state can be kept in it by one player, regardless of the action of the opponent. A doubly invariant equilibrium obtains when each player can make his own subset invariant. Relationships to Nash equilibrium and viability theory are discussed and a necessary and sufficient condition for the existence of a doubly invariant equilibrium is given for the class of linear discrete-time games with polyhedral constraints on the state and strategy spaces.