Double invariance: A new equilibrium concept for two-person dynamic games (Q2701833)

A new concept of equilibrium in terms of invariance of sets of states is proposed, where payoff functions are replaced by subsets of the state space. Informally speaking, a set of states is called invariant if the state can be kept in it by one player regardless of the action of the opponent. A double invariance obtains if each player's subset is invariant. Necessary and sufficient conditions for the existence of a doubly invariant equilibrium are given for linear discrete-time games with polyhedral constraints on the state and strategy spaces. Also the relationships to Nash equilibrium and viability theory are discussed.