Doubly invariant equilibria of linear discrete-time games
It is an interesting paper in studing the equilibrium of the class of two persons linear dynamic games in discrete time, in which the perfect state information, feedback strategies and a performance criterion are specified not in terms of payoffs but by two sets in the state space one for each player, each player tries to keep the state in the region of the state space independently of the action of the rival player. The authors define a doubly invariant DI equilibrium. It is obtained when these sets exhibit a double invariance property. The notion of a DI equilibrium links with the Nash equilibrium concept in game theory and with the viability concept in control. The paper gives in 5 sections existence conditions, criteria and algorithms for the determination of DI equilibria of linear dynamic games in discrete time. Two examples illustrate the results are given. I think that it will be useful for the readers to consult the paper ``On discrete dynamical systems associated to games'' by \textit{E. Ahmed} and \textit{A. S. Hegazi} in Adv. Complex Syst. 423-430 (1999).
scientific article; zbMATH DE number 1797134