A circular arrangement of equilibria and a procedure for finding the strongest of them (Q2461823)

The author considers a generalization of the classical \(n\)-person noncooperative games where not all the multistrategies of the players are admissible. For such games, he defines several new kinds of equilibrium, called \(A\)-equilibrium, complete equilibrium; strongly dependent equilibrium; \(C\)-equilibrium and \(D\)-equilibrium. These equilibria are closely related to each other and to Nash equilibria. The main result of the paper describes the circular diagram defining hierarchical relationships between the introduced equilibria. With the help of this diagram, a method for finding the strongest equilibrium is suggested. The possibilities of the circular diagram are illustrated in three interesting examples of constrained modifications for a bimatrix game, three-person finite game, and for a differential game, respectively.