Circular structures of conflict equilibria in dynamical systems

Extending the theory of conflict equilibria

“…On the one hand, the paper proposes new concepts of equilibria, never considered before, and on the other hand, it gives a complete presentation of hierarchical orders of well-known base conflict equilibria [1,2]. 225 1060-0396/07/4302-0225…”

“…It takes into account competitive relations between any coalitions of the participants and is called in [1, p. 118] an extended base system. The experience of solving conflict problems shows that the need for such "coalition" equilibria arises quite often, when it is impossible (even using an iterative scheme to generate new equilibria, formulated in Theorem 1.1.9 in [1], and applying nonsymmetric base equilibria [1, p. 34-36]) to select the strongest equilibrium among several most strong equilibria indistinguishable within the framework of the base system of equilibria.Though the idea of forming "coalition" equilibria is demonstrated in [1, p. 118] by formulating an A¢-equilibrium, it is obviously insufficient, even for an expert, to use this idea to formulate correctly the whole set of "coalition" equilibria.The present paper proposes a statement of "coalition" equilibria and uses a conflict problem with three participants (which is considered as a noncooperative game on the one hand and as a cooperative game on the other hand) as an example to show that a final decision that is quite suitable for all the participants and fully satisfies practical requirements can be obtained only in aggregate with the new equilibria being proposed.On the one hand, the paper proposes new concepts of equilibria, never considered before, and on the other hand, it gives a complete presentation of hierarchical orders of well-known base conflict equilibria [1,2]. 225 1060-0396/07/4302-0225…”