ABSTRACT
In almost every journal on game theory or operations research one comes across papers dealing with the Nash equilibrium situation. Why is this solution of non cooperation game used so intensively? For the answer see Section 2.1. There the positive and negative aspects of this solution are revealed. In order to overcome some of the negative aspects such as improvability and the lack of intrinic stability, the objection and counter-objection equilibrium is used. Therefore, in Section 2.2 for the “static” game (without uncertainty) the possible notions of the objection and counter-objection equilibrium and active equilibrium are presented and their properties are investigated. Theorem 2.2.2 is the main result here which establishes the existence of the objection and counter-objection equilibrium for the class of games. Though, as is known, “comparaison n’est pas raison”*, in Section 2.3 a detailed comparison of the Nash equilibrium situation with the objection and counter-objection equilibrium is carried out. The advantages of the latter are demonstrated by the example of the model of a market with two producers. The rest of the chapter deals with differential games of two persons under uncertainty,
where the notion of solution is based on the combination of the objection and counter-objection concepts with the vector maximin and the vector saddle point (see Zhukovskiy and Chikriy [1]). Thus, in Section 2.4 for the differential linear quadratic positional game of two persons under uncertainty a chain of solutions is defined which are based on the combination of the objection and counter-objection concepts and the vector saddle point concept, and the properties of such solutions are investigated.
