Open AccessA differential game of N persons in which there is Pareto equilibrium of objections and counterobjections and no Nash equilibrium
Author(s) -
В.И. Жуковский,
Yu.S. Mukhina,
V.E. Romanova
Publication year - 2021
Language(s) - English
DOI - 10.35634/2226-3594-2021-57-04
Subject(s) - nash equilibrium , epsilon equilibrium , mathematical economics , equilibrium selection , correlated equilibrium , symmetric equilibrium , best response , differential game , risk dominance , mathematics , pareto principle , solution concept , differential (mechanical device) , repeated game , game theory , economics , mathematical optimization , physics , thermodynamics
A linear-quadratic positional differential game of N persons is considered. The solution of a game in the form of Nash equilibrium has become widespread in the theory of noncooperative differential games. However, Nash equilibrium can be internally and externally unstable, which is a negative in its practical use. The consequences of such instability could be avoided by using Pareto maximality in a Nash equilibrium situation. But such a coincidence is rather an exotic phenomenon (at least we are aware of only three cases of such coincidence). For this reason, it is proposed to consider the equilibrium of objections and counterobjections. This article establishes the coefficient criteria under which in a differential positional linear-quadratic game of N persons there is Pareto equilibrium of objections and counterobjections and at the same time no Nash equilibrium situation; an explicit form of the solution of the game is obtained.