Robust Nash Equilibrium in multi-model LQ differential games: analysis and extraproximal numerical procedure

2007 ◽  
Vol 28 (2) ◽  
pp. 117-141 ◽  
Author(s):  
Manuel Jiménez-Lizárraga ◽  
Alex Poznyak
Keyword(s):  
Nash Equilibrium ◽  
Differential Games ◽  
Numerical Procedure

scholarly journals A differential game of N persons in which there is Pareto equilibrium of objections and counterobjections and no Nash equilibrium

2021 ◽  
Vol 57 ◽  
pp. 104-127
Author(s):  
V.I. Zhukovskii ◽  
Yu.S. Mukhina ◽  
V.E. Romanova
Keyword(s):  
Nash Equilibrium ◽  
Differential Games ◽  
Explicit Form ◽  
Differential Game ◽  
Linear Quadratic ◽  
Equilibrium Situation ◽  
Pareto Equilibrium ◽  
Noncooperative Differential Games

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.

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