Geodesic
A differential game of $n$ persons in which there is Pareto equilibrium of objections and counterobjections and no Nash equilibrium
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 57 (2021), pp. 104-127

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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.
Keywords: differential noncooperative games, Nash equilibrium situation, equilibrium of objections and counterobjections, Pareto efficiency. 
@article{IIMI_2021_57_a3,
     author = {V. I. Zhukovskii and Yu. S. Mukhina and V. E. Romanova},
     title = {A differential game of $n$ persons in which there is {Pareto} equilibrium of objections and counterobjections and no {Nash} equilibrium},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {104--127},
     publisher = {mathdoc},
     volume = {57},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2021_57_a3/}
}
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V. I. Zhukovskii; Yu. S. Mukhina; V. E. Romanova. A differential game of $n$ persons in which there is Pareto equilibrium of objections and counterobjections and no Nash equilibrium. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 57 (2021), pp. 104-127. http://geodesic.mathdoc.fr/item/IIMI_2021_57_a3/