Geodesic
On search of Nash equilibrium in~quasiconcave~quadratic games
Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 1, pp. 67-84

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The Nash equilibrium problem with nonconcave quadratic payoff functions is considered. We analyze conditions which provide quasiconcavity of payoff functions in their own variables on the respective strategy sets and, consequently, guarantee existence of an equilibrium point. One of such conditions is that the matrix of every payoff function has exactly one positive eigenvalue; this condition is viewed as a basic assumption in the paper. We propose an algorithm that either converges to an equilibrium point or declares that the game has no equilibria. It is shown that some stages of the algorithm are noticeably simplified for quasiconcave games. The algorithm is tested on small-scale instances. Illustr. 1, bibliogr. 30.
Keywords: Nash equilibrium, quasiconcave functions, global optimization. 
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     title = {On search of {Nash} equilibrium in~quasiconcave~quadratic games},
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I. M. Minarchenko. On search of Nash equilibrium in~quasiconcave~quadratic games. Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 1, pp. 67-84. http://geodesic.mathdoc.fr/item/DA_2023_30_1_a3/