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4126. Discontinuous Game and Nash Equilibrium

Invited abstract in session TC-36: Game Theory, Solutions and Structures VII, stream Game Theory, Solutions and Structures.

Tuesday, 12:30-14:00
Room: 32 (building: 306)

Authors (first author is the speaker)

1. Inese Bula
Department of Mathematics, University of Latvia, and Institute of Mathematics and Computer Science of University of Latvia

Abstract

We consider convex game with discontinuous payoff functions. A good overview of some key results in the literature on the existence of Nash equilibria in discontinuous games is given in [3].

We will look at the discontinuity in a certain form: we will look at w-continuous functions, which means that the discontinuity measure is not greater than the specified positive number w. Functions of this type can be approximated by continuous functions ([1,2]). If the approximation is also a concave or quasi-concave function, then a Nash equilibrium exists in the game. This equilibrium can be thought of as a quasi-Nash equilibrium with respect to the discontinuous payoff function of the original game. We would prefer that in the case where a Nash equilibrium exists in the original game, it is also found in a quasi-sense. If no equilibrium exists in the original game, then one would want the quasi-Nash equilibrium to provide the best possible solution. We will look at examples and conditions under which this is possible.

[1] Bula, I. On the stability of Bohl-Brouwer-Schauder theorem. Nonlinear Analysis, Theory, Methods, and Applications, V26, 1859—1868, 1996.
[2] Bula, I. Discontinuous functions in Gale economic model. Mathematical Modelling and Analysis, V.8(2), 93—102, 2003.
[3] Reny, P. J. Nash Equilibrium in Discontinuous Games. Annual Review of Economics, V.12, 439—470, 2020.

Keywords

Status: accepted

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