Existence of Quasi-Nash Equilibrium in Game with Discontinuous Payoff Functions

Inese Bula

doi:10.1007/978-3-031-73997-2_17

Existence of Quasi-Nash Equilibrium in Game with Discontinuous Payoff Functions

Inese Bula^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › Research › peer-review

Abstract

In the paper a convex game with discontinuous payoff functions is considered. This paper introduces the concept of quasi-Nash equilibrium, which allows us to analyze games with discontinuous payoff functions by approximating them with continuous and concave functions. We show that if the approximation is close enough, then the quasi-Nash equilibrium is close to the true Nash equilibrium (if it exists).

Original language	English
Title of host publication	Information Processing and Management of Uncertainty in Knowledge-Based Systems - 20th International Conference, IPMU 2024, Proceedings
Editors	Marie-Jeanne Lesot, Bernadette Bouchon-Meunier, Susana Vieira, Marek Z. Reformat, João Paulo Carvalho, Fernando Batista, Ronald R. Yager
Place of Publication	Cham
Publisher	Springer
Pages	195-204
ISBN (Print)	978-303173996-5
DOIs	https://doi.org/10.1007/978-3-031-73997-2_17
Publication status	Published - 2025

Publication series

Name	Lecture Notes in Networks and Systems
Volume	1176 LNNS
ISSN (Print)	2367-3370
ISSN (Electronic)	2367-3389

OECD Field of Science

1.1 Mathematics

Keywords

Convex game
Discontinuity of payoff function
Nash equilibrium
Quasi-equilibrium

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10.1007/978-3-031-73997-2_17

Cite this

Bula, I. (2025). Existence of Quasi-Nash Equilibrium in Game with Discontinuous Payoff Functions. In M.-J. Lesot, B. Bouchon-Meunier, S. Vieira, M. Z. Reformat, J. P. Carvalho, F. Batista, & R. R. Yager (Eds.), Information Processing and Management of Uncertainty in Knowledge-Based Systems - 20th International Conference, IPMU 2024, Proceedings (pp. 195-204). (Lecture Notes in Networks and Systems; Vol. 1176 LNNS). Springer. https://doi.org/10.1007/978-3-031-73997-2_17

Bula, Inese. / Existence of Quasi-Nash Equilibrium in Game with Discontinuous Payoff Functions. Information Processing and Management of Uncertainty in Knowledge-Based Systems - 20th International Conference, IPMU 2024, Proceedings. editor / Marie-Jeanne Lesot ; Bernadette Bouchon-Meunier ; Susana Vieira ; Marek Z. Reformat ; João Paulo Carvalho ; Fernando Batista ; Ronald R. Yager. Cham : Springer, 2025. pp. 195-204 (Lecture Notes in Networks and Systems).

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abstract = "In the paper a convex game with discontinuous payoff functions is considered. This paper introduces the concept of quasi-Nash equilibrium, which allows us to analyze games with discontinuous payoff functions by approximating them with continuous and concave functions. We show that if the approximation is close enough, then the quasi-Nash equilibrium is close to the true Nash equilibrium (if it exists).",

keywords = "Convex game, Discontinuity of payoff function, Nash equilibrium, Quasi-equilibrium",

author = "Inese Bula",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.",

year = "2025",

doi = "10.1007/978-3-031-73997-2\_17",

language = "English",

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editor = "Marie-Jeanne Lesot and Bernadette Bouchon-Meunier and Susana Vieira and Reformat, \{Marek Z.\} and Carvalho, \{Jo{\~a}o Paulo\} and Fernando Batista and Yager, \{Ronald R.\}",

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Bula, I 2025, Existence of Quasi-Nash Equilibrium in Game with Discontinuous Payoff Functions. in M-J Lesot, B Bouchon-Meunier, S Vieira, MZ Reformat, JP Carvalho, F Batista & RR Yager (eds), Information Processing and Management of Uncertainty in Knowledge-Based Systems - 20th International Conference, IPMU 2024, Proceedings. Lecture Notes in Networks and Systems, vol. 1176 LNNS, Springer, Cham, pp. 195-204. https://doi.org/10.1007/978-3-031-73997-2_17

Existence of Quasi-Nash Equilibrium in Game with Discontinuous Payoff Functions. / Bula, Inese.
Information Processing and Management of Uncertainty in Knowledge-Based Systems - 20th International Conference, IPMU 2024, Proceedings. ed. / Marie-Jeanne Lesot; Bernadette Bouchon-Meunier; Susana Vieira; Marek Z. Reformat; João Paulo Carvalho; Fernando Batista; Ronald R. Yager. Cham: Springer, 2025. p. 195-204 (Lecture Notes in Networks and Systems; Vol. 1176 LNNS).

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › Research › peer-review

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T1 - Existence of Quasi-Nash Equilibrium in Game with Discontinuous Payoff Functions

AU - Bula, Inese

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

PY - 2025

Y1 - 2025

N2 - In the paper a convex game with discontinuous payoff functions is considered. This paper introduces the concept of quasi-Nash equilibrium, which allows us to analyze games with discontinuous payoff functions by approximating them with continuous and concave functions. We show that if the approximation is close enough, then the quasi-Nash equilibrium is close to the true Nash equilibrium (if it exists).

AB - In the paper a convex game with discontinuous payoff functions is considered. This paper introduces the concept of quasi-Nash equilibrium, which allows us to analyze games with discontinuous payoff functions by approximating them with continuous and concave functions. We show that if the approximation is close enough, then the quasi-Nash equilibrium is close to the true Nash equilibrium (if it exists).

KW - Convex game

KW - Discontinuity of payoff function

KW - Nash equilibrium

KW - Quasi-equilibrium

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A2 - Lesot, Marie-Jeanne

A2 - Bouchon-Meunier, Bernadette

A2 - Vieira, Susana

A2 - Reformat, Marek Z.

A2 - Carvalho, João Paulo

A2 - Batista, Fernando

A2 - Yager, Ronald R.

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Bula I. Existence of Quasi-Nash Equilibrium in Game with Discontinuous Payoff Functions. In Lesot MJ, Bouchon-Meunier B, Vieira S, Reformat MZ, Carvalho JP, Batista F, Yager RR, editors, Information Processing and Management of Uncertainty in Knowledge-Based Systems - 20th International Conference, IPMU 2024, Proceedings. Cham: Springer. 2025. p. 195-204. (Lecture Notes in Networks and Systems). doi: 10.1007/978-3-031-73997-2_17

Existence of Quasi-Nash Equilibrium in Game with Discontinuous Payoff Functions

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