Optimization approach to Berge equilibrium for bimatrix game

Enkhbat, Rentsen; Sukhee, Batbileg

doi:10.1007/s11590-020-01688-8

Cited by 8 publications

(3 citation statements)

References 13 publications

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“…Existence theorems for Nash and Berge equilibria were studied and proven in [26] and [14,15]. In [12] and [15] we formulated and proved the following series of theorems : Theorem 2.1.…”

Section: Methodsmentioning

confidence: 98%

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Comparison of Nash and Berge Equilibrium’s in Bimatrix Game

Sagaarinqin,

Sukhee

2023

J. Inst. Math. Digit. Technol.

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Game theory has numerous applications in applied mathematics, economics, and decision theory. There are several books and articles that deal with Nash and Berge equilibriums. To our knowledge, there are no comparisons or conclusive results related to the optimal decision-making between Nash and Berge equilibriums. We provide numerical experiments for both equilibria. Биматрицан Тоглоом Дахь Нэш, Бержийн Тэнцвэрийн Харьцуулалт Хураангуй: Тоглоомын онол нь эдийн засаг, шийдвэр гаргалтын онол, бизнес, улс төр, хэрэглээний математик зэрэг салбарт хэрэглээ ихтэй. Бержийн тэнцвэрийн талаар хэд хэдэн судалгаа, зохиолууд байдаг боловч бидний одоогийн судалснаар түүний Бержийн тэнцвэрийн оновчтой шийдийн хувьд Нэшийн тэнцвэртэй харьцуулсан судалгааны ажил байхгүй байна. Бидний ажил нь энэ харьцуулалтыг хийж Берж ба Нэшийн тэнцвэрүүдийн хувьд тоглогчдын хожлын утгын хувьд харьцуулсан дүгнэлт гаргах зорилготой. Тоон туршилт хийж үр дүнг гаргасан.Түлхүүр үгс: Бержийн ба Нэшийн тэнцвэр, локал ба глобал оновчтой шийд, глобал оновчтойнөхцөл

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“…Existence theorems for Nash and Berge equilibria were studied and proven in [26] and [14,15]. In [12] and [15] we formulated and proved the following series of theorems : Theorem 2.1.…”

Section: Methodsmentioning

confidence: 98%

“…Existence theorems for Nash and Berge equilibria were studied and proven in [26] and [14,15]. In [12] and [15] we formulated and proved the following series of theorems : Theorem 2.1. [12] A pair strategy (x * , y * ) ∈ X × Y is a Nash equilibrium if and only if F (x, y, p, q) = ⟨x T (A + B)y⟩ − p − q (2.5)…”

Section: Methodsmentioning

confidence: 98%

Comparison of Nash and Berge Equilibrium’s in Bimatrix Game

Sagaarinqin,

Sukhee

2023

J. Inst. Math. Digit. Technol.

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“…As an important tool in the field of optimization, GAVE is widely used to solve problems in diverse fields, including nonnegative constrained least squares problems, quadratic programming, complementarity problem, bimatrix games (e.g. [14,16,27,46]). In this paper, we prove that GAVE is equivalent to a smooth nonspareable linearly constraint convex-concave minimax problem as follows: Moreover, we also focus on the well-known linear regression problems with joint linearly constraints and strongly-convex-strongly-concave quadratic objective functions.…”

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confidence: 99%

Optimality Conditions and Numerical Algorithms for A Class of Linearly Constrained Minimax Optimization Problems

Dai¹,

Wang²,

Zhang³

2022

Preprint

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It is well known that there have been many numerical algorithms for solving nonsmooth minimax problems, numerical algorithms for nonsmooth minimax problems with joint linear constraints are very rare. This paper aims to discuss optimality conditions and develop practical numerical algorithms for minimax problems with joint linear constraints. First of all, we use the properties of proximal mapping and KKT system to establish optimality conditions. Secondly, we propose a framework of alternating coordinate algorithm for the minimax problem and analyze its convergence properties. Thirdly, we develop a proximal gradient multi-step ascent decent method (PGmsAD) as a numerical algorithm and demonstrate that the method can find an -stationary point for this kind of nonsmooth nonconvex-nonconcave problem in O −2 log −1 iterations. Finally, we apply PGmsAD to generalized absolute value equations, generalized linear projection equations and linear regression problems and report the efficiency of PGmsAD on large-scale optimization.

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