A branch-and-prune algorithm for discrete Nash equilibrium problems

We present a branch-and-prune procedure for discrete Nash equilibrium problems with a convex description of each player's strategy set. The derived pruning criterion does not require player convexity, but only strict convexity of some player's objective function in a single variable. If sa...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 86; no. 2; pp. 491 - 519
Main Authors: Schwarze, Stefan, Stein, Oliver
Format: Journal Article
Language:English
Published: New York, NY Springer US 01.11.2023
Springer Nature B.V
Subjects:
Algorithms
Branch and bound
Branch and prune
Convex and Discrete Geometry
Convexity
Discrete game
Equilibrium
Game theory
Integer programming
Management Science
Mathematical analysis
Mathematics
Mathematics and Statistics
Nash equilibrium problem
Operations Research
Operations Research/Decision Theory
Optimization
Statistics
Variables
Nash equilibrium problem
Branch and prune
Discrete game
Branch and bound
ISSN:1573-2894, 0926-6003, 1573-2894
Online Access:Get full text
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Summary:We present a branch-and-prune procedure for discrete Nash equilibrium problems with a convex description of each player's strategy set. The derived pruning criterion does not require player convexity, but only strict convexity of some player's objective function in a single variable. If satisfied, it prunes choices for this variable by stating activity of certain constraints. This results in a synchronous branching and pruning method. An algorithmic implementation and numerical tests are presented for randomly generated instances with convex polyhedral strategy sets and convex quadratic as well as non-convex quadratic objective functions.
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ISSN:1573-2894
0926-6003
1573-2894
DOI:10.1007/s10589-023-00500-4