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

Stefan Schwarze () and Oliver Stein ()
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Stefan Schwarze: Institute for Operations Research (IOR), Karlsruhe Institute of Technology (KIT)
Oliver Stein: Institute for Operations Research (IOR), Karlsruhe Institute of Technology (KIT)

Computational Optimization and Applications, 2023, vol. 86, issue 2, No 3, 519 pages

Abstract: Abstract 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.

Keywords: Nash equilibrium problem; Discrete game; Branch and bound; Branch and prune (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-023-00500-4

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