Decomposable penalty method for generalized game problems with joint constraints. (2nd December 2021)

• Record Type: Journal Article
• Authors: Konnov, I. V.
• Is Part Of: Optimization. Volume 70:Number 12(2021)
• Page Start: 2655
• Page End: 2673
• Publication Date: 2021-12-02
• Subjects: Non-cooperative games -- joint constraints -- generalized equilibrium points -- decomposable penalty method -- variational inequality; 91A10 -- 91A40 -- 90C33; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1793153
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We consider an extension of a non-cooperative game problem where players have joint binding constraints. In this case, justification of a generalized equilibrium point needs a reasonable mechanism for attaining this state. We combine a penalty method and shares allocation of right-hand sides, which replaces the initial problem with a sequence of the usual Nash equilibrium problems together with an upper level variational inequality as a master problem. In order to obtain a completely decomposable problem at the lower level, we apply its additional equivalent transformation. Convergence of solutions of these auxiliary penalized problems to a solution of the initial game problem is established under weak coercivity conditions.