Exact Penalization of Generalized Nash Equilibrium Problems

Qin Ba () and Jong-Shi Pang ()
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Qin Ba: Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90089
Jong-Shi Pang: Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90089

Operations Research, 2022, vol. 70, issue 3, 1448-1464

Abstract: This paper presents an exact penalization theory of the generalized Nash equilibrium problem (GNEP) that has its origin from the renowned Arrow–Debreu general economic equilibrium model. Whereas the latter model is the foundation of much of mathematical economics, the GNEP provides a mathematical model of multiagent noncooperative competition that has found many contemporary applications in diverse engineering domains. The most salient feature of the GNEP that distinguishes it from a standard noncooperative (Nash) game is that each player’s optimization problem contains constraints that couple all players’ decision variables. Extending results for stand-alone optimization problems, the penalization theory aims to convert the GNEP into a game of the standard kind without the coupled constraints, which is known to be more readily amenable to solution methods and analysis. Starting with an illustrative example to motivate the development, this paper focuses on two kinds of coupled constraints, shared (i.e., common) and finitely representable. Constraint residual functions and the associated error bound theory play an important role throughout the development.

Keywords: Special Issue: Mathematical Models of Individual and Group Decision Making in Operations Research (in honor of Kenneth Arrow); generalized Nash games; exact penalization; error bounds; constraint qualifications (search for similar items in EconPapers)
Date: 2022
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