Minimax Theory and its Applications 09 (2024), No. 1, 001--018
Copyright Heldermann Verlag 2024
Semi-Infinite Models for Equilibrium Selection
Maren Beck
Institute for Operations Research (IOR), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
maren.beck@kit.edu
Oliver Stein
Institute for Operations Research (IOR), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
stein@kit.edu
In their seminal work "A General Theory of Equilibrium Selection in Games" [The MIT Press, Cambridge 1988] J. C. Harsanyi and R. Selten introduce the notion of payoff dominance to explain how players select some solution of a Nash equilibrium problem from a set of nonunique equilibria. We formulate this concept for generalized Nash equilibrium problems, relax payoff dominance to the more widely applicable requirement of payoff nondominatedness, and show how different characterizations of generalized Nash equilibria yield different semi-infinite optimization problems for the computation of payoff nondominated equilibria. Since all these problems violate a standard constraint qualification, we also formulate regularized versions of the optimization problems. Under additional assumptions we state a nonlinear cutting algorithm and provide numerical results for a multi-agent portfolio optimization problem.
Keywords: Equilibrium selection, Nash game, payoff dominance, semi-infinite optimization, cutting algorithm.
MSC: 90C33, 90C34, 90C30, 65K15.
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