In their seminal work `A General Theory of Equilibrium Selection in Games’ (The MIT Press, 1988) Harsanyi and 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.
Citation
Minimax Theory and its Applications, Vol. 9 (2024), 1-18.