Dec 6, 2022
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Pseudo-games are a natural and well-known generalization of normal-form games, in which the actions taken by each player affect not only the other players’ payoffs, as in games, but also the other players’ strategy sets. The solution concept par excellence for pseudo-games is the generalized Nash equilibrium (GNE), i.e., a strategy profile at which each player’s strategy is feasible and no player can improve their payoffs by unilaterally deviating to another strategy in the strategy set determined by the other players’ strategies. The computation of GNE in pseudo-games has long been a problem of interest, due to applications in a wide variety of fields, from environmental protection to logistics to telecommunications. Although the computation of GNE is PPAD-hard in general, it is still of interest to try to compute them in restricted classes of pseudo-games. The literature thus far has focused on asymptotic convergence of search procedures; there are very few, if any, results on the computational complexity of GNE. In this paper, we develop fast exploitability-minimization methods that compute exact or approximate GNE in pseudo-games with jointly convex constraints. We derive convergence guarantees for our methods, and we demonstrate their superiority in experiments over a baseline algorithm for a variety of benchmark pseudo-games.Pseudo-games are a natural and well-known generalization of normal-form games, in which the actions taken by each player affect not only the other players’ payoffs, as in games, but also the other players’ strategy sets. The solution concept par excellence for pseudo-games is the generalized Nash equilibrium (GNE), i.e., a strategy profile at which each player’s strategy is feasible and no player can improve their payoffs by unilaterally deviating to another strategy in the strategy set determin…
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