On solving generalized Nash equilibrium problems via optimization |
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Authors: | Barbara Panicucci Massimo Pappalardo Mauro Passacantando |
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Institution: | (1) Department of Applied Mathematics, University of Pisa, via Buonarroti 1/c, 56127 Pisa, Italy |
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Abstract: | This paper deals with the generalized Nash equilibrium problem (GNEP), i.e. a noncooperative game in which the strategy set
of each player, as well as his payoff function, depends on the strategies of all players. We consider an equivalent optimization
reformulation of GNEP using a regularized Nikaido–Isoda function so that solutions of GNEP coincide with global minima of
the optimization problem. We then propose a derivative-free descent type method with inexact line search to solve the equivalent
optimization problem and we prove that our algorithm is globally convergent. The convergence analysis is not based on conditions
guaranteeing that every stationary point of the optimization problem is a solution of GNEP. Finally, we present the performance
of our algorithm on some examples. |
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Keywords: | Generalized Nash equilibrium problem Nikaido– Isoda function Descent method |
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