Interactions Between Bilevel Optimization and Nash Games

Lorenzo Lampariello (), Simone Sagratella (), Vladimir Shikhman () and Oliver Stein ()
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Lorenzo Lampariello: Roma Tre University
Simone Sagratella: Sapienza University of Rome
Vladimir Shikhman: Chemnitz Technical University
Oliver Stein: Karlsruhe Institute of Technology (KIT)

Chapter Chapter 1 in Bilevel Optimization, 2020, pp 3-26 from Springer

Abstract: Abstract We aim at building a bridge between bilevel programming and generalized Nash equilibrium problems. First, we present two Nash games that turn out to be linked to the (approximated) optimistic version of the bilevel problem. Specifically, on the one hand we establish relations between the equilibrium set of a Nash game and global optima of the (approximated) optimistic bilevel problem. On the other hand, correspondences between equilibria of another Nash game and stationary points of the (approximated) optimistic bilevel problem are obtained. Then, building on these ideas, we also propose different Nash-like models that are related to the (approximated) pessimistic version of the bilevel problem. This analysis, being of independent theoretical interest, leads also to algorithmic developments. Finally, we discuss the intrinsic complexity characterizing both the optimistic bilevel and the Nash game models.

Keywords: Optimistic bilevel problem; Pessimistic bilevel problem; Generalized Nash equilibrium problem; Approximation techniques; Constraint qualifications; Degeneracies (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-52119-6_1

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DOI: 10.1007/978-3-030-52119-6_1

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