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Interactions Between Bilevel Optimization and Nash Games

In: Bilevel Optimization

Author

Listed:
  • Lorenzo Lampariello

    (Roma Tre University)

  • Simone Sagratella

    (Sapienza University of Rome)

  • Vladimir Shikhman

    (Chemnitz Technical University)

  • Oliver Stein

    (Karlsruhe Institute of Technology (KIT))

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.

Suggested Citation

  • Lorenzo Lampariello & Simone Sagratella & Vladimir Shikhman & Oliver Stein, 2020. "Interactions Between Bilevel Optimization and Nash Games," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 3-26, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-52119-6_1
    DOI: 10.1007/978-3-030-52119-6_1
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