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Viscosity Solutions for Bilevel Problems with Nash Equilibrium Constraints

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A regularization method for bilevel problems with lower level defined by Nash equilibria is considered and a concept of \viscosity solution" associated to such a regularization is introduced. Sufficient conditions for the existence of viscosity solutions are given and applications to optimistic and pessimistic bilevel optimization problems are presented.

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  • M. Beatrice Lignola & Jacqueline Morgan, 2014. "Viscosity Solutions for Bilevel Problems with Nash Equilibrium Constraints," CSEF Working Papers 367, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 02 Oct 2014.
    • Handle: RePEc:sef:csefwp:367
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    Cited by:

    1. M. Beatrice Lignola & Jacqueline Morgan, 2015. "MinSup Problems with Quasi-equilibrium Constraints and Viscosity Solutions," CSEF Working Papers 393, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    2. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2019. "Subgame Perfect Nash Equilibrium: A Learning Approach via Costs to Move," Dynamic Games and Applications, Springer, vol. 9(2), pages 416-432, June.
    3. M. Beatrice Lignola & Jacqueline Morgan, 2017. "Inner Regularizations and Viscosity Solutions for Pessimistic Bilevel Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 183-202, April.

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