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Sufficient conditions to compute any solution of a quasivariational inequality via a variational inequality

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Abstract

We define the concept of reproducible map and show that, whenever the constraint map defining the quasivariational inequality (QVI) is reproducible then one can characterize the whole solution set of the QVI as a union of solution sets of some variational inequalities (VI). By exploiting this property, we give sufficient conditions to compute any solution of a generalized Nash equilibrium problem (GNEP) by solving a suitable VI. Finally, we define the class of pseudo-Nash equilibrium problems, which are (not necessarily convex) GNEPs whose solutions can be computed by solving suitable Nash equilibrium problems.

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Authors and Affiliations

  1. PROMES UPR CNRS 8521, University of Perpignan, Perpignan, France

    Didier Aussel

  2. Department of Computer, Control and Management Engineering, Sapienza University of Rome, via Ariosto 25, 00185, Rome, Italy

    Simone Sagratella

Authors
  1. Didier Aussel
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  2. Simone Sagratella
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Corresponding author

Correspondence to Didier Aussel.

Additional information

The first author wants to sincerely thank Jen-Chih Yao and the National Sun-Yat-Tsen University of Kaohsiung, Taiwan for its hospitality. Indeed a part of this research has been done during the visit of this author in Kaohsiung.

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Aussel, D., Sagratella, S. Sufficient conditions to compute any solution of a quasivariational inequality via a variational inequality. Math Meth Oper Res 85, 3–18 (2017). https://doi.org/10.1007/s00186-016-0565-x

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  • DOI: https://doi.org/10.1007/s00186-016-0565-x

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