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. © 2016, Springer-Verlag Berlin Heidelberg.

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

SAGRATELLA, SIMONE
2017-01-01

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. © 2016, Springer-Verlag Berlin Heidelberg.
2017
Generalized Nash equilibrium problem
Quasiconvexity
Quasivariational inequality
Reproducible set-valued map
Software
Mathematics (all)
Management Science and Operations Research
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12606/26607
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