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

Didier Aussel () and Simone Sagratella ()
Additional contact information
Didier Aussel: University of Perpignan
Simone Sagratella: Sapienza University of Rome

Mathematical Methods of Operations Research, 2017, vol. 85, issue 1, No 2, 3-18

Abstract: 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.

Keywords: Quasivariational inequality; Generalized Nash equilibrium problem; Reproducible set-valued map; Quasiconvexity; 49J40; 49J53; 91B26; 49J52 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (18)

Downloads: (external link)
http://link.springer.com/10.1007/s00186-016-0565-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:85:y:2017:i:1:d:10.1007_s00186-016-0565-x

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-016-0565-x

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().