About the Links Between Equilibrium Problems and Variational Inequalities

  • D. Aussel
  • J. DuttaEmail author
  • T. Pandit
Part of the Indian Statistical Institute Series book series (INSIS)


In this chapter, we seek to study the interrelation between an equilibrium problem and the variational inequality problem. Under most natural assumption, the equilibrium problem is equivalent to an associated variational inequality. Hence, the existence results for equilibrium problems can be obtained from the existence results for variational inequality problems and vice versa. We study a problem of existence of Nash equilibrium in an oligopolistic market and show that it is equivalent to a variational inequality under the most natural economic assumption. We also study the relation between quasi-equilibrium problem and quasi-variational inequality.


Equilibrium problem Variational inequality problem Oligopolistic market 


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Lab. PROMES, UPR CNRS 8521University of PerpignanPerpignanFrance
  2. 2.Department of Economic SciencesIIT KanpurKanpurIndia
  3. 3.Department of Mathematics and StatisticsIndian Institute of TechnologyKanpurIndia

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