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Mathematical Programming and Game Theory pp 115–130Cite as

About the Links Between Equilibrium Problems and Variational Inequalities

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Abstract

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.

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Authors and Affiliations

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

    D. Aussel

  2. Department of Economic Sciences, IIT Kanpur, Kanpur, India

    J. Dutta

  3. Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India

    T. Pandit

Authors
  1. D. Aussel
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  2. J. Dutta
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  3. T. Pandit
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Corresponding author

Correspondence to J. Dutta .

Editor information

Editors and Affiliations

  1. Indian Statistical Institute, New Delhi, India

    S.K. Neogy

  2. Indian Statistical Institute, New Delhi, India

    Ravindra B. Bapat

  3. Indian Statistical Institute, New Delhi, India

    Dipti Dubey

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Aussel, D., Dutta, J., Pandit, T. (2018). About the Links Between Equilibrium Problems and Variational Inequalities. In: Neogy, S., Bapat, R., Dubey, D. (eds) Mathematical Programming and Game Theory. Indian Statistical Institute Series. Springer, Singapore. https://doi.org/10.1007/978-981-13-3059-9_6

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