Approximizations of Nash equilibria

G. Gürkan, J.S. Pang

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Abstract

Inspired by previous works on approximations of optimization problems and recent papers on the approximation of Walrasian and Nash equilibria and on stochastic variational inequalities, the present paper investigates the approximation of Nash equilibria and clarifies the conditions required for the convergence of the approximate equilibria via a direct approach, a variational approach, and an optimization approach. Besides directly addressing the issue of convergence of Nash equilibria via approximation, our investigation leads to a deeper understanding of various notions of functional convergence and their interconnections; more importantly, the investigation yields improved conditions for convergence of the approximate Nash equilibria via the variational approach. An illustrative application of our results to the approximation of a Nash equilibrium in a competitive capacity expansion model under uncertainty is presented.
Original languageEnglish
Pages (from-to)223-253
JournalMathematical Programming
Volume117
Issue number1-2
Publication statusPublished - 2009

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Nash Equilibrium
Approximation
Variational Approach
Walrasian Equilibrium
Capacity Expansion
Interconnection
Variational Inequalities
Optimization Problem
Uncertainty
Optimization

Cite this

Gürkan, G. ; Pang, J.S. / Approximizations of Nash equilibria. In: Mathematical Programming . 2009 ; Vol. 117, No. 1-2. pp. 223-253.
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Gürkan, G & Pang, JS 2009, 'Approximizations of Nash equilibria', Mathematical Programming , vol. 117, no. 1-2, pp. 223-253.

Approximizations of Nash equilibria. / Gürkan, G.; Pang, J.S.

In: Mathematical Programming , Vol. 117, No. 1-2, 2009, p. 223-253.

Research output: Contribution to journalArticleScientificpeer-review

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AB - Inspired by previous works on approximations of optimization problems and recent papers on the approximation of Walrasian and Nash equilibria and on stochastic variational inequalities, the present paper investigates the approximation of Nash equilibria and clarifies the conditions required for the convergence of the approximate equilibria via a direct approach, a variational approach, and an optimization approach. Besides directly addressing the issue of convergence of Nash equilibria via approximation, our investigation leads to a deeper understanding of various notions of functional convergence and their interconnections; more importantly, the investigation yields improved conditions for convergence of the approximate Nash equilibria via the variational approach. An illustrative application of our results to the approximation of a Nash equilibrium in a competitive capacity expansion model under uncertainty is presented.

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