Approximations of Nash equilibria (English)

In: Mathematical Programming   ;  117 ,  1  ;  223-253  ;  2007

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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.

Table of contents – Volume 117, Issue 1

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Foreword: Special issue on nonlinear programming, variational inequalities, and stochastic programming
Pangc, Jong-Shi / Ralph, Daniel | 2007
Tame functions are semismooth
Bolte, Jérôme / Daniilidis, Aris / Lewis, Adrian | 2007
No-gap second-order optimality conditions for optimal control problems with a single state constraint and control
Frédéric Bonnans, J. / Hermant, Audrey | 2007
Robust solution of monotone stochastic linear complementarity problems
Chen, Xiaojun / Zhang, Chao / Fukushima, Masao | 2007
Variable-Number Sample-Path Optimization
Deng, Geng / Ferris, Michael C. | 2007
Optimization with multivariate stochastic dominance constraints
Dentcheva, Darinka / Ruszczyński, Andrzej | 2007
Robinson’s implicit function theorem and its extensions
Dontchev, A. L. / Rockafellar, R. T. | 2007
On the necessity of the Moreau-Rockafellar-Robinson qualification condition in Banach spaces
Ernst, Emil / Théra, Michel | 2007
Generalized Nash equilibrium problems and Newton methods
Facchinei, Francisco / Fischer, Andreas / Piccialli, Veronica | 2007
Z-transformations on proper and symmetric cones
Gowda, M. Seetharama / Tao, Jiyuan | 2007
Approximations of Nash equilibria
Gürkan, Gül / Pang, Jong-Shi | 2007
Regularity estimates for convex multifunctions
Ioffe, A. D. / Sekiguchi, Y. | 2007
On attraction of Newton-type iterates to multipliers violating second-order sufficiency conditions
Izmailov, A. F. / Solodov, M. V. | 2007
Optimization methods and stability of inclusions in Banach spaces
Klatte, Diethard / Kummer, Bernd | 2007
Multiobjective optimization problems with equilibrium constraints
Mordukhovich, Boris S. | 2007
An accelerated Newton method for equations with semismooth Jacobians and nonlinear complementarity problems
Oberlin, Christina / Wright, Stephen J. | 2007
A coordinate gradient descent method for nonsmooth separable minimization
Tseng, Paul / Yun, Sangwoon | 2007
Largest dual ellipsoids inscribed in dual cones
Todd, M. J. | 2007
Primal-dual interior-point methods for PDE-constrained optimization
Ulbrich, Michael / Ulbrich, Stefan | 2007