Iterative Techniques for the Nash Solution in Quadratic Games with Unknown Parameters

Abstract

Previous article Iterative Techniques for the Nash Solution in Quadratic Games with Unknown ParametersG. P. PapavassilopoulosG. P. Papavassilopouloshttps://doi.org/10.1137/0324052PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractWe study adaptive schemes for repeated quadratic Nash games in a deterministic and a stochastic framework. The convergence of the schemes is demonstrated under certain conditions.[1] T. Basar and , G. J. Olsder, Dynamic noncooperative game theory, Mathematics in Science and Engineering, Vol. 160, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1982xii+430 83i:90169 0479.90085 Google Scholar[2] T. Basar, Equilibrium solutions in two-person quadratic decision problems with static information structures, IEEE Trans. Automatic Control, AC-20 (1975), 320–328 10.1109/TAC.1975.1100977 55:7534 0382.90113 CrossrefISIGoogle Scholar[3] G. P. 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The basic probability distribution of the game, Management Sci., 14 (1968), 486–502 39:7955 0177.48501 CrossrefISIGoogle ScholarKeywordsNash equilibriumadaptive Gamesstochastic approximation Previous article FiguresRelatedReferencesCited ByDetails Adaptive rules for discrete-time Cournot games of high competition level marketsOperational Research, Vol. 21, No. 4 | 9 October 2019 Cross Ref An Inverse-Adjusted Best Response Algorithm for Nash EquilibriaFrancesco Caruso, Maria Carmela Ceparano, and Jacqueline MorganSIAM Journal on Optimization, Vol. 30, No. 2 | 18 June 2020AbstractPDF (667 KB)Pretending in Dynamic Games, Alternative Outcomes and Application to Electricity MarketsDynamic Games and Applications, Vol. 8, No. 4 | 28 August 2017 Cross Ref Convergence analysis on variable sample distributed methods for stochastic Nash equilibrium2016 Chinese Control and Decision Conference (CCDC) | 1 May 2016 Cross Ref Cheating in adaptive games motivated by electricity markets2014 6th International Symposium on Communications, Control and Signal Processing (ISCCSP) | 1 May 2014 Cross Ref Bilevel direct search method for leader–follower problems and application in health insuranceComputers & Operations Research, Vol. 41 | 1 Jan 2014 Cross Ref On generalized Nash games and variational inequalitiesOperations Research Letters, Vol. 35, No. 2 | 1 Mar 2007 Cross Ref Exact penalty functions for generalized Nash problemsLarge-Scale Nonlinear Optimization | 1 Jan 2006 Cross Ref Coupled constraint Nash equilibria in environmental gamesResource and Energy Economics, Vol. 27, No. 2 | 1 Jun 2005 Cross Ref Distributed computation of Pareto solutions inn-player gamesMathematical Programming, Vol. 74, No. 1 | 1 Jul 1996 Cross Ref On distributed computation of Pareto solutions for two decision makersIEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, Vol. 26, No. 4 | 1 Jul 1996 Cross Ref On relaxation algorithms in computation of noncooperative equilibriaIEEE Transactions on Automatic Control, Vol. 39, No. 6 | 1 Jun 1994 Cross Ref Learning algorithms for repeated bimatrix Nash games with incomplete informationJournal of Optimization Theory and Applications, Vol. 62, No. 3 | 1 Sep 1989 Cross Ref Distributed algorithms for the computation of noncooperative equilibriaAutomatica, Vol. 23, No. 4 | 1 Jul 1987 Cross Ref Decentralised adaptive control in a game situation for discrete-time, linear, time-invariant systemsProceedings of 1994 American Control Conference - ACC '94 Cross Ref Volume 24, Issue 4| 1986SIAM Journal on Control and Optimization589-834 History Submitted:26 June 1984Published online:17 February 2012 InformationCopyright © 1986 Society for Industrial and Applied MathematicsKeywordsNash equilibriumadaptive Gamesstochastic approximationMSC codes60G4262L2090D0590D15PDF Download Article & Publication DataArticle DOI:10.1137/0324052Article page range:pp. 821-834ISSN (print):0363-0129ISSN (online):1095-7138Publisher:Society for Industrial and Applied Mathematics