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

1986; Society for Industrial and Applied Mathematics; Volume: 24; Issue: 4 Linguagem: Inglês

10.1137/0324052

1095-7138

George P. Papavassilopoulos,

Air Traffic Management and Optimization

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