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Mathematical Foci

Author

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  • Correa Romar

    (University of Mumbai – Economics, Mumbai 400 054, India)

Abstract

We address the converse of a Wald–Vorob'ev theorem. In a non cooperative game, if the strategy set of any individual player is precompact, we show that the strategy sets of all the other players is precompact.

Suggested Citation

  • Correa Romar, 2014. "Mathematical Foci," Mathematical Economics Letters, De Gruyter, vol. 2(1-2), pages 5-11, August.
    • Handle: RePEc:bpj:maecol:v:2:y:2014:i:1-2:p:7:n:1
    DOI: 10.1515/mel-2013-0008
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    References listed on IDEAS

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    1. Roger B. Myerson, 2009. "Learning from Schelling's Strategy of Conflict," Journal of Economic Literature, American Economic Association, vol. 47(4), pages 1109-1125, December.
    2. Vincent P. Crawford & Uri Gneezy & Yuval Rottenstreich, 2008. "The Power of Focal Points Is Limited: Even Minute Payoff Asymmetry May Yield Large Coordination Failures," American Economic Review, American Economic Association, vol. 98(4), pages 1443-1458, September.
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    Citations

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    Cited by:

    1. Jinpeng Ma & Qiongling Li, 2016. "Convergence of price processes under two dynamic double auctions," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 1-44, December.
    2. R. Cominetti, 1997. "Coupling the Proximal Point Algorithm with Approximation Methods," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 581-600, December.
    3. E. Mijangos, 2006. "Approximate Subgradient Methods for Nonlinearly Constrained Network Flow Problems," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 167-190, January.
    4. Z. Wei & L. Qi & H. Jiang, 1997. "Some Convergence Properties of Descent Methods," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 177-188, October.
    5. Zengru Cui & Gonglin Yuan & Zhou Sheng & Wenjie Liu & Xiaoliang Wang & Xiabin Duan, 2015. "A Modified BFGS Formula Using a Trust Region Model for Nonsmooth Convex Minimizations," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-15, October.
    6. Sitters, R.A., 2009. "Efficient algorithms for average completion time scheduling," Serie Research Memoranda 0058, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    7. Gürkan, G. & Ozge, A.Y., 1996. "Sample-Path Optimization of Buffer Allocations in a Tandem Queue - Part I : Theoretical Issues," Other publications TiSEM 77da022b-635b-46fd-bf4a-f, Tilburg University, School of Economics and Management.
    8. Gürkan, G. & Ozge, A.Y., 1996. "Sample-Path Optimization of Buffer Allocations in a Tandem Queue - Part I : Theoretical Issues," Discussion Paper 1996-98, Tilburg University, Center for Economic Research.
    9. J. R. Birge & L. Qi & Z. Wei, 1998. "Convergence Analysis of Some Methods for Minimizing a Nonsmooth Convex Function," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 357-383, May.
    10. J. P. Penot & P. H. Sach, 1997. "Generalized Monotonicity of Subdifferentials and Generalized Convexity," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 251-262, July.
    11. T. T. Hue & J. J. Strodiot & V. H. Nguyen, 2004. "Convergence of the Approximate Auxiliary Problem Method for Solving Generalized Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 119-145, April.
    12. Zhou, Bojian & Bliemer, Michiel & Yang, Hai & He, Jie, 2015. "A trial-and-error congestion pricing scheme for networks with elastic demand and link capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 77-92.
    13. K. C. Kiwiel, 2000. "Efficiency of Proximal Bundle Methods," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 589-603, March.
    14. Jie Shen & Ya-Li Gao & Fang-Fang Guo & Rui Zhao, 2018. "A Redistributed Bundle Algorithm for Generalized Variational Inequality Problems in Hilbert Spaces," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(04), pages 1-18, August.
    15. Y. R. He, 2001. "Minimizing and Stationary Sequences of Convex Constrained Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 111(1), pages 137-153, October.
    16. O. Cornejo & A. Jourani & C. Zălinescu, 1997. "Conditioning and Upper-Lipschitz Inverse Subdifferentials in Nonsmooth Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 127-148, October.
    17. A. I. Rauf & M. Fukushima, 2000. "Globally Convergent BFGS Method for Nonsmooth Convex Optimization1," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 539-558, March.
    18. Larsson, Torbjorn & Patriksson, Michael & Stromberg, Ann-Brith, 2003. "On the convergence of conditional [var epsilon]-subgradient methods for convex programs and convex-concave saddle-point problems," European Journal of Operational Research, Elsevier, vol. 151(3), pages 461-473, December.
    19. J.-P. Penot & P. H. Quang, 1997. "Generalized Convexity of Functions and Generalized Monotonicity of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 343-356, February.

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    More about this item

    Keywords

    Multiple Equilibria; Leadership; Multiple Equilibria; Leadership;
    All these keywords.

    JEL classification:

    • B32 - Schools of Economic Thought and Methodology - - History of Economic Thought: Individuals - - - Obituaries
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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