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Values of Large Games, I: A Limit Theorem

Author

Listed:
  • N. Z. Shapiro

    (Rand Corporation, 1700 Main Street, Santa Monica, California 90406)

  • L. S. Shapley

    (Rand Corporation, 1700 Main Street, Santa Monica, California 90406)

Abstract

This paper gives an analysis of what happens in a weighted majority game when a block of votes is broken up and distributed among a large number of players. It is shown that the value of the game to the other players converges to a limit as the size of the largest fragment tends to zero. An explicit expression is given for the limit.

Suggested Citation

  • N. Z. Shapiro & L. S. Shapley, 1978. "Values of Large Games, I: A Limit Theorem," Mathematics of Operations Research, INFORMS, vol. 3(1), pages 1-9, February.
    • Handle: RePEc:inm:ormoor:v:3:y:1978:i:1:p:1-9
    DOI: 10.1287/moor.3.1.1
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    Citations

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    Cited by:

    1. Levy, Anat & Shapley, Lloyd S, 1997. "Individual and Collective Wage Bargaining," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(4), pages 969-991, November.
    2. Mikołaj Jasiński, 2013. "The Terms of Cooperation’s Stability. What is the Reason of Flow Between Coalitions?," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 32, pages 55-76.
    3. André Casajus & Helfried Labrenz & Tobias Hiller, 2009. "Majority shareholder protection by variable qualified majority rules," European Journal of Law and Economics, Springer, vol. 28(1), pages 9-18, August.
    4. Pierre Degond & Jian-Guo Liu & Christian Ringhofer, 2014. "Evolution of wealth in a nonconservative economy driven by local Nash equilibria," Working Papers hal-00967662, HAL.
    5. Crama, Yves & Leruth, Luc, 2007. "Control and voting power in corporate networks: Concepts and computational aspects," European Journal of Operational Research, Elsevier, vol. 178(3), pages 879-893, May.
    6. Leech, Dennis, 1999. "Minority Control: An Analysis of British Companies using Voting Power Indices," Economic Research Papers 269251, University of Warwick - Department of Economics.
    7. Pierre Degond & Jian-Guo Liu & Christian Ringhofer, 2013. "Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria," Papers 1307.1685, arXiv.org.
    8. Pierre Degond & Jian-Guo Liu & Christian Ringhofer, 2014. "Evolution of wealth in a nonconservative economy driven by local Nash equilibria," Papers 1403.7800, arXiv.org.
    9. Leech, Dennis, 2001. "An Empirical Comparison of the Performance of Classical Power Indices," Economic Research Papers 269334, University of Warwick - Department of Economics.
    10. Neyman, Abraham, 2010. "Singular games in bv'NA," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 384-387, July.
    11. Artyom Jelnov & Yair Tauman, 2014. "Voting power and proportional representation of voters," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 747-766, November.
    12. Taylan Mavruk & Conny Overland & Stefan Sjögren, 2020. "Keeping it real or keeping it simple? Ownership concentration measures compared," European Financial Management, European Financial Management Association, vol. 26(4), pages 958-1005, September.
    13. Abraham Neyman & Rann Smorodinsky, 2004. "Asymptotic Values of Vector Measure Games," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 739-775, November.
    14. Zaremba Leszek & Zaremba Cezary S. & Suchenek Marek, 2017. "Modification Of Shapley Value And Its Implementation In Decision Making," Foundations of Management, Sciendo, vol. 9(1), pages 257-272, October.
    15. Leech, Dennis, 2010. "Power Indices in Large Voting Bodies," The Warwick Economics Research Paper Series (TWERPS) 942, University of Warwick, Department of Economics.
    16. Sascha Kurz, 2016. "The inverse problem for power distributions in committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 65-88, June.
    17. Casajus, André & Labrenz, Helfried, 2014. "A property rights based consolidation approach," Working Papers 126, University of Leipzig, Faculty of Economics and Management Science.
    18. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
    19. Leech, Dennis, 2010. "Power Indices in Large Voting Bodies," Economic Research Papers 270996, University of Warwick - Department of Economics.
    20. Dennis Leech, 2013. "Power indices in large voting bodies," Public Choice, Springer, vol. 155(1), pages 61-79, April.
    21. Pierre Degond & Jian-Guo Liu & Christian Ringhofer, 2014. "Evolution of wealth in a nonconservative economy driven by local Nash equilibria," Post-Print hal-00967662, HAL.
    22. Chung, Kee H. & Kim, Jeong-Kuk, 1999. "Corporate ownership and the value of a vote in an emerging market," Journal of Corporate Finance, Elsevier, vol. 5(1), pages 35-54, March.

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