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Majority Stable Production Equilibria: A Multivariate Mean Shareholders Theorem

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  • Hervé Crès

Abstract

In a simple parametric general equilibrium model with S states of nature and K · S ¯rms |and thus potentially incomplete markets|, rates of super majority rule ½ 2 [0; 1] are computed which guarantee the existence of ½{majority stable production equilibria: within each ¯rm, no alternative production plan can rally a proportion bigger than ½ of the shareholders, or shares (depending on the governance), against the equilibrium. Under some assumptions of concavity on the distributions of agents' types, the smallest ½ are shown to obtain for announced production plans whose span contains the ideal securities of all K mean shareholders. These rates of super majority are always smaller than Caplin and Nalebu® (1988, 1991) bound of 1¡1=e ¼ 0:64. Moreover, simple majority production equilibria are shown to exist for any initial distribution of types when K = S ¡1, and for symmetric distributions of types as soon as K ¸ S=2.

Suggested Citation

  • Hervé Crès, 2000. "Majority Stable Production Equilibria: A Multivariate Mean Shareholders Theorem," Sciences Po publications 706/2000, Sciences Po.
  • Handle: RePEc:spo:wpmain:info:hdl:2441/10284
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    File URL: http://spire.sciencespo.fr/hdl:/2441/10284/resources/cres-crhec-2000.pdf
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    References listed on IDEAS

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    1. Grossman, Sanford J & Hart, Oliver D, 1979. "A Theory of Competitive Equilibrium in Stock Market Economies," Econometrica, Econometric Society, vol. 47(2), pages 293-329, March.
    2. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    3. Alessandro Citanna & Antonio Villanacci, 2004. "Pooling and endogenous market incompleteness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(3), pages 549-560, October.
    4. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    5. Cres, Herve & Tvede, Mich, 2001. "Ordering Pareto-optima through majority voting," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 295-325, May.
    6. Egbert Dierker & Hildegard Dierker & Birgit Grodal, 1999. "Incomplete Markets and the Firm," CIE Discussion Papers 1999-05, University of Copenhagen. Department of Economics. Centre for Industrial Economics.
    7. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
    8. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    9. Geanakoplos, J. & Magill, M. & Quinzii, M. & Dreze, J., 1990. "Generic inefficiency of stock market equilibrium when markets are incomplete," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 113-151.
    10. Peter M. DeMarzo, 1993. "Majority Voting and Corporate Control: The Rule of the Dominant Shareholder," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 713-734.
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    More about this item

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • G39 - Financial Economics - - Corporate Finance and Governance - - - Other

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