A Geometric Study of Shareholders’ Voting in Incomplete Markets: Multivariate Median and Mean Shareholder Theorems
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- handle: 10670/1.gxrjhl
- hal: hal-03598169
- doi: 10.1007/s00355-006-0138-7
- SCIENCESPO: 2441/10263
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Hervé Crès, « A Geometric Study of Shareholders’ Voting in Incomplete Markets: Multivariate Median and Mean Shareholder Theorems », Archive ouverte de Sciences Po (SPIRE), ID : 10.1007/s00355-006-0138-7
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Résumé
A simple parametric general equilibrium model with S states of natureand K < S firms is considered. Since markets are incomplete, at a (financial) equilibriumshareholders typically disagree on whether to keep or not the status quoproduction plans. Hence each firm faces a genuine problem of social choice. Thesetup proposed in the present paper allows to study these problems within a classical(Downsian) spatial voting model. Given the multidimensional nature of thelatter, super majority rules with rate ρ ∈ [1/2, 1] are needed to guarantee existenceof politically stable production plans. A simple geometric argument is proposedshowingwhy a 50%-majority stable production equilibrium exists when K = S−1.When the degree of incompleteness is more severe, under more restrictive assumptionson agents’ preferences and the distribution of agents’ types, equilibria areshown to exist for rates ρ smaller than Caplin and Nalebuff (Econometrica 59:1–23, 1991) bound of 0.64: they obtain for production plans whose span containsthe ‘ideal securities’ of all K mean shareholders.