Majority stable production equilibria : a multivariate mean shareholders theorem

In a simple parametric general equilibrium model with S states of nature and K < S firms - and thus potentially incomplete markets-, rates of super majority rule p€[1/2, 1] are computed which guarantee the existence of p -majority stable production equilibria : within each firm, no alternative production plan can rally a proportion bigger than p of the shareholders, or shares (depending on the governance), against the equilibrium. The smallest p are obtained for announced production plans whose span contains the ideal consumptions of all K mean shareholders. This is done under various governances. These rates of super majority are shown to be always smaller than Caplin and Nalebuff (1988, 1991) bound of 1-1/e ~ 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. Finally, through parametric examples, these rates are shown to decrease with the homogeneity of the shareholders' beliefs on the probabilities of the states of nature, and to increase with the shareholders' pessimism.