Voting in assemblies of shareholders and incomplete markets

An economy with two dates is considered, one state at the first date and a finite number of states at the last date. Shareholders determine production plans by voting - one share, one vote - and at <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\rho$</EquationSource> </InlineEquation>-majority stable stock market equilibria, alternative production plans are supported by at most <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\rho \times 100$</EquationSource> </InlineEquation> percent of the shareholders. It is shown that a <InlineEquation ID="Equ3"> <EquationSource Format="TEX">$\rho$</EquationSource> </InlineEquation>-majority stable stock market equilibrium exists if <InlineEquation ID="Equ4"> <EquationSource Format="TEX">$$ \rho\ \geq\ \dfrac{S-J}{S-J + 1}, $$</EquationSource> </InlineEquation> where S is the number of states at the last date and J is the number of firms. Moreover, an example shows that <InlineEquation ID="Equ5"> <EquationSource Format="TEX">$\rho$</EquationSource> </InlineEquation>-majority stable stock market equilibria need not exist for smaller <InlineEquation ID="Equ6"> <EquationSource Format="TEX">$\rho$</EquationSource> </InlineEquation>’s. Copyright Springer-Verlag Berlin/Heidelberg 2005