Existence of Equilibria in Incomplete Markets with Non-Ordered Preferences

We consider a two-period exchange economy with a finite set of consumers, states of nature, independent assets and a single consumption good. We prove the existence of competitive equilibrium in incomplete markets, when consumption set is not assumed to be compact, set of assets is linearly independent, and individuals' preferences are not assumed to be complete or transitive. Our study therefore generalizes various results in the existing literature.