Dropping the Cass Trick and Extending Cass' Theorem to Asymmetric Information

In a celebrated 1984 paper, David Cass provided an existence theorem for financial equilibria in incomplete markets with exogenous yields. The theorem showed that, when agents had symmetric information and ordered preferences, equilibria existed on purely financial markets, supported by any collection of state prices. This theorem built on the so-calles "Cass trick", along which one agent had an Arrow-Debreu budget set, with one single constraint, while the other agents were constrained à la Radner (1972), that is, in every state of nature. The current paper extends Cass' theorem to economies with asymmetric information and non-ordered preferences. It refines De Boisdeffre (2007), which characterized the existence of equilibria with asymmetric information by the no-arbitrage condition on purely financial markets. The paper defines no arbitrage prices with asymmetric information. It shows that any collection of state prices, in the agents' commonly expected states, supports an equilibrium. This result is proved without using the Cass trick, in the sense that budget sets are defined symmetrically across all agents. Thus, the paper suggests, in the symmetric information case, an alternative proof to Cass'.