Existence and Regularity of Partially Revealing Rational Expectations Equilibrium in Finite Economies
Résumé
We consider an incomplete financial market exchange economy with nominal assets and a finite number of traders, goods, states and signals. In this framework, we prove the existence and regularity of rational expectations equilibria for any informational structure derived from prices. We provide a proof that completes the characterization of existence of equilibrium in these economies, in the following sense: while Polemarchakis and Siconolfi [Polemarchakis, H., Siconolfi, P., 1993. Asset markets and the information revealed by prices. Economic Theory, Vol. 3, pp. 645-661.] show existence only of fully nonrevealing equilibrium, and Rahi [Rahi, R., 1995. Partially revealing rational expectations equilibria with nominal assets. Journal of Mathematical Economics, Vol. 24, pp. 137-146.] finds partially revealing equilibria for all economies satisfying a restrictive condition on the traders' equilibrium information structure, we dispense with Rahi's condition, and offer a strategy of proof that applies directly to all cases of revelation. Our proof of existence is based on homotopy methods. Given the way we construct our proof, we can easily link the asymmetric information model to the linear restricted participation models. We show how to apply the "Cass trick" in asymmetric information economies to control for asset prices, even if all agents are restricted, that is, partially informed.