Circumventing the Hart Puzzle

The paper demonstrates the existence of sequential equilibria in a pure exchange economy, where asymmetrically informed agents exchange consumption goods and securities of all kinds, on incomplete markets. Standard models rely on Radner's (1972, 1979) rational expectation assumptions, along which agents know the maps between the information signals, the states of nature and the equilibrium prices. As shown by Hart (1975), equilibrium may then fail to exist, even when agents have symmetric information and smooth preferences. In that setting, Duffie-Shafer (1985) shows, from differential topology arguments, that interior equilibria exist generically. The current paper proceeds differently. It drops rational expectations to allow for an infinitesimal uncertainty over future spot prices. This device permits to circumvent Hart's 1975 problem, without using differential topology. Then, the paper shows that a generic condition on payoffs and forecasts guarantees the existence of equilibria. It is consistent with non-transitive preferences, non-interior consumptions, asymmetric information and normalized spot prices at equilibrium. It also serves to prove existence in a more general model, which drops Radner's rational expectations.