Financial equilibrium with differential information: An existence theorem

We propose a proof of existence of equilibrium in a pure exchange economy where agents are asymmetrically informed, exchange commodities, on spot markets and securities of all kinds, on incomplete financial markets. The proof does not use Grasmanians, nor differential topology. We show first that the set of payoff matrixes, whose spans never collapse is open and everywhere dense. Then, we show by standard fixed-point-like arguments that an economy where the span of asset's payoffs cannot fall always admits an equilibrium. The resulting existence property is said to be "weakly generic". As a corollary, we prove the full existence of financial equilibrium for numeraire assets, extending Geanakoplos-Polemarchakis (1986) to the asymmetric information setting. The paper, which still retains Radner's (1972) standard perfect foresight assumption, also serves to prove in a companion article, the existence of sequential equilibrium when both Radner's (1972 & 1979) classical rational expectation assumptions are dropped, that is, when agents have private characteristics and beliefs and no model to forecast prices.