Sequential equilibrium without rational expectations of prices: A theorem of full existence

URL des Documents de travail : https://centredeconomiesorbonne.univ-paris1.fr/documents-de-travail-du-ces/Documents de travail du Centre d'Economie de la Sorbonne 2017.36R - ISSN : 1955-611X.Version originale Juin 2017, révisée en Juin 2018We consider a pure exchange economy, where agents, typically asymmetrically informed, exchange securities, on financial markets and commodities, on spot markets. Consumers have private characteristics, anticipations and beliefs and no model to forecast prices. They are dispensed with rational expectation and bounded rationality assumptions, such as Radner's (1972, 1979), Kurz' (1994) or Koutsougeras-Yannelis' (1999). We show that they face an incompressible uncertainty represented by a so-called "minimum uncertainty set". This uncertainty typically adds to the exogenous one, on the state of nature, an ‘endogenous uncertainty’ over future spot prices. At equilibrium, all agents expect the ‘true’ price on every spot market as a possible outcome and elect optimal strategies, ex ante, which clear on all markets ex post. We show this sequential equilibrium exists whenever agents' prior anticipations embed the minimum uncertainty set. This outcome differs from the standard generic existence results of Hart (1975), Radner (1979) and Duffie-Shaffer (1985), among others, based on the rational expectations of prices