EX ANTE VERSUS INTERIM RATIONALITY AND THE EXISTENCE OF BUBBLES

Tirole (1982) is commonly interpreted as proving that bubbles are impo ssible with finitely many rational traders with common priors. We stud y a simple variation of his model in which bubbles can occur, even tho ugh traders have common priors and common knowledge that the asset has no fundamental value. In equilibrium, agents purchase the asset at su ccessively higher prices until the bubble ''bursts'' and no subsequent trade occurs. Each trader's initial wealth determines the last date a t which he could possibly trade. The date at which the bubble bursts i s a function of these finite ''truncation dates'' for the individual t raders. Since initial wealth is private information, no trader knows w hen the bubble will burst. There are two key differences between our m odel and Tirole's which enable us to construct equilibrium bubbles thi s way. First, Tirole requires ex ante optimality, while we only requir e every trader's strategy to be optimal conditional on his information - i.e., interim optimal. As we argue in the text, this would seem to be the relevant definition of optimality. Second, Tirole considers com petitive equilibria, while we analyze a simple bargaining game.