Strong Bubbles and Common Expected Bubbles in a Finite Horizon Model

An expected bubble is said to exist if it is mutual knowledge that the price of the asset is higher than the expected dividend. A strong bubble exists if everyone knows that the price is higher than the maximum possible dividend. Substituting common knowledge for mutual knowledge, I develop the new concepts of a common expected bubble and a common strong bubble. In a simple finite horizon model with asymmetric information and short sales constraints following the framework of Allen, Morris and Postlewaite (1993), I show that the following results hold for any finite number of agents: First, under the implicit assumption of perfect memory, common strong bubbles never exist in any rational expectations equilibrium. Second, it is possible to have a bubble that is both a strong bubble and a common expected bubble in a rational expectations equilibrium. Furthermore, the second result is robust to both strongly symmetric perturbations in beliefs and very symmetric perturbations in dividends. A counterexample of the first result is possible when agents are forgetful.

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