Abstract
Efficiency is not commonly related to the crash of bubbles. However in the presence of wary agents, infinite-lived agents that are worried about distant losses, efficient bubbles may occur and, in a stochastic setting, these bubbles can crash. In this paper we characterize the Arrow–Debreu (AD) price and establish the relationship between the agents’ concern about distant losses and the existence of pure charges in the AD price. We show that this pure charge induces efficient bubbles in the positive net-supply assets that complete the markets and that, as we enter some sub-tree, that pure charge may no longer present in the AD price for the sub-economy, implying the crash of the bubble. Finally, we give an example in which there is an efficient bubble with infinitely many crashes.