Multi-Belief Rational-Expectations Equilibria: Indeterminacy, Complexity And Sustained Deflation

In this paper, we extend the concept of rational-expectations equilibrium, from a traditional single-belief framework to a multi-belief one. In the traditional framework of single belief, agents are supposed to know the equilibrium price "correctly." We relax this requirement in the framework of multiple beliefs. While agents do not have to know the equilibrium price exactly, they must be correct in that it must be always contained in the support of each probability distribution they think possible. We call this equilibrium concept a multibelief rational-expectations equilibrium. We then show that such an equilibrium exists, that indeterminacy and complexity of equilibria can happen even when the degree of risk aversion is moderate and, in particular, that a decreasing price sequence can be an equilibrium. The last property is highlighted in a linear-utility example where any decreasing price sequence is a multi-belief rational-expectations equilibrium while only possible single-belief rational-expectations equilibrium price sequences are those which are constant over time.