Revised-Path Dependence

Abstract

In this article, we define a class of revised path—dependent processes and characterize their basic properties. A process exhibits revised-path dependence if the current outcome can revise the value of a past outcome. A revision could be a change to that outcome or a reinterpretation. We first define a revised path—dependent process called the accumulation process: in each period, a randomly chosen past outcome is changed to match the current outcome and show that it converges to identical outcomes. We then construct a general class of models that includes the Bernoulli process, the Polya process, and the accumulation process as special cases. For this general class, we show that, apart from knife-edge cases, all processes converge either to homogeneous equilibria or to an equal probability distribution over types. We also show that if random draws advantage one outcome over the other, then the process has a unique equilibrium.