Dynamically stable preferences

In the framework of dynamic choice under uncertainty, we define dynamic stability as a combination of two assumptions prevalent in the literature: dynamic consistency and the requirement that updated preferences belong to the same class as ex ante ones. Maxmin preferences are shown to be not dynamically stable, and any dynamically stable subset in that class can contain only expected utility preferences. Dynamic stability also turns out to be a defining characteristic of the multiplier preferences of Hansen and Sargent (2001) within the scope of variational preferences. Restrictions imposed by dynamic stability are shown to be related to invariance of preferences.