Optimal learning under robustness and time-consistency

We model learning in a continuous-time Brownian setting where there is prior ambiguity. The associated model of preference values robustness and is time-consistent. It is applied to study optimal learning when the choice between actions can be postponed, at a per-unit-time cost, in order to observe a signal that provides information about an unknown parameter. The corresponding optimal stopping problem is solved in closed form, with a focus on two specific settings: Ellsberg’s two-urn thought experiment expanded to allow learning before the choice of bets, and a robust version of the classical problem of sequential testing of two simple hypotheses about the unknown drift of a Wiener process. In both cases, the link between robustness and the demand for learning is studied.Accepted manuscrip

Time Consistency and Bureaucratic Budget Competition

High employment protection in the public sector results in strategic over-employment if government divisions compete for budgets in a dynamic setting. Bureaucrats who are interested in maximising their divisions’ output employ excess labor, since this induces the sponsor to provide complementary inputs in the future. Restrictions on hiring decisions in the public sector can be regarded as provisions to reduce strategic hiring. We also provide evidence from a survey of decision makers in a public sector bureaucracy with very high employment protection. The results confirm that decision makers are aware of the strategic effects of their hiring decisions on budget allocation.bureaucratic competition, time consistency, labor intensity, public sector

Time consistency of dynamic risk measures in markets with transaction costs

The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be made in a basket of currencies or assets. Time consistency of scalar risk measures can be generalized to set-valued risk measures in different ways. The most intuitive generalization is called time consistency. We will show that the equivalence between a recursive form of the risk measure and time consistency, which is a central result in the scalar case, does not hold in the set-valued framework. Instead, we propose an alternative generalization, which we will call multi-portfolio time consistency and show in the main result of the paper that this property is indeed equivalent to the recursive form as well as to an additive property for the acceptance sets. Multi-portfolio time consistency is a stronger property than time consistency. In the scalar case, both notions coincide

On Time Consistency in Stackelberg Differential Games

This paper explores a class of Stackelberg differential games in which the open-loop strategies of the leader satisfies time consistency. We show that in this class of games the open-loop equilibrium coincides with the corresponding feedback equilibrium. The analytical framework used in this paper involves the models examined by the several recent contributions to the time consistency issue as special cases.Stackelberg differential game, open-loop equilibrium, feedback equilibrium, time consistency