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

The time consistency of monetary and fiscal policies

We show that optimal monetary and fiscal policies are time consistent for a class of economies often used in applied work, economies appealing because they are consistent with the growth facts. We establish our results in two steps. We first show that for this class of economies, the Friedman rule of setting nominal interest rates to zero is optimal under commitment. We then show that optimal policies are time consistent if the Friedman rule is optimal. For our benchmark economy in which the time consistency problem is most severe, the converse also holds: if optimal policies are time consistent, then the Friedman rule is optimal.Monetary policy ; Fiscal policy ; Interest rates

A consistency test of the time trade-off

This paper tests the internal consistency of time trade-off utilities. We find significant violations of consistency in the direction predicted by loss aversion. The violations disappear for higher gauge durations. We show that loss aversion can also explain that for short gauge durations time trade-off utilities exceed standard gamble utilities. Our results suggest that time trade-off measurements that use relatively short gauge durations, like the widely used EuroQol algorithm (Dolan 1997), are affected by loss aversion and lead to utilities that are too high.Cost-Utility Analysis, Time Trade-Off, Loss Aversion

Consistency of multi-time Dirac equations with general interaction potentials

In 1932, Dirac proposed a formulation in terms of multi-time wave functions as candidate for relativistic many-particle quantum mechanics. A well-known consistency condition that is necessary for existence of solutions strongly restricts the possible interaction types between the particles. It was conjectured by Petrat and Tumulka that interactions described by multiplication operators are generally excluded by this condition, and they gave a proof of this claim for potentials without spin-coupling. Under smoothness assumptions of possible solutions we show that there are potentials which are admissible, give an explicit example, however, show that none of them fulfills the physically desirable Poincar\'e invariance. We conclude that in this sense Dirac's multi-time formalism does not allow to model interaction by multiplication operators, and briefly point out several promising approaches to interacting models one can instead pursue