Recursive Vector Expected Utility

This paper proposes and axiomatizes a recursive version of the vector expected utility (VEU) decision model (Siniscalchi, 2009). Recursive VEU preferences are dynamically consistent and “consequentialist.” Dynamic consistency implies standard Bayesian updating of the baseline (reference) prior in the VEU representation, but imposes no constraint on the adjustment functions and one-step-ahead adjustment factors. This delivers both tractability and flexibility. Recursive VEU preferences are also consistent with a dynamic, i.e. intertemporal extension of atemporal VEU preferences. Dynamic consistency is characterized by a timeseparability property of adjustments—the VEU counterpart of Epstein and Schneider (2003)’s rectangularity for multiple priors. A simple exchangeability axiom ensures that the baseline prior admits a representation à la de Finetti, as an integral of i.i.d. product measures with respect to a unique probability μ. Jointly with dynamic consistency, the same axiom also implies that μ is updated via Bayes’ Rule to provide an analogous representation of baseline posteriors. Finally, an application to a dynamic economy à la Lucas (1978) is sketched.