Ambiguity and Robust Statistics in Economic Modelling - Maccheroni

Team Members

Pierpaolo Battigalli              (Università Bocconi)
Erio Castagnoli                    (Università Bocconi)
Simone Cerreia Vioglio      (Università Bocconi)
Marzia De Donno                 (Università degli Studi di Pisa)
Massimo Marinacci             (Università Bocconi)
Alberto Zaffaroni                   (Università degli Studi di Modena e Reggio Emilia)

This research unit is part of the project Robust Decision in Markets and Organizations , which consists of 5 Research Units coordinated by Marco Li Calzi (Università Ca' Foscari, Venezia).

Abstract
Starting with the seminal paper of Gilboa and Schmeidler (1989) an analogy between the maxmin approach of decision theory under Ambiguity and the minimax approach of Robust Statistics ( e.g., Blum and Rosenblatt 1967) has been hinted at.

This research project formally clarifies this relation by showing the conditions under which the two approaches are equivalent. This brings us to consider the case where decision makers know that payoff relevant observations are generated by a process that belongs to a given class M, as postulated in Wald (1950). We intend to show that this leads to a two-stages subjective expected utility model that accounts for both state and model uncertainty.

In a game theoretic framework, we propose to bring together two conceptually complementary ideas: self-confirming equilibrium and uncertainty aversion. In such a context, players can be interpreted as long-run empiricists and equilibria are rest points of learning dynamics in a game played recurrently. At this point, many distribution are plausible with the players' observations. We study the case in which players/decision makers negatively react to such uncertainty. As a further step, we will study learning dynamics in such a context.