Why the Restricted Bayes/Hurwicz Criterion is Savagian: A Game-Theoretic Perspective of Ambiguity

Abstract

Ellsberg (1961) introduced the Ellsberg urns experiments as evidence against Savage's theory of subjective expected utility. The restrictive Bayes/Hurwicz criterion (Ellsberg, 2001) is proposed to explain the phenomena of subjects shunning the ambiguous urns. Modeling the interaction between the experimenter and the subject as a game, we find sufficient and necessary conditions for the subject to modify beliefs with the reduced-form criterion. We postulate that diverse ambiguity attitudes result from different perceptions about the payoff structure. As a horse race gambler should adjust his belief after the gambling company publishes new odds, the subject can form different beliefs facing different choice problems. The revealed belief discrepancies can be a result of these modifications, and thus does not violate the Savage axioms about the preferences at the moment of each decision. The ambiguity game interpretation is supported by various neuroscientific and behavioral studies.

Keywords: Ambiguity Attitude, Restricted Bayes/Hurwicz Criterion, Restricted Hurwicz Criterion, Ambiguity Aversion/Seeking, Ellsberg Paradox, Ellsberg Urns Experiments, Baboon Infanticide Game

JEL Classification: C72, D81, D83