Jean-Marc Tallon and Jean-Christophe Vergnaud 7.1 INTRODUCTION In this chapter, we apply the decision theoretic approach to the representation and updating of beliefs. The standard Bayesian approach developed by Savage (1954) sets out the conditions under which a decision maker whose preferences satisfy a certain number of ‘rationality’ axioms (among which is the famous ‘Sure-thing principle’) will have probabilistic beliefs. When these axioms are satisﬁed any decision maker is able (or acts as if he were able) to come up with a probability distribution over the possible states of nature (i.e. the sources of uncertainty) and also acts as if maximizing an expected utility with respect to this prior. This construction underlies most of economic theory. However, as early as 1921, Keynes (1921) and Knight (1921) had already suggested that probabilistic beliefs failed to address an important issue, namely the conﬁdence agents have in their own beliefs. Doubts about the fact that probabilistic beliefs could represent all types of uncertainty were also raised by Shackle (1952). These theoretical concerns were backed by experimental evidence showing that subjects often failed to deal with probabilistic information in the way predicted by the theory (Allais 1953). Moreover, the evidence showed that subjects found it difﬁcult to come up with probabilistic priors when information was a priori too scarce (Ellsberg 1961). In more recent years, more general axiomatic models of decision under uncertainty have emerged in which agents can have non-additive beliefs (Schmeidler 1989) or multiple-prior beliefs (Gilboa and Schmeidler 1989)...
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