Preference for Flexibility in a Savage Framework

Abstract

We study preferences over Savage acts that map states to opportunity sets and satisfy the Savage axioms. Preferences over opportunity sets may exhibit a preference for flexibility due to an implicit uncertainty about future preferences reflecting anticipated unforeseen contingencies. The main result of this paper characterizes maximization of the expected indirect utility in terms of an ‘Indirect Stochastic Dominance’ axiom that expresses a preference for ‘more opportunities in expectation.’ The key technical tool of the paper, a version of Möbius inversion, has been imported from the theory of nonadditive belief functions; it allows an alternative representation using Choquet integration, and yields a simple proof of Kreps' (1979) classic result.

A Subjective Spin on Roulette Wheels

“…The notion of subjective mixture can also be employed to model phenomena that are not necessarily related to the presence of ambiguity. For example, we can provide (along the lines of Ozdenoren (2002)) a subjective mixture version of the models based on Kreps (1979), such as Kreps (1992), Nehring (1999), Dekel, Lipman and Rustichini (2001) and Gul and Pesendorfer (2001).…”

Rationalizability of menu preferences

“…Among the numerous more recent papers are those of Ahn and Sarver (2013), Dekel et al (2009), Epstein et al (2007), Olszewski (2007, and Stovall (2010). As mentioned by Dekel et al (2009, p. 938), "[a] menu can be interpreted either literally or as an action which affects subsequent opportunities."…”

“…2 Note that we deliberately avoid "modeling the set of alternatives as lotteries and utilizing the resulting linear structure by imposing the von Neumann-Morgenstern axioms" Pesendorfer 2001, p. 1406); a practice pioneered by Dekel et al (2001) and Gul and Pesendorfer (2001) and adopted in much of the ensuing menu-preference literature. (Some exceptions include Ergin 2003, Gul and Pesendorfer 2005, and Nehring 1999. While it has the advantage of facilitating precise identification of model components, such as the subjective state space in Dekel et al (2001), the lottery formulation can be viewed as a purely technical device to the extent that objective risk is not essential to the phenomenon of interest (e.g., temptation).…”

Unawareness of theorems

“…Kreps (1992) interpreted this as a model of unforeseen contingencies. Ghirardato (2001), Mukerji (1997), Skiadas (1997) and Nehring (1999) also model unforeseen contingencies. Dekel et al (2001) derives an essentially unique subjective state space and shows that its size provides a measure of the agent's uncertainty about future contingencies.…”