Symmetry of evidence without evidence of symmetry

The de Finetti Theorem is a cornerstone of the Bayesian approach. Bernardo (1996) writes that its "message is very clear: if a sequence of observations is judged to be exchangeable, then any subset of them must be regarded as a random sample from some model, and there exists a prior distribution on the parameter of such model, hence requiring a Bayesian approach." We argue that while exchangeability, interpreted as symmetry of evidence, is a weak assumption, when combined with subjective expected utility theory, it implies also complete confidence that experiments are identical. When evidence is sparse, and there is little evidence of symmetry, this implication of de Finetti's hypotheses is not intuitive. This motivates our adoption of multiple-priors utility as the benchmark model of preference. We provide two alternative generalizations of the de Finetti Theorem for this framework. A model of updating is also provided.Ambiguity, exchangeability, symmetry, updating, learning, multiple-priors

Coarse contingencies and ambiguity

The paper considers an agent who must choose an action today under uncertainty about the consequence of any chosen action but without having in mind a complete list of all the contingencies that could influence outcomes. She conceives of some relevant (subjective) contingencies but she is aware that these contingencies are coarse---they leave out some details that may affect outcomes. Though she may not be able to describe these finer details, she is aware that they exist and this may affect her behavior.Uncertainty, states of the world, ambiguity, coarse contingencies

Coarse Contingencies

The paper considers an agent who must choose an action today under uncertainty about the consequence of any chosen action but without having in mind a complete list of all the contingencies that could influence outcomes. She conceives of some relevant (subjective) contingencies but she is aware that these contingencies are coarse - they leave out some details that may affect outcomes. Though she may not be able to describe these finer details, she is aware that they exist and this may affect her behavior.Unforeseen Contingencies, Ambiguity, Menu Choices

Bundling, information aggregation and entry deterrence

This paper provides an explanation for bundling based on its information aggregation effect. Using bundling, the monopolist can hide the information of each monopoly market by aggregating information. We show that the monopolist chooses bundling in an early period because bundling removes potential competition in the following period.Bundling Entry deterrence Information aggregation Information asymmetry

Symmetry of evidence without evidence of symmetry

[This item is a preserved copy. To view the original, visit http://econtheory.org/] The de Finetti Theorem is a cornerstone of the Bayesian approach. Bernardo (1996) writes that its "message is very clear: if a sequence of observations is judged to be exchangeable, then any subset of them must be regarded as a random sample from some model, and there exists a prior distribution on the parameter of such model, hence requiring a Bayesian approach." We argue that while exchangeability, interpreted as symmetry of evidence, is a weak assumption, when combined with subjective expected utility theory, it implies also complete confidence that experiments are identical. When evidence is sparse, and there is little evidence of symmetry, this implication of de Finetti's hypotheses is not intuitive. This motivates our adoption of multiple-priors utility as the benchmark model of preference. We provide two alternative generalizations of the de Finetti Theorem for this framework. A model of updating is also provided

Subjective states: a more robust model

Following Kreps [11], Nehring [15, 16] and Dekel, Lipman and Rustichini [5], we study the demand for ‡exibility and what it reveals about subjective uncertainty. As in the cited papers, the latter is represented by a subjective state space consisting of possible future preferences over actions to be chosen ex post. One contribution is to provide axiomatic foundations for a range of alternative hypotheses about the nature of these ex post preferences. Secondly, we establish a sense in which the subjective state space is uniquely pinned down by the agent’s ex ante ranking of (random) menus. For both purposes, we show that it is advantageous to assume that the agent ranks random menus, and to think of ex post upper contour sets rather than ex post preferences. Finally, we demonstrate the tractability of our representation by showing that it can model the two comparative notions “2 desires more ‡exibility than 1”and “2 is more averse to ‡exibility-risk than is 1.

Perceived ambiguity and relevant measures

We axiomatize preferences that can be represented by a monotonic aggregation of subjective expected utilities generated by a utility function and some set of i.i.d. probability measures over a product state space, S1. For such preferences, we define relevant measures, show that they are treated as if they were the only marginals possibly governing the state space and connect them with the measures appearing in the aforementioned representation. These results allow us to interpret relevant measures as reflecting part of perceived ambiguity, meaning subjective uncertainty about probabilities over states. Under mild conditions, we show that increases or decreases in ambiguity aversion cannot affect the relevant measures. This property, necessary for the conclusion that these measures reflect only perceived ambiguity, distinguishes the set of relevant measures from the leading alternative in the literature. We apply our findings to a number of well-known models of ambiguity-sensitive preferences. For each model, we identify the set of relevant measures and the implications of comparative ambiguity aversion

Subjective states: A more robust model

We study the demand for flexibility and what it reveals about subjective uncertainty. As in Kreps [D. Kreps, 1979. A representation theorem for 'preference for flexibility'. Econometrica 47, 565-577], Nehring [K. Nehring, 1996. Preference for flexibility and freedom of choice in a Savage framework. UC Davis Working Paper; K. Nehring, 1999. Preference for flexibility in a Savage framework. Econometrica 67, 101-119] and Dekel et al. [E. Dekel, B. Lipman, A. Rustichini, 2001. Representing preferences with a unique subjective state space. Econometrica 69, 891-934], the latter is represented by a subjective state space consisting of possible future preferences over actions to be chosen ex post. One contribution is to provide axiomatic foundations for a range of alternative hypotheses about the nature of these ex post preferences. Secondly, we establish a sense in which the subjective state space is uniquely pinned down by the ex ante ranking of (random) menus. Finally, we demonstrate the tractability of our representation by showing that it can model the two comparative notions "2 desires more flexibility than 1" and "2 is more averse to flexibility-risk than is 1."