Foundations of Bayesian Theory

This paper states necessary and sufficient conditions for the existence, uniqueness, and updating according to Bayes?rule, of subjective probabilities representing individuals?beliefs. The approach is preference based, and the result is an axiomatic subjective expected utility model of Bayesian decision making under uncertainty with statedependent preferences. The theory provides foundations for the existence of prior probabilities representing decision makers?beliefs about the likely realization of events and for the updating of these probabilities according to Bayes?rule.

A Theory of Bayesian Decision Making

This paper presents a complete, choice-based, axiomatic Bayesian decision theory. It introduces a new choice set consisting of information-contingent plans for choosing actions and bets and subjective expected utility model with effect-dependent utility functions and action-dependent subjective probabilities which, in conjunction with the updating of the probabilities using Bayes' rule, gives rise to a unique prior and a set of action-dependent posterior probabilities representing the decision maker's prior and posterior beliefs.

Why Does it Matter that Beliefs and Valuations be Correctly Represented?

This paper contains an analysis of a simple principal-agent problem illustrating possible problems that may arise when the prinicpal ascribes to the agent subjective probabilities and utilities that are implied by the subjective expected utility model but do not represent the agent's beliefs and valuations. In particular, it is possible that an incentive contract designed by the principal indices the agent to choose an action that is not in the principal's best interest.principal agent theory;moral hazard

Moral Sentiments and Social Choice: Fairness Considerations in University Admissions

We examine the implications for social choice of individuals having an intrinsic sense of fairness. Taking the viewpoint that social justice reflects the moral attitudes of the constituent members, we analyze the effect of the intensity of the individual sense of fairness on university admission policies. Assuming that these policies are determined by bargaining over test scores to be used as cut-off points for admission of members of diverse social groups show that, in general, a more intense sense of fairness of the members of a group leads to an admission policy that is more compatible with their idea of fairness. Consequently, a society whose members have a common notion tends to implement fairer admission policies when the intensity of the sense of fairness of individual memebrs increase. This is even if the policies are ultimately determined by the bargaining power of the different groups.

Objective and Subjective Expected Utility with Incomplete Preferences

This paper extends the expected utility models of decision making under risk and under uncertainty to include incomplete beliefs and tastes. The main results are two axiomatizations of the multi-prior expected multi-utility representations of preference relation under uncertainty, thereby resolving long standing open questions. The Knightian uncertainty model and expected multi-utility model with complete beliefs are obtained as special cases. In addition, the von Neumann-Morgenstern expected utility model with incomplete preferences is revisited using a "constructive" approach, as opposed to earlier treatments that use convex analysis.

A dynamic mechanism and surplus extraction under ambiguity

We study the question of auction design in an IPV setting characterized by ambiguity. We assume that the preferences of agents exhibit ambiguity aversion; in particular, they are represented by the epsilon-contamination model. We show that a simple variation of a discrete Dutch auction can extract almost all surplus. This contrasts with optimal auctions under IPV without ambiguity as well as with optimal static auctions with ambiguity—in all of these, types other than the lowest participating type obtain a positive surplus. An important point of departure is that the modified Dutch mechanism is dynamic rather than static, establishing that under ambiguity aversion—even when the setting is IPV in all other respects—a dynamic mechanism can have additional bite over its static counterparts. A further general insight is that the standard revelation principle does not automatically extend to environments not characterized by subjective expected utility

Defects, Super-Poincar\'{e} line bundle and Fermionic T-duality

Topological defects are interfaces joining two conformal field theories, for which the energy momentum tensor is continuous across the interface. A class of the topological defects is provided by the interfaces separating two bulk systems each described by its own Lagrangian, where the two descriptions are related by a discrete symmetry. In this paper we elaborate on the cases in which the discrete symmetry is a bosonic or a fermionic T- duality. We review how the equations of motion imposed by the defect encode the general bosonic T- duality transformations for toroidal compactifications. We generalize this analysis in some detail to the case of topological defects allowed in coset CFTs, in particular to those cosets where the gauged group is either an axial or vector U(1). This is discussed in both the operator and Lagrangian approaches. We proceed to construct a defect encoding a fermionic T-duality. We show that the fermionic T-duality is implemented by the Super-Poincar\'{e} line bundle. The observation that the exponent of the gauge invariant flux on a defect is a kernel of the Fourier-Mukai transform of the Ramond-Ramond fields, is generalized to a fermionic T-duality. This is done via a fiberwise integration on supermanifolds.Comment: 41 page

Ambiguity Attitudes and Social Interactions: An Experimental Investigation

This paper reports the results of experiments designed to test (a) whether and to what extent individuals display non-neutral ambiguity attitudes in their choice behavior and (b) if and how do ambiguity attitudes change as a result of interpersonal interactions and persuasion. To address the first question we designed and conducted experiments involving individual choice between betting on ambiguous and unambiguous events of their choice. We found that a large majority of subjects display ambiguity-neutral attitudes, many others display ambiguity-incoherent attitudes, and few subjects display either ambiguity-averse attitudes or ambiguity-seeking attitudes. To address the second question we introduced a new experimental design with a built-in incentive to persuade. We found that interpersonal interactions without incentive to persuade have no effect on behavior, but when incentives were introduced, the ambiguity-neutral subjects were better able to persuade ambiguity seeking and ambiguity-incoherent subjects to follow ambiguity-neutral choice behavior. No such influence was detected with respect to ambiguity-neutral subjects.