David S. Ahn

Estimating ambiguity aversion in a portfolio choice experiment

We report a laboratory experiment that enables us to estimate parametric models of ambiguity aversion at the level of the individual subject. We use two main specifications, a “kinked” specification that nests Maxmin Expected Utility, Choquet Expected Utility, α-Maxmin Expected Utility, and Contraction Expected Utility and a “smooth” specification that nests the various theories referred to collectively as Recursive Expected Utility. Our subjects solved a series of portfolio-choice problems. The assets are Arrow securities corresponding to three states of nature, where the probability of one state is known and the remaining two are ambiguous. The sample exhibits considerable heterogeneity in preferences, as captured by parameter estimates. Nonetheless, there exists a strong tendency to equalize the demands for the securities that pay off in the ambiguous states, a feature more easily accommodated by the kinked specification than by the smooth specification. We also find that a large number of subjects are well described by the ambiguity-neutral Subjective Expected Utility model.

Preference for Flexibility and Random Choice

We study a two-stage model where the agent has preferences over menus as in Dekel, Lipman, and Rustichini (2001) in the first period and then makes random choices from menus as in Gul and Pesendorfer (2006) in the second period. Both preference for flexibility in the first period and strictly random choices in the second period can be, respectively, rationalized by subjective state spaces. Our main result characterizes the representation where the two state spaces align, so the agent correctly anticipates her future choices. The joint representation uniquely identifies probabilities over subjective states and magnitudes of utilities across states. We also characterize when the agent completely overlooks some subjective states that realize at the point of choice.

Hierarchies of Ambiguous Beliefs

Abstract We present a theory of interactive beliefs analogous to Mertens and Zamir [Formulation of Bayesian analysis for games with incomplete information, Int. J. Game Theory 14 (1985) 1–29] and Brandenburger and Dekel [Hierarchies of beliefs and common knowledge, J. Econ. Theory 59 (1993) 189–198] that allows for hierarchies of ambiguity. Each agent is allowed a compact set of beliefs at each level, rather than just a single belief as in the standard model. We propose appropriate definitions of coherency and common knowledge for our types. Common knowledge of coherency closes the model, in the sense that each type homeomorphically encodes a compact set of beliefs over the others’ types. This space universally embeds every implicit type space of ambiguous beliefs in a beliefs-preserving manner. An extension to ambiguous conditional probability systems [P. Battigalli, M. Siniscalchi, Hierarchies of conditional beliefs and interactive epistemology in dynamic games, J. Econ. Theory 88 (1999) 188–230] is presented. The standard universal type space and the universal space of compact continuous possibility structures are epistemically identified as subsets.

Approval Voting and Scoring Rules with Common Values

We compare approval voting with other scoring rules for environments with common values and private information. For finite electorates, the best equilibrium under approval voting is superior to plurality rule or negative voting. For large electorates, if any scoring rule yields a sequence of equilibria that efficiently aggregates information, then approval voting must do so as well.

The Condorcet Jur(ies) Theorem

Should two issues be decided jointly by a single committee or in separately by different committees? Similarly, should two defendants be tried together in a joint trial or tried separately in severed trials? Multiplicity of issues or defendants introduces novel strategic considerations. As in the standard Condorcet Jury Theorem, we consider large committees with common values and incomplete information. Our main result is that the joint trial by a single committee can aggregate information if and only if the severed trials by separate committees can aggregate information. Specifically, suppose that either for the joint trial or for the severed trials there exists a sequence of equilibria that implements the optimal outcome with probability approaching one as the number of voters goes to infinity. Then a sequence of equilibria with similar asymptotic efficiency exists for the other format. Thus, the advantage of either format cannot hinge on pure information aggregation with many signals.

Naiveté About Temptation and Self-Control: Foundations for Naive Quasi-Hyperbolic Discounting

We introduce and characterize a recursive model of dynamic choice that accommodates naiveté about present bias. The model incorporates costly self-control in the sense of Gul and Pesendorfer (2001) to overcome the technical hurdles of the Strotz representation. The important novel condition is an axiom for naiveté. We first introduce appropriate definitions of absolute and comparative naiveté for a simple two-period model, and explore their implications for the costly self-control model. We then extend this definition for infinite-horizon environments, and discuss some of the subtleties involved with the extension. Incorporating the definition of absolute naiveté as an axiom, we characterize a recursive representation of naive quasi-hyperbolic discounting with self-control for an individual who is jointly overoptimistic about her present-bias factor and her ability to resist instant gratification. We study the implications of our proposed comparison of naiveté for the parameters of the recursive representation. Finally, we discuss the obstacles that preclude more general notions of naiveté, and illuminate the impossibility of a definition that simultaneously incorporates both random choice and costly self-control.