Research

Abstract: We study a model where ambiguity introduces additional information asymmetry between analysts and investors and thus affects analysts’ information production strategically. The model predicts a distinct pattern: Forecast errors and forecast revisions exhibit a positive (negative) correlation when the revisions are negative (positive). Our empirical analysis confirms this pattern for both short- and long-term forecasts and shows that ambiguity exaggerates these correlations. Our findings highlight the importance of ambiguity in the process of financial information production.

Abstract: This paper explores whether and to what extent ambiguous communication can be beneficial to the sender in a persuasion problem, when the receiver (and possibly the sender) is ambiguity averse. We provide a concavification-like characterization of the sender’s optimal ambiguous communication. The characterization highlights the necessity of using a collection of experiments that form a splitting of an obedient experiment, that is, whose recommendations are incentive compatible for the receiver. At least some of the experiments in the collection must be Pareto-ranked in the sense that both the sender and receiver agree on their payoff ranking. The existence of a binary such Pareto-ranked splitting is necessary for ambiguous communication to benefit the sender, and, if an optimal Bayesian persuasion experiment can be split in this way, this is sufficient for an ambiguity-neutral sender as well as the receiver to benefit. We show such gains are impossible when the receiver has only two actions available. Such gains persist even when the sender is ambiguity averse, as long as not too much more so than the receiver and not infinitely averse.

Abstract: A Blackwell-monotone information cost function assigns higher costs to Blackwell more informative experiments. This paper provides simple necessary and sufficient conditions for a cost function to be Blackwell monotone over finite experiments. The key condition involves a system of linear differential inequalities. By using this characterization, we show that when a cost function is additively separable, it is Blackwell monotone if and only if it is the sum of sublinear functions. This identifies a wide range of practical information cost functions. Finally, we apply our results to bargaining and persuasion problems with costly information, broadening and strengthening earlier findings.

Abstract: A decision-maker (DM) faces uncertainty governed by a data-generating process (DGP), which is only known to belong to a set of sequences of independent but possibly non-identical distributions. A robust decision maximizes the DM’s expected payoff against the worst possible DGP in this set. This paper studies how such robust decisions can be improved with data, where improvement is measured by expected payoff under the true DGP. In this paper, I fully characterize when and how such an improvement can be guaranteed under all possible DGPs and develop inference methods to achieve it. These inference methods are needed because, as this paper shows, common inference methods (e.g., maximum likelihood or Bayesian) often fail to deliver such an improvement. Importantly, the developed inference methods are given by simple augmentations to standard inference procedures, and are thus easy to implement in practice.

Abstract: Consider a persuasion game where both the sender and receiver are ambiguity averse with maxmin expected utility (MEU) preferences and the sender can choose to design an ambiguous information structure. This paper studies the game with an ex-ante formulation: The sender first commits to a (possibly ambiguous) information structure and then the receiver best responds by choosing an ex-ante message-contingent action plan. Under this formulation, I show it is never strictly beneficial for the sender to use an ambiguous information structure as opposed to a standard (unambiguous) information structure. This result is shown to be robust to the receiver having non-MEU Uncertainty Averse preferences but not to the sender having non-MEU preferences.

Abstract: This paper proposes and axiomatizes a new updating rule: Relative Maximum Likelihood (RML) updating for ambiguous beliefs represented by a set of priors (C). This rule takes the form of applying Bayes’ rule to a subset of C. This subset is a linear contraction of C towards its subset assigning a maximal probability to the observed event. The degree of contraction captures the extent of willingness to discard priors based on likelihood when updating. Two well-known updating rules of multiple priors, Full Bayesian (FB) and Maximum Likelihood (ML), are included as special cases of RML. An axiomatic characterization of conditional preferences generated by RML updating is provided when the preferences admit Maxmin Expected Utility representations. The axiomatization relies on weakening the axioms characterizing FB and ML. The axiom characterizing ML is identified for the first time in this paper, addressing a long-standing open question in the literature.

Abstract: This note shows that the value of ambiguous persuasion characterized in Beauchêne, Li, and Li(2019) can be given by a concavification program as in Bayesian persuasion (Kamenica and Gentzkow, 2011). In addition, it implies that an ambiguous persuasion game can be equivalently formalized as a Bayesian persuasion game by distorting the utility functions. This result is obtained under a novel construction of ambiguous persuasion.

Abstract: Cheng (2021) proposes and characterizes the Relative Maximum Likelihood (RML) updating rule when the ambiguous beliefs are represented by a set of priors. Relatedly, this note proposes and characterizes the Extended RML updating rule when the ambiguous beliefs are represented by a convex capacity. Two classical updating rules for convex capacities, Dempster-Shafer (Shafer, 1976) and Fagin-Halpern rules (Fagin and Halpern, 1990) are included as special cases of Extended RML.