Research

A Blackwell-monotone information cost function assigns higher costs to Blackwell more informative experiments. This paper provides simple necessary and sufficient conditions for Blackwell monotonicity over finite experiments. The key condition is a system of linear differential inequalities that are convenient to check given an arbitrary cost function. When the cost function is additively separable across signals, our characterization implies that Blackwell monotonicity is equivalent to sublinearity. This identifies a wide range of practical information cost functions. Finally, we apply our results to bargaining and persuasion problems with costly information.

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.

We introduce a model in which analysts disclose forecasts strategically to help ambiguity-averse investors learn about firms, which predicts an asymmetric relation between analyst forecast errors and revisions that is inconsistent with classic theories. The relation is confirmed in both the US and international markets, for both short- and long-term forecasts, and is further supported by empirical analyses in settings in which investors face varying degrees of ambiguity and analyses of market reactions. Our results highlight the strategic nature of analyst forecasts and suggest a new channel to understand when analyst forecasts have higher market impact.

We explore whether and to what extent using ambiguous communication can be beneficial for the sender in persuasion when the receiver is ambiguity averse. In our model, ambiguity enters only through how (and if) the sender chooses to allow the realization of some payoff-irrelevant ambiguous events to determine which statistical experiment is used to generate action recommendations for the receiver and dynamic inconsistency plays no role. An ambiguous communication strategy is a source of ambiguity together with a collection of statistical experiments, one for each ambiguous event. We provide a concavification 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 experiment 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 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. They are also robust to the receiver being more ambiguity averse than the sender thought. An illustrative example in the context of banking regulation and stress testing is provided.

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 have non-MEU Uncertainty Averse preferences but not to the sender having non-MEU preferences.

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.

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.

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.