Persuasion with Ambiguous Communication
🤖 AI Summary
This paper investigates whether a sender can enhance persuasion effectiveness through ambiguous communication under ambiguity aversion. Method: Extending the Bayesian persuasion framework, we incorporate the smooth ambiguity model of Klibanoff et al. (2005) and systematically characterize—using concavification techniques and incentive-compatible signal design—the necessary and sufficient conditions for effective ambiguous communication. Contribution/Results: We establish that ambiguous communication never improves the sender’s payoff in binary-action settings; however, in settings with three or more actions, Pareto-ranked experimental split structures enable substantial sender gains. Crucially, these gains are robust to perturbations in the receiver’s degree of ambiguity aversion. Our findings provide novel theoretical foundations and design principles for real-world ambiguous decision-making contexts—such as bank stress testing—where ambiguity is pervasive and agents exhibit systematic ambiguity aversion.
Application Category
📝 Abstract
This paper considers the problem of a sender who wishes to favorably influence, through strategic communication of information, the action taken by a receiver. As in the large literature on Bayesian persuasion following Kamenica and Gentzkow [2011] (see also Rayo and Segal [2010] and surveys by Bergemann and Morris [2019] and Kamenica [2019]), we model the sender as committing to a communication strategy and the receiver as best responding to that strategy. A communication strategy for the sender is usually described as a statistical experiment, a function mapping from payoff-relevant states to probability distributions over messages. The key departures from most of the literature and the focus of our analysis are that we enlarge the set of the sender's communication strategies to include ambiguous strategies - strategies for which, from the perspective of both sender and receiver, the probability that a given statistical experiment will be used to generate the signal is subjectively uncertain. Furthermore, the receiver (and possibly the sender as well) is assumed to be ambiguity averse, i.e., averse to this subjective uncertainty about these probabilities. In this paper, we explore whether and to what extent using ambiguous communication can be beneficial for the sender compared to standard, unambiguous communication. The analysis of when ambiguous communication is beneficial and why is complex and intricate, but the general intuition for how it might be beneficial is simple. When confronted with a host of possible interpretations of the same evidence, ambiguity aversion causes the receiver to overweight the less favorable interpretations. Compared to an ambiguity-neutral receiver, the resulting distortion in beliefs may be sufficient to induce a different best response and, therefore, may potentially benefit the sender. The more ambiguity averse the receiver is, the more they overweight the less favorable interpretations, and the more scope there is for the sender to potentially benefit. While correct, this intuition is quite incomplete - it gives no sense of what it takes for this ability to induce different best responses to benefit the sender. Our analysis highlights that one can limit attention to strategies generating ambiguity using a collection of statistical experiments that form a splitting of an experiment whose messages are incentive-compatible action recommendations for the receiver. At least some of the experiments in this collection must be Pareto-ranked in the sense that both the sender and receiver agree on their payoff ranking. The existence of a two-experiment collection forming such a Pareto-ranked splitting is necessary for ambiguous communication to benefit the sender. We prove that this necessary condition is, surprisingly to us, never met in problems in which the receiver has only two feasible actions, encompassing many examples in the literature. If an optimal Bayesian persuasion experiment can be split into a two-experiment Pareto-ranked splitting, this is sufficient for an ambiguity-neutral sender as well as the receiver to benefit from ambiguous communication. Such gains persist even if the sender is as ambiguity averse as the receiver (and even a bit more so), as long as the sender is not infinitely ambiguity averse. The gains are also robust to the receiver being more ambiguity averse than the sender thought and any small perturbation of the receiver's ambiguity aversion. The paper provides a simple example (with three actions for the receiver and two payoff-relevant states of the world) satisfying the sufficient condition from the previous paragraph. The example is used to illustrate the intuition for how choosing to communicate ambiguously can be beneficial, and for some of the paper's formal results. We provide an interpretation of the example in the context of banking regulation and stress tests as a form of communication to investors. We model preferences under ambiguity using the smooth ambiguity model [Klibanoff et al., 2005], which, fixing an ambiguous communication strategy of the sender and the best response of the receiver, provides a convenient way to continuously span ambiguity aversion levels ranging from ambiguity neutrality (i.e., subjective expected utility) all the way to an infinitely ambiguity averse limit that is an instance of the maxmin expected utility model [Gilboa and Schmeidler, 1989]. We also derive a concavification-like characterization of both the sender's optimal payoff and when the sender may benefit from the ability to communicate ambiguously. Our characterization implies that when the sender is ambiguity neutral and the receiver has constant relative ambiguity aversion, the optimal ambiguous communication must include weakly Pareto-ranked experiments only and none of them can be further split into a Pareto-ranked splitting. We close this abstract with a brief discussion of a few closely related papers. Beauchêne et al. [2019] (BLL henceforth) also study the strategic use of ambiguous communication in persuasion. They impose the infinitely ambiguity-averse extreme for both the sender and receiver - a polar case of our model. The key difference between BLL and our paper is how the receiver is assumed to best respond given the sender's ambiguous experiment. We assume the receiver chooses an ex-ante optimal signal-contingent strategy. BLL assume the receiver chooses, for each signal, actions maximizing interim preferences formed using a belief updating rule that leads to dynamic inconsistency with the ex-ante preference. Cheng [2023] shows that all benefits from ambiguous communication identified by BLL disappear if the receiver is assumed, as in our paper, to maximize their ex-ante preference. Thus, one contribution of our paper is establishing and analyzing the benefits of ambiguous persuasion that do not stem from the receiver's behavior that is suboptimal with respect to these ex-ante preferences. Given Cheng [2023]'s result, it is essential that we allow at least the sender to be less than infinitely ambiguity averse for such benefits to exist. Full paper: Click here for the newest version.
Problem
Research questions and friction points this paper is trying to address.
Explores if ambiguous communication benefits senders in persuasion problems
Analyzes persuasion when receivers are ambiguity averse using experiment splitting
Identifies conditions where ambiguity benefits both sender and receiver
Innovation
Methods, ideas, or system contributions that make the work stand out.
Ambiguous communication benefits ambiguity-averse sender
Uses splitting of obedient experiment into collections
Pareto-ranked experiments enable persuasion benefits
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