Leveraging robustness for information design in uncertain environments

Abstract

Information sharing between platforms and users is becoming increasingly important, with platforms often having information that is not directly visible to users. The platform's information advantage can influence users' decisions, as platforms often have more information about factors that impact outcomes. Consequently, platforms face challenges of sharing information or making recommendations that persuade users to act in ways that result in desirable outcomes. Certainly, the platform cannot make arbitrary recommendations to users without taking into account their incentives as the users may not follow the recommendations. Therefore, platforms seek to send recommendations that are likely to be adopted by users while simultaneously furthering platforms' objectives, such as long-term revenue maximization and welfare outcomes. The field of information design seeks to study such questions by developing systematic approaches to information-sharing strategies tailored to such objectives. This thesis addresses these questions through the work of two papers, each employing a robustness framework to mitigate uncertainties in information design. These studies were conducted in collaboration with Prof. Krishnamurthy Iyer and Prof. Haifeng Xu. To develop our robustness approach, we first study how the platform makes recommendations with limited knowledge of the payoff-relevant state distribution. Specifically, we consider a static persuasion setting with known payoff-relevant state distribution but impose the restriction that the recommended action must be persuasive for all distributions in the neighborhood of the actual state distribution, i.e., we require the persuasion to be robust. For this problem, we analyze the cost of robust persuasion, i.e., the loss in the platform's expected utility from requiring the action recommendations to be persuasive for all distributions in the neighborhood. We provide upper and lower bounds of the loss under some mild regularity conditions. Using this characterization, we study two information design problems faced by platforms. The first problem is the repeated persuasion setting between the platform and the users where neither the platform nor the users know the payoff-relevant distribution, and hence the platform has to persuade while learning the distribution. Our first contribution is the notion of robust persuasiveness in this setting with the detailed justification supporting the notion. Given this notion, our main result is an algorithm that, with high probability, is robustly persuasive. Using our characterization of the cost of robust persuasion, we show that our algorithm achieves vanishing average regret. We further prove that no algorithm can achieve better regret (up to logarithmic terms). The second problem we study is a model of Markovian persuasion where the platform shares information about an evolving state and the state transitions are Markovian conditional on the users' actions. In such settings, given the underlying Markovian dynamics, the effectiveness of persuasion is impacted by the users' knowledge of the history, e.g., full knowledge vs. no knowledge of the history. We find sufficient conditions under which the platform's ability to persuade is unaffected by the users' historical information. In general, we consider settings where each user observes the history with an ℓ period lag, where the lag captures the degree of historical information of the users. Using the robustness approach, we propose an algorithm that achieves approximately optimal performance when the lag ℓ is large.