Assortative Information Disclosure

Abstract

We consider a standard persuasion problem in which the receiver's action and the state of the world are both one-dimensional. Fully characterizing optimal signals when utilities are non-linear is a daunting task. Instead, we develop a general approach to understanding a key qualitative property of optimal signals: their assortative structure, which describes the overall pattern of what states are pooled together. We derive simple conditions-driven by intuitive economic properties, such as supermodularity and submodularity of preferences-for the optimality of positive and negative assortative patterns of information disclosure. Our approach unifies a wide range of previous findings and generates new applications.

Form of Preference Misalignment Linked to State-pooling Structure in Bayesian Persuasion

“…This result is reminiscent of the result ofKolotilin and Wolitzky (2020) that there is no loss of generality from focusing on pairwise signals in their setup.…”

“…The closest paper to ours is Kolotilin and Wolitzky (2020). However, we differ along several directions, and our paper can be viewed as complementary to theirs.…”

“…The most relevant results from the seminal paper by Kamenica and Gentzkow (2011) are (i) conditions for full disclosure or non-disclosure in the general form and (ii) comparative statics of more aligned preferences. Regarding point (i), we go beyond these two "corner" cases for the optimal signal, similarly as in the recent studies of Arieli et al (2020) and Kolotilin and Wolitzky (2020). We discuss the connection of our work to Kolotilin and Wolitzky (2020) in more detail later in this section.…”

“…Regarding point (i), we go beyond these two "corner" cases for the optimal signal, similarly as in the recent studies of Arieli et al (2020) and Kolotilin and Wolitzky (2020). We discuss the connection of our work to Kolotilin and Wolitzky (2020) in more detail later in this section. Regarding point (ii), we perform a different exercise with preference misalignment: we fix the preferences and analyze how the structure of preference misalignment is related to the structure of state pooling of the optimal signal.…”

Bayesian persuasion and information design: perspectives and open issues

“…This issue is being addressed in two distinct but complementary directions. One direction identifies sufficient conditions for simple information structures to be optimal among all information structures, as in Kolotilin and Wolitzky (2020), Ivanov (2021), and Kolotilin et al (2021). The other direction explicitly incorporates relevant constraints, as in Degan andLi (2021), Di Tillio et al (2021) and Onuchic and Ray (2021).…”