Journal of Economic Literature 2019, 57(1), 44–95 https://doi.org/10.1257/jel.20181489 Information Design: A Unified Perspective† Dirk Bergemann and Stephen Morris* Given a game with uncertain payoffs, information design analyzes the extent to which the provision of information alone can influence the behavior of the players. Information design has a literal interpretation, under which there is a real informa- tion designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used by the analyst to characterize play in the game under many different information structures. We provide an introduction to the basic issues and insights of a rapidly growing literature in information design. We show how the literal and metaphorical interpretations of information design unify a large body of existing work, including that on communica- tion in games (Myerson 1991), Bayesian persuasion (Kamenica and Gentzkow 2011), and some of our own recent work on robust predictions in games of incomplete infor- mation. ( JEL C70, D82, D83) 1. Introduction studies how the information designer, through the choice of the information provided, can layers’ payoffs in a game depend on their influence the individually optimal behavior Pactions and also on the realization of a pay- of the players to achieve her objective. She off-relevant state. An “information designer” can achieve this objective even though she can commit how to provide information about has no ability to change outcomes or force the the states to the players. “Information design” lecture at Harvard University, and the 2016 fall Finance * Bergemann: Department of Economics, Yale Univer- Theory group conference at Princeton. Some of the sity. Morris: Department of Economics, Princeton Univer- material in this paper was previewed in Bergemann and sity. We acknowledge financial support from NSF Grants Morris (2016b). We have benefited from discussions and SES 0851200 and 1459899. We are grateful for produc- correspondence about the material in this paper with Ben tive suggestions by the Editor, Steven Durlauf, and five Brooks, Laura Doval, Jeff Ely, Francoise Forges, Drew anonymous referees. This material has been presented in Fudenberg, Olivier Gossner, Tibor Heumann, Atsushi lectures at the 2015 Istanbul meetings of the Society of Kajii, Emir Kamenica, Rohit Lamba, Laurent Mathevet, Economic Design, the 2015 Delhi School of Economics Roger Myerson, Tymofiy Mylanov, Alessandro Pavan, Eran Winter School, the 2016 AEA meetings, the North Amer- Shmaya, Jonathan Weinstein, and Juan Pablo Xandri; and ican Summer Meeting of the Econometric Society, the from valuable research assistance from Ian Ball, Leon Gerzensee Summer Symposium in Economic Theory, Musolff, Denis Shishkin, Áron Tóbiás and Xinyang Wang. the Becker Friedman Institute conference on Frontiers † Go to https://doi.org/10.1257/jel.20181489 to visit the and Economic Theory and Computer Science, the Harris article page and view author disclosure statement(s). 44 Bergemann and Morris: Information Design: A Unified Perspective 45 players to choose particular actions that deter- the information designer has an informa- mine outcomes.1 tional advantage over the players. This case The past decade has seen a rapidly growing has been the focus of some our own work body of literature in information design. An (Bergemann and Morris 2013b, 2016a), influential paper by Kamenica and Gentzkow where we show that the set of outcomes that (2011) phrased the optimal design of infor- can arise in this setting corresponds to a ver- mation as a “Bayesian persuasion” problem sion of incomplete information equilibrium between a sender and single receiver. A (Bayes-correlated equilibrium, or BCE) that large body of work fits this rubric, includ- allows outcomes to be conditioned on states ing important contributions of Brocas and that the players do not know. Carrillo (2007) and Rayo and Segal (2010). A second purpose of the paper is to high- The economic applications of information light a distinction between literal informa- design have been investigated in areas as far tion design and metaphorical information apart as grade disclosure and matching mar- design. The information design problem has kets (Ostrovsky and Schwarz 2010), voter a literal interpretation (given above): there mobilization (Alonso and Câmara 2016), really is an information designer (or media- traffic routing (Das, Kamenica, and Mirka tor, or sender) who can commit to provide 2017), rating systems (Duffie, Dworczak, extra information to players to serve her own and Zhu 2017), and transparency regula- interests. While the commitment assump- tion (Asquith, Covert, and Pathak 2013) tion may be problematic in many settings, it in financial markets, price discrimination provides a useful benchmark. But the infor- (Bergemann, Brooks, and Morris 2015), and mation design formulation might also be a stress tests in banking regulation (Inostroza metaphor that the analyst uses as a tool. For and Pavan 2017). example, we might be interested in finding an One purpose of the paper is to provide an upper bound (across information structures) overview of information design that unifies on the aggregate variance of output in a given this recent work with a number of litera- economy with idiosyncratic and common tures sometimes treated as distinct. If we shocks to agents’ productivity (Bergemann, assume that there are many players, but the Heumann, and Morris 2015). We can under- information designer (or “mediator”) has no stand this as an information design problem, informational advantage over the players, where the information designer is interested this problem reduces to the analysis of com- in choosing an information structure to max- munication in games (Myerson 1991, section imize aggregate variance in output. But in 6.3) and, more generally, the literature on this case, we do not have in mind that there correlated equilibrium in incomplete infor- is an actual information designer maximiz- mation games (Forges 1993). If there is only ing aggregate variance. We will discuss this one player (or “receiver”) but the informa- application, and other applications where tion designer (or “sender”) has an informa- information design is metaphorical, below. tional advantage over the player, the problem This survey reviews the pure information reduces to the “Bayesian persuasion” prob- design problem where a designer can commit lem of Kamenica and Gentzkow (2011). to a certain information structure for the play- Information design concerns the general ers but has no control over outcomes. This case where there are both many players and problem is a special case of the more general mechanism design problem where a mech- 1 We follow Taneva (2015) in our use of the term “infor- anism designer can control outcomes but mation design” in this context. may also be able to manipulate information 46 Journal of Economic Literature, Vol. LVII (March 2019) in the course of doing so.2 We study the case one-player case. But we will also describe where all information structures are available a general partial order on information to the designer. It is thus possible to appeal structures—generalizing the Blackwell order to the revelation principle from the general for the one-player case—which characterizes mechanism design problem, and without the right definition of “more information” in loss of generality restrict attention to infor- this context (Bergemann and Morris 2016a). mation structures where the signals that the Third, we can ask whether the information information designer sends to a player can designer prefers to give the information to be identified with action recommendations. players in a public or in a private message. This revelation principle/mechanism design Of course, this last question only arises once approach to information design thus contrasts we have multiple players. Public information with work where there is no commitment is optimal if the information designer wants to the information structure or attention is perfect correlation between players’ actions; restricted to a parameterized class of infor- otherwise private information will be optimal. mation structures. While the information designer may have We use a family of two-player, two-action, intrinsic preferences over whether players’ and two-state examples to survey the litera- actions are correlated (or not), the designer ture, and to provide some graphical illustra- may care about correlation for purely instru- tions. We start with the leading example of mental reasons: if there are strategic com- Bayesian persuasion (with a single player/ plementarities between the players’ actions, receiver with no prior information) from the she may want to correlate players’ actions to work of Kamenica and Gentzkow (2011). We relax the obedience constraints on her abil- can use extensions of this example—with ity to attain specific outcomes. The converse many players and prior information—to holds for strategic substitutability. We will illustrate many of the key ideas in the survey. illustrate the case when there are only instru- Three key substantive general insights are mental preferences over correlation. illustrated in these examples. The examples also illustrate a methodolog- First, it is often optimal for the informa- ical point. The information design problem tion designer to