On Information Design in Games

Abstract

Information provision in games influences behavior by affecting agents' beliefs about the state as well as their higher-order beliefs. We first characterize the extent to which a designer can manipulate agents' beliefs by disclosing information. We then describe the structure of optimal belief distributions, including a concave-envelope representation that subsumes the single-agent result of Kamenica and Gentzkow. This result holds under various solution concepts and outcome selection rules. Finally, we use our approach to compute an optimal information structure in an investment game under adversarial equilibrium selection.We are grateful to the editor, Emir Kamenica, and to three anonymous referees for their comments and suggestions, which significantly improved the paper. Special thanks are due to Anne-Katrin Roesler for her insightful comments as a discussant at the 2016 Cowles

Feasible Joint Posterior Beliefs

“…Related literature. Mathevet et al (2019) study Bayesian persuasion with multiple receivers and finite signals. They find an implicit characterization of feasibility: considering the entire belief hierarchy, they show that feasibility is equivalent to consistency of the hierarchy.…”

Stress Tests and Information Disclosure

“…For example, consider 43 So, the market can be viewed as having a quadratic utility function: (x ) 2 . 44 More recent approaches (e.g., Gentzkow and Kamenica, 2016; Kolotilin, forthcoming; Dworczak and Martini, 2017) also have limited applicability in characterizing optimal disclosure rules in our setting. 45 If the bank observes its type, the regulator's payo¤ is r if x ( ) and r Pr(" 1 ) if x < ( ).…”

“…In particular, the equilibrium price x is a …xed point ofÊ( j ( ) x), whereÊ denotes the expected value given the market's posterior beliefs, and the condition ( ) x re ‡ects the fact that the bank agrees to sell only if the price is above its reservation price. 44 If the bank does not observe its type, the equilibrium price is simply x =Ê( ), but the standard concavi…cation approach still has limited applicability in characterizing optimal disclosure rules, because the regulator's payo¤ depends on the bank's type:…”

Collusion and delegation under information control

“…See Ivanov (2010) for an analysis of information control in this model. 11 See also the literature on information design in games (Bergemann and Morris 2013, 2016, Taneva 2019, Mathevet et al 2020. agent to the supervisor.…”