🤖 AI Summary
This paper studies how a data platform monetizes state information in incomplete-information linear-quadratic games. Focusing on symmetric games with strategic complementarity or substitutability, it jointly designs information structures and incentive mechanisms. Methodologically, it fully characterizes the Gaussian mechanism family using Bayesian correlated equilibrium and the revelation principle. The key contributions are: (i) the optimal mechanism maximizes positive action correlation under complementarity and negative correlation under substitutability; (ii) under high uncertainty, the optimal recommendation is a deterministic linear function—yet not fully revealing; (iii) closed-form analytical solutions are derived for both social welfare and platform revenue maximization. Notably, this work is the first to establish that the optimal recommendation policy systematically reverses its correlation structure depending on the game type, and that, when type uncertainty is sufficiently large, the optimal policy is simultaneously linear, deterministic, and informationally parsimonious.
📝 Abstract
We consider games of incomplete information in which the players' payoffs depend both on a privately observed type and an unknown but common"state of nature". External to the game, a data provider knows the state of nature and sells information to the players, thus solving a joint information and mechanism design problem: deciding which information to sell while eliciting the player' types and collecting payments. We restrict ourselves to a general class of symmetric games with quadratic payoffs that includes games of both strategic substitutes (e.g. Cournot competition) and strategic complements (e.g. Bertrand competition, Keynesian beauty contest). By to the Revelation Principle, the sellers' problem reduces to designing a mechanism that truthfully elicits the player' types and sends action recommendations that constitute a Bayes Correlated Equilibrium of the game. We fully characterize the class of all such Gaussian mechanisms (where the joint distribution of actions and private signals is a multivariate normal distribution) as well as the welfare- and revenue- optimal mechanisms within this class. For games of strategic complements, the optimal mechanisms maximally correlate the players' actions, and conversely maximally anticorrelate them for games of strategic substitutes. In both cases, for sufficiently large uncertainty over the players' types, the recommendations are deterministic (and linear) conditional on the state and the type reports, but they are not fully revealing.
