Data Monetization through Strategic Coordination of Privately Informed Agents

We consider linear-quadratic games of incomplete information with Gaussian uncertainty, in which players' payoffs depend both on a privately observed type and an unknown but common state. A monopolist data platform observes the state, elicits the players' types, and sells information back to them via (possibly correlated) action recommendations. We fully characterize the class of all such implementable Gaussian mechanisms (where the joint distribution of actions and signals is multivariate normal) as well as the player-optimal and revenue-maximizing mechanisms within this class. For games of strategic complements (substitutes), both optimal mechanisms maximally correlate (anticorrelate) the players' actions. When uncertainty over private types is large, the recommendations are deterministic and linear functions of the state and reported types but are not fully revealing. We apply our results to algorithmic pricing recommendations used by platforms such as Amazon and those challenged in U.S. v. RealPage.