Selling Information in Games with Externalities

TL;DR

This paper models a competitive market as an incomplete information game where a seller offers information to a buyer, analyzing optimal pricing and menu design to balance profit and externalities in binary action games.

Contribution

It introduces a product versioning framework for selling information in competitive settings and characterizes optimal menus considering externalities and incentives.

Findings

Payments incentivize information sharing among firms.

Optimal menus benefit both buyer and seller.

Fierce competition may lead to no information being sold.

Abstract

A competitive market is modeled as a game of incomplete information. One player observes some payoff-relevant state and can sell (possibly noisy) messages thereof to the other, whose willingness to pay is contingent on their own beliefs. We frame the decision of what information to sell, and at what price, as a product versioning problem. The optimal menu screens buyer types to maximize profit, which is the payment minus the externality induced by selling information to a competitor, that is, the cost of refining a competitor's beliefs. For a class of games with binary actions and states, we derive the following insights: (i) payments are necessary to provide incentives for information sharing amongst competing firms; (ii) the optimal menu benefits both the buyer and the seller; (iii) the seller cannot steer the buyer's actions at the expense of social welfare; (iv) as such, as competition grows fiercer it can be optimal to sell no information at all.