Sameer Mathur, Kannan Srinivasan, Baohong Sun
(in preparation for second review at Quantitative Marketing and Economics)

Abstract: 
Advances in information technology increasingly allow firms to identify expensive, high-cost customers, who are not only individually less profitable for firms but also raise the average marginal cost incurred by firms and thus impose a negative externality on inexpensive customers. Should competing firms share information that identifies such customers? The answer to this question has important implications for firm profitability, consumer welfare, and privacy laws that currently constrain firms’ ability to share information legally. 
Considering consumers to be heterogeneous in terms of the cost they impose on firms, this paper presents an analytical model to examine the conditions in which two differentiated Bertrand competitors prefer to share information. The firms’ incentives to share information differ according to the degree of product differentiation and the proportion of expensive customers in the market. When firms sell moderately substitutable products and the proportion of expensive customers is high, a Prisoner’s Dilemma results. The competing firms unilaterally benefit from sharing information, but the benefits from reneging on an information-sharing agreement are even higher; paradoxically, in equilibrium, both firms therefore keep their information private. A third-party agency such as an industry trade association might serve to supervise and coordinate information-sharing agreements between competing firms.
This paper also establishes that information sharing decreases the welfare of expensive customers but increases that of inexpensive customers. Privacy laws thus protect expensive customers more than inexpensive customers. In certain conditions, total consumer welfare might increase with information sharing about expensive customers. This research recommends relatively weaker, not stronger, privacy laws, which is counterintuitive to the recommendations of the popular press.

Keywords: Customer knowledge, Expensive customers, Information sharing, Trade association, Privacy laws, Game theory