Spying in Bertrand Markets Under Incomplete Information: Who Benefits and Is It Stable?

Abstract

We analyze spying out a rival’s price in a general duopoly model with differentiated prod- ucts where payoff functions are strictly supermodular and firms are subject to incomplete information about costs. Spying has two effects: it induces a sequential game and eliminates the spying firm’s uncertainty. In sharp contrast to the case of complete information, spying does not benefit both firms: it adversely affects the spied-at firm if its cost is low and may expose the spying firm to a negative value of information. We decompose the impact of spy- ing into its sequential moves effect and its information effect and find conditions for profitable espionage. We also show that the spied-at firm cannot benefit from bypassing the spy if its cost is low by delaying its pricing decision (or firing the spy) because this would trigger a devastating cascade of belief changes.