Spying in Bertrand markets under incomplete information: Who benefits and is it stable?

We analyze spying out a rival’s price in a general duopoly model with differentiated products 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 spying 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.