This paper studies the behavior of competing firms in a duopoly with rational inattentive con- sumers. Firms play a sequential game in which they decide to obfuscate their individual prices before competing on price. Probabilistic demand functions are endogenously determined by the consumers’ optimal information strategy, which depends on the firms’ obfuscation choice and the consumers’ unrestricted prior beliefs. We show that the game may result in an obfuscation equilibrium with high prices where both firms obfuscate and a transparency equilibrium with low prices and no ob- fuscation, providing an argument for market regulation. Lower information costs and asymmetric prior beliefs about prices reduce the probability of an obfuscation equilibrium. Using data on Swe- den, we document a decrease in price complexity and corresponding prices in the market for mobile phone subscriptions in the last two decades. Our model rationalizes these changes and explains why complexity and high prices persist in some but not all digitalized markets.
SAFE Working Paper No. 306