Pricing with bargain hunting consumers

A single-product retailer faces bargain hunting consumers whose willingness to pay incorporates sensations of gain and loss driven by differences between the observed price and prices they rationally expect in the spirit of Koszegi and Rabin (2006). We examine the Bayesian Nash equilibrium (non-commitment) pricing solution in which (i) the retailer maximizes profit given consumers' beliefs and (ii) consumers' beliefs are consistent with the retailer's choice. We show two novel results: First, a pure-strategy, uniform-price, equilibrium does not exist when consumers are bargain hunters who value gains more than losses. Second, in this case there exists a mixed strategy equilibrium and all mixed strategy equilibria involve the same retailer profit. The equilibrium retailer profit is (weakly) lower than in the absence of reference effects.