Limited memory, categorization, and competition

This paper investigates the effects of a limited consumer memory on the price competition between firms. It studies a specific aspect of memory–namely, the categorization of available price information that the consumers may need to recall for decision making. This paper analyzes competition between firms in a market with uninformed consumers who do not compare prices, informed consumers who compare prices but with limited memory, and informed consumers who have perfect memory. Consumers, aware of their memory limitations, choose how to encode the prices into categories, whereas firms take the limitations of consumers into account in choosing their pricing strategies. Two distinct types of categorization processes are investigated: (1) a symmetric one in which consumers compare only the labels of price categories from the competing firms and (2) an asymmetric one in which consumers compare the recalled price of one firm with the actual price of the other. We find that the equilibrium partition for the consumers calls for finer categorization toward the bottom of the price distribution. Thus consumers have a motivation to invest in greater memory resources in encoding lower prices to induce firms to charge more favorable prices. The interaction between the categorization strategies of the consumers and the price competition between the firms is such that small initial improvements in recall move the market outcomes quickly toward the case of perfect recall. Even with few memory categories, the expected price consumers pay and their surplus is close to the case of perfect recall. There is thus a suggestion in this model that market competition adjusts to the memory limitations of consumers.