Price Competition over Boundedly Rational Agents

We develop a model to study market interaction between rational firms on one side of the market and boundedly rational consumers on the other. A special feature of bounded rationality is modelled here: from psychological evidence, people tend to group events or numbers into categories; therefore we consider consumers who partition the price space into connected sets and regard each price belonging to the same set as equal. According to Rubinstein (1993), we endogenize the choice of the price partition by consumers, who determine the optimal price partition given the constraint imposed on their ability to process information on prices. We develop a model with two firms and two states of nature. We show that we depart from classical Bertrand result when consumers are characterized by a bound on the finiteness of price partition inferior to the cardinality of the space of world states. In other words, in presence of consumers who can partition the price space into two sets and with two states of the world, firms find optimal to set price above marginal cost, making positive profits. The intuition of the result can be explained as follows: when a consumer chooses the price partition, she faces a trade off between the detection of the state of nature and the detection of a deviating behavior of the firm in a given state of nature.