Price–Quantity Competition in a Duopoly Market With Price Similarities

We introduce a form of consumers' bounded rationality, price similarities, in a duopoly market with price–quantity competition. Price similarities occur when consumers do not react to slight differences in prices. In this case, firms' demands are determined by a sharing rule that depends on the quantities produced. Assuming a general form of the proportional sharing rule, we show that a pure strategy Nash equilibrium for the price–quantity game materializes if, and only if, price similarities are in place. We also show that there are two kinds of equilibrium. In the first kind, total supply equals total demand. By contrast, in the second kind, firms overproduce. Finally, we show how to compute the minimum level of the price similarities phenomenon necessary to ensure equilibrium existence given the market conditions.