Information, Bertrand–Edgeworth competition and the law of one price

Abstract

Homogeneous goods often sell at different prices within the same market. This paper proposes a theoretical foundation for this phenomenon in the context of a capacity-constrained price game. Sellers have asymmetric information about the market demand, modelled by a partition of the state space, and evaluate uncertain profits in a way consistent with ambiguity aversion. We demonstrate that a pure strategy price equilibrium exists if the market demand is uniformly elastic in each state. Interestingly, the sellers may choose different prices, violating the law of one price. Moreover, market demand may be rationed between the sellers, resulting in consumers purchasing at different prices.