Price competing firms

This paper preserves all main features of oligopolistic price competition in the Bertrand (1883) setting but the assumption of consumers' always paying the lowest price. Instead, our model allows for the possibility of consumers choosing stochastically (e.g., due to random errors, unobserved attributes/heterogeneity, or inertia in changing shopping habits). This allows us to derive a linear in log differences demand function, which is the only demand function satisfying anonymity (fair price competition, i.e., firms charging the same price face the same demand), independence of irrelevant prices and homogeneity of degree zero (quoting prices in cents rather than dollars does not affect the market). Arguably, the paper has pedagogical value based on the model's simplicity and intuitive comparative statics (our symmetric pure strategy Nash equilibrium lies between perfect competition and monopoly).