Oligopoly and Luce's Choice Axiom

We apply Luce's choice axiomatic framework to oligopoly pricing of quality differentiated goods. The demand system is a probabilistic comparison of surpluses across products. Zero demands arise naturally, in contrast to the related CES and Mixed Logit models. With asymmetric products, high mark-ups and high demands are driven by high quality-costs. The oligopoly price equilibrium delivers a simple surplus–split property. We reconcile the model with standard consumer theory by introducing income, and hence generate a representative consumer formulation, which has a quadratic form in a central case. We further introduce a preference representation based on the Gabszewicz–Thisse vertical quality formulation.