Nash versus consistent equilibrium: A comparative perspective on a mixed duopoly location model of spatial price discrimination with delegation

Abstract

We argue that under the presence of a public firm, discriminatory pricing according to location leads to an efficient consistent equilibrium. We consider a mixed ownership duopoly delegation model with spatial price discrimination and constant, albeit different, marginal production costs. In contrast to what holds true for a private duopoly, we prove that the Nash equilibrium, absent delegation, is both consistent and socially optimal. The consistent equilibrium remains socially optimal regardless of the order in the delegation process. Under Nash conjectures, in most cases, firm owners have a strong incentive to delegate location decisions to managers. In such cases, duopolists locate closer to each other. Nash, compared to consistency of conjectures, leads to lower prices, lower profits, for both firms, and increased surplus for the consumer. The result surprises as it contrasts with respective findings regarding a private duopoly.