A theoretical foundation for the undercut-proof equilibrium

Abstract

This paper develops a theoretical foundation for the undercut-proof equilibrium (see Shy, 1996, 2002; Morgan and Shy, 2015). In a general spatial setting, the set of undercut-proof prices is equivalent to the core of a non-transferable utility coalitional-game, played on the set of outcomes that are feasible in Bertrand competition. The result depends critically on two conditions: First, firms must have unlimited capacity and constant marginal costs. Second, the goods produced by firms must only be differentiated by the spatial characteristics of the market. An application to network markets shows how the undercut-proof equilibrium can be used to describe stable price dispersion and persistent performance differences.