A theoretical foundation for the undercut-proof equilibrium

This paper develops a theoretical foundation for the undercut-proof equilibrium (see Shy, 1996, 2002; Morgan and Shy, 2013). In a general spatial setting, the set of undercut-proof prices is equivalent the core of a non-transferable utility cooperative-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. Examples on the Hotelling line and network markets show how the undercut-proof equilibrium can be used to describe stable price dispersion and persistent performance differences.