We show that the Varian model of sales with more than two firms has two types of equilibria: a unique symmetric equilibrium, and a continuum of asymmetric equilibria. In contrast, the 2-firm game has a unique equilibrium that is symmetric. For the n-firm case the asymmetric equilibria imply mixed strategies that can be ranked by first-order stochastic dominance. This enables one to rule out asymmetric equilibria on economic grounds by constructing a metagame in which both firms and consumers are players. The unique subgame perfect equilibrium of this metagame is symmetric.

doi.org/10.1016/0899-8256(92)90033-O, hdl.handle.net/1765/12422
Games and Economic Behavior
Erasmus School of Economics

Baye, M.R, Kovenock, D, & de Vries, C.G. (1992). It takes two to tango: Equilibria in a model of sales. Games and Economic Behavior, 493–510. doi:10.1016/0899-8256(92)90033-O