The only dance in town: unique equilibrium in a generalized model of price competition

Working paper

We study a canonical model of simultaneous price competition between firms thatWe study a canonical model of simultaneous price competition between firms thatsell a homogeneous good to consumers who are characterized by the number ofprices they are exogenously aware of. Our setting subsumes many employed in theliterature over the last several decades. We show there is a unique equilibrium ifand only if there exist some consumers who are aware of exactly two prices. Theequilibrium we derive is in symmetric mixed strategies. Furthermore, when thereare no consumers aware of exactly two prices, we show there is an uncountableinfinityof asymmetric equilibria in addition to the symmetric equilibrium. Ourresults show the paradigm generically produces a unique equilibrium. We also showthat the commonly-sought symmetric equilibrium (which also nests the textbookBertrand pure strategy equilibrium as a special case) is robust to perturbations inconsumer behavior, while the asymmetric equilibria are not. Revised March 2020.

Authors: Ronayne, D

• Publication status: Published
• Publisher: University of Oxford
• Series: Department of Economics Discussion Paper Series
• Publication date: 2020-04-07
• Paper number: 874
• Keywords: price dispersion; price competition; unique equilibrium