The only Dance in Town: Unique Equilibrium in a Generalized Model of Price Competition*

Abstract

We study a model of simultaneous price competition that subsumes many employed in the literature over the last several decades. Firms sell a homogeneous good to consumers characterized by the number of prices they (exogenously) consider. We show there is a unique equilibrium if and only if some consumers consider exactly two prices. The equilibrium is in symmetric mixed strategies. When no consumer considers exactly two prices, there is, in addition, an uncountable infinity of asymmetric equilibria. Our results show that the paradigm generically produces a unique equilibrium, and only the commonly sought symmetric equilibrium is robust to perturbations in consumer behavior.

When do Co‐located Firms Selling Identical Products Thrive?*

“…Because some consumers know the prices at both cluster stores, there is a unique Perfect Bayesian equilibrium (Baye et al . [1992]; Johnen and Ronayne [2019]). In equilibrium, co‐located stores employ the same pricing strategy $$$ F(p) $$$, and non‐shoppers are equally likely to visit each co‐located store.…”