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The only Dance in Town: Unique Equilibrium in a Generalized Model of Price Competition *
Author(s) -
Johnen Johannes,
Ronayne David
Publication year - 2021
Publication title -
the journal of industrial economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.93
H-Index - 77
eISSN - 1467-6451
pISSN - 0022-1821
DOI - 10.1111/joie.12264
Subject(s) - uncountable set , homogeneous , symmetric equilibrium , competition (biology) , economics , infinity , mathematical economics , microeconomics , mathematics , equilibrium selection , game theory , repeated game , pure mathematics , combinatorics , ecology , mathematical analysis , countable set , biology
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.