| Summary: | We study a canonical model of simultaneous price competition between firms that
sell a homogeneous good to consumers who are characterized by the number of
prices they are exogenously aware of. Our setting subsumes many employed in the
literature over the last several decades. We show there is a unique equilibrium if
and only if there exist some consumers who are aware of exactly two prices. The
equilibrium we derive is in symmetric mixed strategies. Furthermore, when there
are no consumers aware of exactly two prices, we show there is an uncountableinfinity of asymmetric equilibria in addition to the symmetric equilibrium. Our
results show the paradigm generically produces a unique equilibrium. We also show
that the commonly-sought symmetric equilibrium (which also nests the textbook
Bertrand pure strategy equilibrium as a special case) is robust to perturbations in
consumer behavior, while the asymmetric equilibria are not. (JEL: D43, L11)
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