Econometrica: Sep 1984, Volume 52, Issue 5

Bertrand Equilibrium with Capacity Constraints and Restricted Mobility

https://doi.org/0012-9682(198409)52:5<1117:BEWCCA>2.0.CO;2-P
p. 1117-1128

Michael Peters

This paper considers price competition among firms when there are capacity constraints and buyers have limited ability to visit firms. A natural method of allocating buyers among firms arises in the equilibrium of the buyers' search game. Sufficient conditions are given under which the buyers' equilibrium varies continuously with the prices charged by firms. Capacity constraints are used to guarantee that this ensures existence of (mixed strategy) equilibria for the pricing game played by sellers. We show that natural pure strategy equilibria arise when the game is made large in appropriate ways.

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