The timing of consumer arrivals in Edgeworth's duopoly model
In his classic Papers relating to Political Economy (1897), Francis Edgeworth demonstrated that when duopolists have limited productive capacity, there may be no Nash equilibrium in prices. One feature of Edgeworth's model is that consumers are assumed to meet with the duopolists at the same time. ; This paper analyzes a version of the Edgeworth model in which consumers arrive sequentially instead of simultaneously. This departure from Edgeworth's framework should seem reasonable since there are few markets besides auctions in which buyers all meet with sellers at the same time. ; The point of the analysis is to show that when sellers engage in quantity constrained price competition, the timing of consumer arrivals may greatly affect the nature of equilibrium. It turns out that the existence of Nash equilibrium in prices may be restored. It also turns out that the duopolists may be able to maximize joint profits!
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- Levitan, Richard & Shubik, Martin, 1972.
"Price Duopoly and Capacity Constraints,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-22, February.
- William A. Brock & José A. Scheinkman, 1985. "Price Setting Supergames with Capacity Constraints," Review of Economic Studies, Oxford University Press, vol. 52(3), pages 371-382.
- Grossman, Sanford J, 1981. "Nash Equilibrium and the Industrial Organization of Markets with Large Fixed Costs," Econometrica, Econometric Society, vol. 49(5), pages 1149-72, September.
- Peters, Michael, 1984. "Bertrand Equilibrium with Capacity Constraints and Restricted Mobility," Econometrica, Econometric Society, vol. 52(5), pages 1117-27, September.
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