Spatial Competition With Incomplete InformationWorking paper E95-49, first version December 1993, first online version March 1996, Last modified 30 March 1998, comments are welcome, do not quote.
Department of Economics, 3016 Pamplin Hall
Dziepak "at" vt "dot" edu
Abstract: A location model is examined in which consumers have incomplete information about prices. Two firms are located in a unit line with a uniform distribution of consumers, possessing unitary demand. The consumers must walk to a firm (incurring a sunk cost) to obtain full information about prices. After reaching a firm, the consumer decides from which firm to purchase.
The following results are obtained: There exists a pure strategies price equilibrium for location pairs that are not too close nor too far apart. Also, all such equilibria exhibit locational asymmetry and price dispersion. There is no pure strategies equilibrium in locations and prices; however, conditions are such that mixed strategies equilibria exist. Also, if firms are given the option to costlessly reveal prices to customers, the lower-priced firm will reveal its price when firms are sufficiently far apart. Finally, in a unit circle market space, no pure strategies price equilibrium exists because there are no asymmetric locations possible on a unit circle.
*I am grateful to Amoz Kats, Mamoru Kaneko, and Helmuth Cremer for comments.