Instability in the Hotelling’s Non-Price Spatial Competition Model

Yosuke Yasuda

National Graduate Institute for Policy Studies, Tokyo, Japan.

DOI: 10.4236/tel.2013.33A002                

Abstract

This note analyzes a slightly modified Hotelling model in which two firms are allowed to choose multiple store locations. Each firm can endogenously choose the number of stores while opening a store incurs a set-up cost. We show that the principle of minimum differentiation, i.e., both firms open a store each on the center, never holds when the set-up cost is decreasing in the number of stores. Under general cost functions that include non-linear and asymmetric set up costs, we characterize the conditions under which the principle holds. General payoff functions that are non-linear in the market share are also considered.

Keywords

Hotelling Model; Multiple Locations; The Principle of Minimization

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	H. Hotelling, “Stability in Competition,” Economic Journal, Vol. 39, No. 153, 1929, pp. 41-57. doi:10.2307/2224214
[2]	B. C. Eaton and R. G. Lipsey, “Product Differentiation,” In: R. Schmalensee and R. D. Willig, Eds., Handbook of Industrial Organization, Volume I, Elsevier Science Publishers, Amsterdam, 1989, pp. 723-768. doi:10.1016/S1573-448X(89)01015-0
[3]	J. J. Gabszewicz and J.-F. Thisse, “Location,” In: R. J., Aumann and S. Hart, Eds., Handbook of Game Theory with Economic Applications, Volume I, Elsevier Science Publishers, 1992, pp. 281-304.
[4]	A. Downs, “An Economic Theory of Political Action in a Democracy,” Journal of Political Economy, Vol. 65, No. 2, 1957, pp. 135-150. doi:10.1086/257897
[5]	D. Pal and J. Sarkar, “Spatial Competition among Multi-Store Firms,” International Journal of Industrial Organization, Vol. 20, No. 2, 2002, pp. 163-190. doi:10.1016/S0167-7187(00)00080-1
[6]	M. B. Teitz, “Locational Strategies for Competitive Systems,” Journal of Regional Science, Vol. 8, No. 2, 1968, pp. 135-148. doi:10.1111/j.1467-9787.1968.tb01319.x
[7]	X. Martinez-Giralt and D. J. Neven, “Can Price Competition Dominate Market Segmentation?” Journal of Industrial Economics, Vol. 36, No. 4, 1988, pp. 431-442. doi:10.2307/2098448
[8]	M. C. W. Janssen, V. A. Karamychev and P. Van Reeven, “Multi-Store Competition: Market Segmentation or Interlacing?” Regional Science and Urban Economics, Vol. 35, No. 6, 2005, pp. 700-714. doi:10.1016/j.regsciurbeco.2004.12.002
[9]	S.-K. Peng and T. Tabuchi, “Spatial Competition in Variety and Number of Stores,” Journal of Economics and Management Strategy, Vol. 16, No. 1, 2007, pp. 227-250. doi:10.1111/j.1530-9134.2007.00138.x
[10]	J. J. Gabszewicz and J.-F. Thisse, “Spatial Competition and The Location of Firms,” In: J. J. Gabszewicz, J.-F., Thisse, M. Fujita and U. Schweizer, Eds., Location Theory, Harwood Academic Publishers GmbH, Newark, 1986, pp. 1-71.