On competitive sequential location in a network with a decreasing demand intensity

We introduce and analyze a Hotelling like game wherein players can locate in a city, at a fixed cost, according to an exogenously given order. Demand intensity is assumed to be strictly decreasing in distance and players locate in the city as long as it is profitable for them to do so. For a linear city (i) we explicitly determine the number of players who will locate in equilibrium, (ii) we fully characterize and compute the unique family of equilibrium locations, and (iii) we show that players' equilibrium expected profits decline in their position in the order. Our results are then extended to a city represented by an undirected weighted graph whose edge lengths are not too small and co-location on nodes of the graph is not permitted. Further, we compare the equilibrium outcomes with the optimal policy of a monopolist who faces an identical problem and who needs to decide upon the number of stores to open and their locations in the city so as to maximize total profit.

[1]  Oded Berman,et al.  Locating Multiple Competitive Facilities: Spatial Interaction Models with Variable Expenditures , 2002, Ann. Oper. Res..

[2]  W. J. Lane.  Product Differentiation in a Market with Endogenous Sequential Entry , 1980 .

[3]  Steffen Brenner.  Hotelling Games with Three, Four, and More Players , 2005 .

[4]  Z. Drezner.  Note-On a Modified One-Center Model , 1981 .

[5]  S. Hakimi.  p-Median theorems for competitive locations , 1986 .

[6]  S. Hakimi.  On locating new facilities in a competitive environment , 1983 .

[7]  Pierre Hansen,et al.  Algorithms for Voting and Competitive Location on a Network , 1988, Transp. Sci..

[8]  H. Hotelling.  Stability in Competition , 1929 .

[9]  Simon P. Anderson.  Equilibrium existence in the linear model of spatial competition , 1988 .

[10]  R. Lipsey,et al.  The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition , 1975 .

[11]  Charles ReVelle,et al.  Competitive Location and Pricing on Networks , 1999 .

[12]  Nobuo Matsubayashi,et al.  Strategic multi-store opening under financial constraint , 2011, Eur. J. Oper. Res..

[13]  Hubert Beguin,et al.  Private versus public service location behaviour , 1991 .

[14]  N. Megiddo,et al.  The Maximum Coverage Location Problem , 1983 .

[15]  Z. Drezner.  Competitive location strategies for two facilities , 1982 .

[16]  M. Teitz.  LOCATIONAL STRATEGIES FOR COMPETITIVE SYSTEMS , 1968 .

[17]  N. Economides.  Minimal and maximal product differentiation in Hotelling's duopoly , 1986 .

[18]  Damien J. Neven,et al.  Endogenous sequential entry in a spatial model , 1987 .

[19]  Gilbert Laporte,et al.  Location and Pricing Decisions of a Multistore Monopoly in a Spatial Market , 2004 .

[20]  Jacques-François Thisse,et al.  On hotelling's "Stability in competition" , 1979 .

[21]  Georg Götz.  Endogenous sequential entry in a spatial model revisited , 2005 .

[22]  Uday S. Karmarkar,et al.  Production , Manufacturing and Logistics Competitive location , production , and market selection , 2003 .

[23]  Lawrence Kryzanowski,et al.  Alternative specifications of the errors in the Black-Scholes option-pricing model and various implied-variance formulas , 1986 .

[24]  Yu Xia,et al.  Competitive strategies and market segmentation for suppliers with substitutable products , 2011, Eur. J. Oper. Res..

[25]  E. Prescott,et al.  Sequential location among firms with foresight , 1977 .

[26]  Gilbert Laporte,et al.  Sequential location problems , 1997 .

[27]  Hussein Naseraldin,et al.  Integrating the Number and Location of Retail Outlets on a Line with Replenishment Decisions , 2008, Manag. Sci..

[28]  Nicholas Economides,et al.  Does it Pay to Be First? Sequential Locational Choice and Foreclosure , 2002 .