Local market structure in a Hotelling town

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January 2016, 3(1): 75-100. doi: 10.3934/jdg.2016004

Local market structure in a Hotelling town

Alberto A. Pinto ^1, , João P. Almeida ^2, and Telmo Parreira ^3,

1.	LIAAD INESC TEC and Department of Mathematics, Faculty of Sciences, University of Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
2.	LIAAD-INESC TEC and Polytechnic Institute of Bragança, Campus de Santa Apolónia, 5300-253 Bragança, Portugal
3.	Department of Mathematics, University of Minho, Campus de Gualtar Braga, Portugal

Received October 2015 Revised January 2016 Published March 2016

Abstract
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We develop a theoretical framework to study the location-price competition in a Hotelling-type network game, extending the Hotelling model, with linear transportation costs, from a line (city) to a network (town). We show the existence of a pure Nash equilibrium price if, and only if, some explicit conditions on the production costs and on the network structure hold. Furthermore, we prove that the local optimal localization of the firms are at the cross-roads of the town.

Keywords: game theory, oligopoly models., networks, price competition, Hotelling model.

Mathematics Subject Classification: Primary: 91A43, 91A06; Secondary: 91A80, 91A4.

Citation: Alberto A. Pinto, João P. Almeida, Telmo Parreira. Local market structure in a Hotelling town. Journal of Dynamics and Games, 2016, 3 (1) : 75-100. doi: 10.3934/jdg.2016004

References:

[1]	V. Aguirregabiria and G. Vicentini, Dynamic spatial competition between multi-store firms, mimeo., (2015).
[2]	C. D'Aspermont, J. Gabszewicz and J. F. Thisse, On Hotelling's "Stability in competition'', Econometrica, 47 (1979), 1145-1150. doi: 10.2307/1911955.
[3]	F. Bloch and N. Quérou, Pricing in social networks, Games Econom. Behav., 80 (2013), 243-261. doi: 10.1016/j.geb.2013.03.006.
[4]	Y. Bramoullé, R. Kranton and M. D'Amours, Strategic interaction and networks, American Economic Review, 104 (2012), 898-930.
[5]	T. H. Colding and W. P. Minicozzi, Minimal Surfaces, Courant Lecture Notes in Math, (1999).
[6]	Y. Chen and M. H. Riordan, Price and variety in the spokes model, Economic Journal, Royal Economic Society, 117 (2007), 897-921. doi: 10.1111/j.1468-0297.2007.02063.x.
[7]	G. Fournier and M. Scarsini, Hotelling's Games on Networks: Efficiency of Equilibria, Centre d'Economie de la Sorbone, 2014.
[8]	A. Galeotti, S. Goyal and M. Jackson and F. Vega-Redondo and L. Yariv, Network games, The Review of Economic Studies, 77 (2010), 218-244. doi: 10.1111/j.1467-937X.2009.00570.x.
[9]	A. Galeotti and F. Vega-Redondo, Complex networks and local externalities: A strategic approach, International Journal of Economic Theory, 7 (2011), 77-92. doi: 10.1111/j.1742-7363.2010.00149.x.
[10]	S. Goyal, Connections: An introduction to the Economics of Networks, Princeton University Press, (2007).
[11]	R. Gulliver, Removability of singular points on surfaces of bounded mean curvature, The Journal of Differential Geometry, 11 (1976), 345-350.
[12]	D. Graitson, Spatial competition á la Hotelling: A selective survey, The Journal of Industrial Economics, 31 (1982), 11-25. doi: 10.2307/2098001.
[13]	H. Hotelling, Stability in competition, The Economic Journal, 39 (1929), 41-57.
[14]	M. Jorge and W. Maldonado, Price Differentiation and Menu Costs in Credit Card Payments, ANU Working Papers in Economics and Econometrics 2012-592, Australian National University, college of business and economics, school of economics, (2012).
[15]	V. Mazalov and M. Sakaguchi, Location game on the plane, International Game Theory Review, 5 (2003), 13-25. doi: 10.1142/S0219198903000854.
[16]	T. Miller, R. L. Tobin and T. L. Friesz, Network facility-location models in stackelberg-nash-cournot spatial competition, Papers in Regional Science, 71 (1992), 277-291.
[17]	M. J. Osborne and C. Pitchick, Equilibrium in hotelling's model of spatial competition, Econometrica, 55 (1987), 911-922. doi: 10.2307/1911035.
[18]	D. Palvogyi, Hotelling on graphs, mimeo, 2011.
[19]	A. A. Pinto and T. Parreira, A hotelling-type network, in Dynamics, Games and Science I. (Eds. M. Peixoto, A. Pinto and D. Rand), Proceedings in Mathematics Series, Springer-Verlag, 1 (2011), 709-720. doi: 10.1007/978-3-642-11456-4_45.
[20]	A. A. Pinto and T. Parreira, Optimal localization of firms in Hotelling networks, in Modeling, Dynamics, Optimization and Bioeconomy I (Eds. A.A. Pinto and D. Zilberman). Springer Proceedings in Mathematics and Statistics series, Springer-Verlag, 73 (2014), 567-583. doi: 10.1007/978-3-319-04849-9_2.
[21]	A. A. Pinto and T. Parreira, Complete versus incomplete information in the Hotelling model, in Modeling, Dynamics, Optimization and Bioeconomy I (Eds. A.A. Pinto and D. Zilberman). Springer Proceedings in Mathematics and Statistics series, Springer-Verlag, 73 (2014), 17-22. doi: 10.1007/978-3-319-04849-9_33.
[22]	A. A. Pinto and T. Parreira, Maximal differentiation in the Hotelling model with uncertainty, in Modeling, Dynamics, Optimization and Bioeconomy I (Eds. A.A. Pinto and D. Zilberman). Springer Proceedings in Mathematics and Statistics series, Springer-Verlag, 73 (2014), 585-600. doi: 10.1007/978-3-319-04849-9_34.
[23]	A. A. Pinto and T. Parreira, Price competition in the Hotelling model with uncertainty on costs, Optimization: A Journal of Mathematical Programming and Operations Research, 64 (2015), 2477-2493. doi: 10.1080/02331934.2014.917304.
[24]	A. A. Pinto, Game theory and duopoly models,, in preparation., ().
[25]	S. Salop, Monopolistic competition with outside goods, Bell Journal of Economics, 10 (1979), 141-156. doi: 10.2307/3003323.
[26]	A. Soetevent, Price Competition on Graphs, Tinbergen Institute Discussion Papers 10-126/1, (2010).
[27]	T. Tabuchi and J. F. Thisse, Asymmetric equilibria in spatial competition, International Journal of Economic Theory, 13 (1995), 213-227. doi: 10.1016/0167-7187(94)00449-C.

show all references

References:

[1]	V. Aguirregabiria and G. Vicentini, Dynamic spatial competition between multi-store firms, mimeo., (2015).
[2]	C. D'Aspermont, J. Gabszewicz and J. F. Thisse, On Hotelling's "Stability in competition'', Econometrica, 47 (1979), 1145-1150. doi: 10.2307/1911955.
[3]	F. Bloch and N. Quérou, Pricing in social networks, Games Econom. Behav., 80 (2013), 243-261. doi: 10.1016/j.geb.2013.03.006.
[4]	Y. Bramoullé, R. Kranton and M. D'Amours, Strategic interaction and networks, American Economic Review, 104 (2012), 898-930.
[5]	T. H. Colding and W. P. Minicozzi, Minimal Surfaces, Courant Lecture Notes in Math, (1999).
[6]	Y. Chen and M. H. Riordan, Price and variety in the spokes model, Economic Journal, Royal Economic Society, 117 (2007), 897-921. doi: 10.1111/j.1468-0297.2007.02063.x.
[7]	G. Fournier and M. Scarsini, Hotelling's Games on Networks: Efficiency of Equilibria, Centre d'Economie de la Sorbone, 2014.
[8]	A. Galeotti, S. Goyal and M. Jackson and F. Vega-Redondo and L. Yariv, Network games, The Review of Economic Studies, 77 (2010), 218-244. doi: 10.1111/j.1467-937X.2009.00570.x.
[9]	A. Galeotti and F. Vega-Redondo, Complex networks and local externalities: A strategic approach, International Journal of Economic Theory, 7 (2011), 77-92. doi: 10.1111/j.1742-7363.2010.00149.x.
[10]	S. Goyal, Connections: An introduction to the Economics of Networks, Princeton University Press, (2007).
[11]	R. Gulliver, Removability of singular points on surfaces of bounded mean curvature, The Journal of Differential Geometry, 11 (1976), 345-350.
[12]	D. Graitson, Spatial competition á la Hotelling: A selective survey, The Journal of Industrial Economics, 31 (1982), 11-25. doi: 10.2307/2098001.
[13]	H. Hotelling, Stability in competition, The Economic Journal, 39 (1929), 41-57.
[14]	M. Jorge and W. Maldonado, Price Differentiation and Menu Costs in Credit Card Payments, ANU Working Papers in Economics and Econometrics 2012-592, Australian National University, college of business and economics, school of economics, (2012).
[15]	V. Mazalov and M. Sakaguchi, Location game on the plane, International Game Theory Review, 5 (2003), 13-25. doi: 10.1142/S0219198903000854.
[16]	T. Miller, R. L. Tobin and T. L. Friesz, Network facility-location models in stackelberg-nash-cournot spatial competition, Papers in Regional Science, 71 (1992), 277-291.
[17]	M. J. Osborne and C. Pitchick, Equilibrium in hotelling's model of spatial competition, Econometrica, 55 (1987), 911-922. doi: 10.2307/1911035.
[18]	D. Palvogyi, Hotelling on graphs, mimeo, 2011.
[19]	A. A. Pinto and T. Parreira, A hotelling-type network, in Dynamics, Games and Science I. (Eds. M. Peixoto, A. Pinto and D. Rand), Proceedings in Mathematics Series, Springer-Verlag, 1 (2011), 709-720. doi: 10.1007/978-3-642-11456-4_45.
[20]	A. A. Pinto and T. Parreira, Optimal localization of firms in Hotelling networks, in Modeling, Dynamics, Optimization and Bioeconomy I (Eds. A.A. Pinto and D. Zilberman). Springer Proceedings in Mathematics and Statistics series, Springer-Verlag, 73 (2014), 567-583. doi: 10.1007/978-3-319-04849-9_2.
[21]	A. A. Pinto and T. Parreira, Complete versus incomplete information in the Hotelling model, in Modeling, Dynamics, Optimization and Bioeconomy I (Eds. A.A. Pinto and D. Zilberman). Springer Proceedings in Mathematics and Statistics series, Springer-Verlag, 73 (2014), 17-22. doi: 10.1007/978-3-319-04849-9_33.
[22]	A. A. Pinto and T. Parreira, Maximal differentiation in the Hotelling model with uncertainty, in Modeling, Dynamics, Optimization and Bioeconomy I (Eds. A.A. Pinto and D. Zilberman). Springer Proceedings in Mathematics and Statistics series, Springer-Verlag, 73 (2014), 585-600. doi: 10.1007/978-3-319-04849-9_34.
[23]	A. A. Pinto and T. Parreira, Price competition in the Hotelling model with uncertainty on costs, Optimization: A Journal of Mathematical Programming and Operations Research, 64 (2015), 2477-2493. doi: 10.1080/02331934.2014.917304.
[24]	A. A. Pinto, Game theory and duopoly models,, in preparation., ().
[25]	S. Salop, Monopolistic competition with outside goods, Bell Journal of Economics, 10 (1979), 141-156. doi: 10.2307/3003323.
[26]	A. Soetevent, Price Competition on Graphs, Tinbergen Institute Discussion Papers 10-126/1, (2010).
[27]	T. Tabuchi and J. F. Thisse, Asymmetric equilibria in spatial competition, International Journal of Economic Theory, 13 (1995), 213-227. doi: 10.1016/0167-7187(94)00449-C.

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