American Institute of Mathematical Sciences

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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

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 & 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). Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[4]

Y. Bramoullé, R. Kranton and M. D'Amours, Strategic interaction and networks, American Economic Review, 104 (2012), 898-930. Google Scholar

[5]

T. H. Colding and W. P. Minicozzi, Minimal Surfaces, Courant Lecture Notes in Math, (1999). Google Scholar

[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.  Google Scholar

[7]

G. Fournier and M. Scarsini, Hotelling's Games on Networks: Efficiency of Equilibria, Centre d'Economie de la Sorbone, 2014. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[10]

S. Goyal, Connections: An introduction to the Economics of Networks, Princeton University Press, (2007).  Google Scholar

[11]

R. Gulliver, Removability of singular points on surfaces of bounded mean curvature, The Journal of Differential Geometry, 11 (1976), 345-350.  Google Scholar

[12]

D. Graitson, Spatial competition á la Hotelling: A selective survey, The Journal of Industrial Economics, 31 (1982), 11-25. doi: 10.2307/2098001.  Google Scholar

[13]

H. Hotelling, Stability in competition, The Economic Journal, 39 (1929), 41-57. Google Scholar

[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). Google Scholar

[15]

V. Mazalov and M. Sakaguchi, Location game on the plane, International Game Theory Review, 5 (2003), 13-25. doi: 10.1142/S0219198903000854.  Google Scholar

[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. Google Scholar

[17]

M. J. Osborne and C. Pitchick, Equilibrium in hotelling's model of spatial competition, Econometrica, 55 (1987), 911-922. doi: 10.2307/1911035.  Google Scholar

[18]

D. Palvogyi, Hotelling on graphs, mimeo, 2011. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[24]

A. A. Pinto, Game theory and duopoly models,, in preparation., ().   Google Scholar

[25]

S. Salop, Monopolistic competition with outside goods, Bell Journal of Economics, 10 (1979), 141-156. doi: 10.2307/3003323.  Google Scholar

[26]

A. Soetevent, Price Competition on Graphs, Tinbergen Institute Discussion Papers 10-126/1, (2010). Google Scholar

[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.  Google Scholar

show all references

References:
[1]

V. Aguirregabiria and G. Vicentini, Dynamic spatial competition between multi-store firms, mimeo., (2015). Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[4]

Y. Bramoullé, R. Kranton and M. D'Amours, Strategic interaction and networks, American Economic Review, 104 (2012), 898-930. Google Scholar

[5]

T. H. Colding and W. P. Minicozzi, Minimal Surfaces, Courant Lecture Notes in Math, (1999). Google Scholar

[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.  Google Scholar

[7]

G. Fournier and M. Scarsini, Hotelling's Games on Networks: Efficiency of Equilibria, Centre d'Economie de la Sorbone, 2014. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[10]

S. Goyal, Connections: An introduction to the Economics of Networks, Princeton University Press, (2007).  Google Scholar

[11]

R. Gulliver, Removability of singular points on surfaces of bounded mean curvature, The Journal of Differential Geometry, 11 (1976), 345-350.  Google Scholar

[12]

D. Graitson, Spatial competition á la Hotelling: A selective survey, The Journal of Industrial Economics, 31 (1982), 11-25. doi: 10.2307/2098001.  Google Scholar

[13]

H. Hotelling, Stability in competition, The Economic Journal, 39 (1929), 41-57. Google Scholar

[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). Google Scholar

[15]

V. Mazalov and M. Sakaguchi, Location game on the plane, International Game Theory Review, 5 (2003), 13-25. doi: 10.1142/S0219198903000854.  Google Scholar

[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. Google Scholar

[17]

M. J. Osborne and C. Pitchick, Equilibrium in hotelling's model of spatial competition, Econometrica, 55 (1987), 911-922. doi: 10.2307/1911035.  Google Scholar

[18]

D. Palvogyi, Hotelling on graphs, mimeo, 2011. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[24]

A. A. Pinto, Game theory and duopoly models,, in preparation., ().   Google Scholar

[25]

S. Salop, Monopolistic competition with outside goods, Bell Journal of Economics, 10 (1979), 141-156. doi: 10.2307/3003323.  Google Scholar

[26]

A. Soetevent, Price Competition on Graphs, Tinbergen Institute Discussion Papers 10-126/1, (2010). Google Scholar

[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.  Google Scholar

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