American Institute of Mathematical Sciences

Advanced
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.  doi: 10.2307/1911955.  Google Scholar

[3]

F. Bloch and N. Quérou, Pricing in social networks,, Games Econom. Behav., 80 (2013), 243.  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.   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, 117 (2007), 897.  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.  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.  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.   Google Scholar

[12]

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

[13]

H. Hotelling, Stability in competition,, The Economic Journal, 39 (1929), 41.   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, (2012), 2012.   Google Scholar

[15]

V. Mazalov and M. Sakaguchi, Location game on the plane,, International Game Theory Review, 5 (2003), 13.  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.   Google Scholar

[17]

M. J. Osborne and C. Pitchick, Equilibrium in hotelling's model of spatial competition,, Econometrica, 55 (1987), 911.  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, 1 (2011), 709.  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, 73 (2014), 567.  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, 73 (2014), 17.  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, 73 (2014), 585.  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.  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.  doi: 10.2307/3003323.  Google Scholar

[26]

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

[27]

T. Tabuchi and J. F. Thisse, Asymmetric equilibria in spatial competition,, International Journal of Economic Theory, 13 (1995), 213.  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.  doi: 10.2307/1911955.  Google Scholar

[3]

F. Bloch and N. Quérou, Pricing in social networks,, Games Econom. Behav., 80 (2013), 243.  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.   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, 117 (2007), 897.  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.  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.  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.   Google Scholar

[12]

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

[13]

H. Hotelling, Stability in competition,, The Economic Journal, 39 (1929), 41.   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, (2012), 2012.   Google Scholar

[15]

V. Mazalov and M. Sakaguchi, Location game on the plane,, International Game Theory Review, 5 (2003), 13.  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.   Google Scholar

[17]

M. J. Osborne and C. Pitchick, Equilibrium in hotelling's model of spatial competition,, Econometrica, 55 (1987), 911.  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, 1 (2011), 709.  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, 73 (2014), 567.  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, 73 (2014), 17.  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, 73 (2014), 585.  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.  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.  doi: 10.2307/3003323.  Google Scholar

[26]

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

[27]

T. Tabuchi and J. F. Thisse, Asymmetric equilibria in spatial competition,, International Journal of Economic Theory, 13 (1995), 213.  doi: 10.1016/0167-7187(94)00449-C.  Google Scholar

[1]

Ali Naimi-Sadigh, S. Kamal Chaharsooghi, Marzieh Mozafari. Optimal pricing and advertising decisions with suppliers' oligopoly competition: Stakelberg-Nash game structures. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2020028
[2]

Heikki Haario, Leonid Kalachev, Marko Laine. Reduction and identification of dynamic models. Simple example: Generic receptor model. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 417-435. doi: 10.3934/dcdsb.2013.18.417
[3]

Serap Ergün, Bariş Bülent Kırlar, Sırma Zeynep Alparslan Gök, Gerhard-Wilhelm Weber. An application of crypto cloud computing in social networks by cooperative game theory. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-15. doi: 10.3934/jimo.2019036
[4]

Astridh Boccabella, Roberto Natalini, Lorenzo Pareschi. On a continuous mixed strategies model for evolutionary game theory. Kinetic & Related Models, 2011, 4 (1) : 187-213. doi: 10.3934/krm.2011.4.187
[5]

Anna Lisa Amadori, Astridh Boccabella, Roberto Natalini. A hyperbolic model of spatial evolutionary game theory. Communications on Pure & Applied Analysis, 2012, 11 (3) : 981-1002. doi: 10.3934/cpaa.2012.11.981
[6]

Alberto A. Pinto, Telmo Parreira. Localization and prices in the quadratic Hotelling model with uncertainty. Journal of Dynamics & Games, 2016, 3 (2) : 121-142. doi: 10.3934/jdg.2016006
[7]

King-Yeung Lam. Dirac-concentrations in an integro-pde model from evolutionary game theory. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 737-754. doi: 10.3934/dcdsb.2018205
[8]

Yuwei Shen, Jinxing Xie, Tingting Li. The risk-averse newsvendor game with competition on demand. Journal of Industrial & Management Optimization, 2016, 12 (3) : 931-947. doi: 10.3934/jimo.2016.12.931
[9]

Tao Li, Suresh P. Sethi. A review of dynamic Stackelberg game models. Discrete & Continuous Dynamical Systems - B, 2017, 22 (1) : 125-159. doi: 10.3934/dcdsb.2017007
[10]

Bertrand Haut, Georges Bastin. A second order model of road junctions in fluid models of traffic networks. Networks & Heterogeneous Media, 2007, 2 (2) : 227-253. doi: 10.3934/nhm.2007.2.227
[11]

Sourabh Bhattacharya, Abhishek Gupta, Tamer Başar. Jamming in mobile networks: A game-theoretic approach. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 1-30. doi: 10.3934/naco.2013.3.1
[12]

Eduardo Espinosa-Avila, Pablo Padilla Longoria, Francisco Hernández-Quiroz. Game theory and dynamic programming in alternate games. Journal of Dynamics & Games, 2017, 4 (3) : 205-216. doi: 10.3934/jdg.2017013
[13]

Massimiliano Caramia, Giovanni Storchi. Evaluating the effects of parking price and location in multi-modal transportation networks. Networks & Heterogeneous Media, 2006, 1 (3) : 441-465. doi: 10.3934/nhm.2006.1.441
[14]

Hans-Otto Walther. Convergence to square waves for a price model with delay. Discrete & Continuous Dynamical Systems - A, 2005, 13 (5) : 1325-1342. doi: 10.3934/dcds.2005.13.1325
[15]

Ábel Garab, Veronika Kovács, Tibor Krisztin. Global stability of a price model with multiple delays. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 6855-6871. doi: 10.3934/dcds.2016098
[16]

Peng Liu, Jinfeng Wang, Lijie Feng. The game of government-industry-university-institute collaborative innovation based on static game theory. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020276
[17]

Tinggui Chen, Yanhui Jiang. Research on operating mechanism for creative products supply chain based on game theory. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1103-1112. doi: 10.3934/dcdss.2015.8.1103
[18]

Marianne Akian, Stéphane Gaubert, Antoine Hochart. A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectors. Discrete & Continuous Dynamical Systems - A, 2020, 40 (1) : 207-231. doi: 10.3934/dcds.2020009
[19]

Carlo Brugna, Giuseppe Toscani. Boltzmann-type models for price formation in the presence of behavioral aspects. Networks & Heterogeneous Media, 2015, 10 (3) : 543-557. doi: 10.3934/nhm.2015.10.543
[20]

Dong-Mei Zhu, Wai-Ki Ching, Robert J. Elliott, Tak-Kuen Siu, Lianmin Zhang. Hidden Markov models with threshold effects and their applications to oil price forecasting. Journal of Industrial & Management Optimization, 2017, 13 (2) : 757-773. doi: 10.3934/jimo.2016045

 Impact Factor: 

Tools

Metrics

  • PDF downloads (22)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences