IDEAS home Printed from https://ideas.repec.org/a/eee/regeco/v40y2010i2-3p155-160.html
   My bibliography  Save this article

Existence of equilibrium in a differential game of spatial competition with advertising

Author

Listed:
  • Bertuzzi, Giorgia
  • Lambertini, Luca

Abstract

We investigate a differential duopoly game with horizontal product differentiation and advertising efforts aimed at increasing market demand, to show that the standard approach to spatial competition fails to produce a pure-strategy price equilibrium in a dynamic game framework. This holds independently of the shape of the transportation cost function. Then, we introduce an endogenous cost associated with the choice of location and characterise the feedback equilibrium, identifying the necessary and sufficient condition for the existence of the pure-strategy (stationary) price equilibrium. The same condition is singled out for the static game where consumer population is constant. Finally, we show that the static game cannot be viewed as a special case of the dynamic one.

Suggested Citation

  • Bertuzzi, Giorgia & Lambertini, Luca, 2010. "Existence of equilibrium in a differential game of spatial competition with advertising," Regional Science and Urban Economics, Elsevier, vol. 40(2-3), pages 155-160, May.
    • Handle: RePEc:eee:regeco:v:40:y:2010:i:2-3:p:155-160
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0166-0462(10)00007-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nils-Henrik M. von der Fehr & Kristin Stevik, 1998. "Persuasive Advertising and Product Differentiation," Southern Economic Journal, John Wiley & Sons, vol. 65(1), pages 113-126, July.
    2. Bester, Helmut & Petrakis, Emmanuel, 1995. "Price competition and advertising in oligopoly," European Economic Review, Elsevier, vol. 39(6), pages 1075-1088, June.
    3. Neven, Damien J., 1986. "On Hotelling's competition with non-uniform customer distributions," Economics Letters, Elsevier, vol. 21(2), pages 121-126.
    4. Gene M. Grossman & Carl Shapiro, 1984. "Informative Advertising with Differentiated Products," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(1), pages 63-81.
    5. Fershtman, Chaim & Nitzan, Shmuel, 1991. "Dynamic voluntary provision of public goods," European Economic Review, Elsevier, vol. 35(5), pages 1057-1067, July.
    6. Lambertini, Luca, 1997. "Unicity of the equilibrium in the unconstrained Hotelling model," Regional Science and Urban Economics, Elsevier, vol. 27(6), pages 785-798, November.
    7. Meurer, Michael & Stahl, Dale II, 1994. "Informative advertising and product match," International Journal of Industrial Organization, Elsevier, vol. 12(1), pages 1-19, March.
    8. Lambertini, Luca, 1997. "Optimal Fiscal Regime in a Spatial Duopoly," Journal of Urban Economics, Elsevier, vol. 41(3), pages 407-420, May.
    9. Anderson, Simon, 1987. "Spatial competition and price leadership," International Journal of Industrial Organization, Elsevier, vol. 5(4), pages 369-398.
    10. Konrad Stahl, 1982. "Location and Spatial Pricing Theory with Nonconvex Transportation Cost Schedules," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 575-582, Autumn.
    11. repec:ulb:ulbeco:2013/1759 is not listed on IDEAS
    12. Nikolaos Vettas, 1998. "Demand and Supply in New Markets: Diffusion with Bilateral Learning," RAND Journal of Economics, The RAND Corporation, vol. 29(1), pages 215-233, Spring.
    13. de Palma, A, et al, 1985. "The Principle of Minimum Differentiation Holds under Sufficient Heterogeneity," Econometrica, Econometric Society, vol. 53(4), pages 767-781, July.
    14. Claudio A. Piga, 1998. "A Dynamic Model of Advertising and Product Differentiation," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 13(5), pages 509-522, October.
    15. Tabuchi, Takatoshi & Thisse, Jacques-Francois, 1995. "Asymmetric equilibria in spatial competition," International Journal of Industrial Organization, Elsevier, vol. 13(2), pages 213-227.
    16. Economides, Nicholas, 1986. "Minimal and maximal product differentiation in Hotelling's duopoly," Economics Letters, Elsevier, vol. 21(1), pages 67-71.
    17. Novshek, William, 1980. "Equilibrium in simple spatial (or differentiated product) models," Journal of Economic Theory, Elsevier, vol. 22(2), pages 313-326, April.
    18. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    19. Anderson, Simon P. & Goeree, Jacob K. & Ramer, Roald, 1997. "Location, Location, Location," Journal of Economic Theory, Elsevier, vol. 77(1), pages 102-127, November.
    20. repec:bla:econom:v:51:y:1984:i:23:p:271-81 is not listed on IDEAS
    21. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    22. Beath,John & Katsoulacos,Yannis, 1991. "The Economic Theory of Product Differentiation," Cambridge Books, Cambridge University Press, number 9780521335263, September.
    23. James W. Friedman, 1983. "Advertising and Oligopolistic Equilibrium," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 464-473, Autumn.
    24. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
    25. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, September.
    26. Kohlberg, Elon & Novshek, William, 1982. "Equilibrium in a simple price-location model," Economics Letters, Elsevier, vol. 9(1), pages 7-15.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Changying Li & Jianhu Zhang, 2013. "Dynamic Games of R&D Competition in a Differentiated Duopoly," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 169(4), pages 660-679, December.
    2. Tenryu, Yohei & Kamei, Keita, 2014. "Welfare Analysis of Dynamic Voluntary Advertising in Covered Markets," MPRA Paper 60694, University Library of Munich, Germany.
    3. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    4. Yohei Tenryu & Keita Kamei, 2014. "Dynamic Voluntary Advertising under Partial Market Coverage," KIER Working Papers 909, Kyoto University, Institute of Economic Research.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. G. Bertuzzi & L. Lambertini, 2001. "Advertising in a Differential Game of Spatial Competition," Working Papers 400, Dipartimento Scienze Economiche, Universita' di Bologna.
    2. Lambertini, Luca, 2002. "Equilibrium locations in a spatial model with sequential entry in real time," Regional Science and Urban Economics, Elsevier, vol. 32(1), pages 47-58, January.
    3. L. Lambertini, 2001. "Dynamic Hotelling Duopoly with Linear Transportation Costs," Working Papers 398, Dipartimento Scienze Economiche, Universita' di Bologna.
    4. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899.
    5. Brekke, Kurt R. & Straume, Odd Rune, 2004. "Bilateral monopolies and location choice," Regional Science and Urban Economics, Elsevier, vol. 34(3), pages 275-288, May.
    6. Nils‐Henrik M. von der Fehr & Kristin Stevik, 1998. "Persuasive Advertising and Product Differentiation," Southern Economic Journal, John Wiley & Sons, vol. 65(1), pages 113-126, July.
    7. Anderson, Simon P. & Goeree, Jacob K. & Ramer, Roald, 1997. "Location, Location, Location," Journal of Economic Theory, Elsevier, vol. 77(1), pages 102-127, November.
    8. Hehenkamp, Burkhard & Wambach, Achim, 2010. "Survival at the center--The stability of minimum differentiation," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 853-858, December.
    9. Matteo Bassi & Marco Pagnozzi & Salvatore Piccolo, 2015. "Product Differentiation by Competing Vertical Hierarchies," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 24(4), pages 904-933, October.
    10. Barigozzi, Francesca & Ma, Ching-to Albert, 2018. "Product differentiation with multiple qualities," International Journal of Industrial Organization, Elsevier, vol. 61(C), pages 380-412.
    11. Ralph Braid, 2013. "The locations of firms on intersecting roadways," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 50(3), pages 791-808, June.
    12. Amit Pazgal & David Soberman & Raphael Thomadsen, 2022. "Consumer informedness: A key driver of differentiation," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 31(2), pages 356-368, April.
    13. Becchetti, Leonardo & Solferino, Nazaria, 2005. "The dynamics of ethical product differentiation and the habit formation of socially responsible consumers," AICCON Working Papers 8-2005, Associazione Italiana per la Cultura della Cooperazione e del Non Profit.
    14. R. Cellini & L. Lambertini, 2003. "Advertising in a Differential Oligopoly Game," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 61-81, January.
    15. Meagher, Kieron J. & Zauner, Klaus G., 2004. "Product differentiation and location decisions under demand uncertainty," Journal of Economic Theory, Elsevier, vol. 117(2), pages 201-216, August.
    16. Kieron Meagher & Arghya Ghosh, 2004. "Political Economy of Infrastructure Investment: A Spatial Approach," Econometric Society 2004 North American Summer Meetings 561, Econometric Society.
    17. L. Lambertini, 2002. "the Specialization of Production and Labour Mobility Under Endogenous Differentiation," Working Papers 453, Dipartimento Scienze Economiche, Universita' di Bologna.
    18. Toshihiro Matsumura & Noriaki Matsushima, 2010. "Patent licensing, bargaining, and product positioning," ISER Discussion Paper 0775, Institute of Social and Economic Research, Osaka University.
    19. Eleftherios Zacharias, 2013. "Strategic Positioning of Goods in a Market with a Niche," Working Paper series 36_13, Rimini Centre for Economic Analysis.
    20. Ralph Braid, 2014. "The socially optimal and equilibrium locations of two stores or libraries with consumer search," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(1), pages 123-136, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:regeco:v:40:y:2010:i:2-3:p:155-160. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/regec .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.