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

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  • 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.

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Bibliographic Info

Article provided by Elsevier in its journal Regional Science and Urban Economics.

Volume (Year): 40 (2010)
Issue (Month): 2-3 (May)
Pages: 155-160

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Handle: RePEc:eee:regeco:v:40:y:2010:i:2-3:p:155-160

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Related research

Keywords: Horizontal differentiation Advertising Steady state Differential games;

References

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  1. Victor Ginsburgh & André De Palma & Yorgo Papageorgiou & Jacques-François Thisse, 1985. "The principle of minimum differentiation holds under sufficient heterogeneity," ULB Institutional Repository 2013/1759, ULB -- Universite Libre de Bruxelles.
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  3. Luca Lambertini, 1994. "Optimal Fiscal Regime in a Spatial Duopoly," Working Papers 205, Dipartimento Scienze Economiche, Universita' di Bologna.
  4. Meurer, Michael & Stahl, Dale II, 1994. "Informative advertising and product match," International Journal of Industrial Organization, Elsevier, vol. 12(1), pages 1-19, March.
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  6. Beath,John & Katsoulacos,Yannis, 1991. "The Economic Theory of Product Differentiation," Cambridge Books, Cambridge University Press, number 9780521335263, April.
  7. Fershtman, C. & Nitzan, S., 1988. "Dynamic Voluntary Provision Of Public Goods," Papers 21-88, Tel Aviv.
  8. Grossman, Gene M & Shapiro, Carl, 1984. "Informative Advertising with Differentiated Products," Review of Economic Studies, Wiley Blackwell, vol. 51(1), pages 63-81, January.
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  11. 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.
  12. Tabuchi, Takatoshi & Thisse, Jacques-Francois, 1995. "Asymmetric equilibria in spatial competition," International Journal of Industrial Organization, Elsevier, vol. 13(2), pages 213-227.
  13. Nils-Henrik M. von der Fehr & Kristin Stevik, 1998. "Persuasive Advertising and Product Differentiation," Southern Economic Journal, Southern Economic Association, vol. 65(1), pages 113-126, July.
  14. 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, April.
  15. Anderson, Simon, 1987. "Spatial competition and price leadership," International Journal of Industrial Organization, Elsevier, vol. 5(4), pages 369-398.
  16. 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.
  17. Beath,John & Katsoulacos,Yannis, 1991. "The Economic Theory of Product Differentiation," Cambridge Books, Cambridge University Press, number 9780521335522, April.
  18. Anderson, Simon P. & Goeree, Jacob K. & Ramer, Roald, 1997. "Location, Location, Location," Journal of Economic Theory, Elsevier, vol. 77(1), pages 102-127, November.
  19. Kohlberg, Elon & Novshek, William, 1982. "Equilibrium in a simple price-location model," Economics Letters, Elsevier, vol. 9(1), pages 7-15.
  20. 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.
  21. Fershtman, Chaim, 1984. "Goodwill and Market Shares in Oligopoly," Economica, London School of Economics and Political Science, vol. 51(23), pages 271-81, August.
  22. Novshek, William, 1980. "Equilibrium in simple spatial (or differentiated product) models," Journal of Economic Theory, Elsevier, vol. 22(2), pages 313-326, April.
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Cited by:
  1. 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.

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