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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.

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
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    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.

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