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On the existence and social optimality of equilibria in a Hotelling game with uncertain demand and linearquadratic costs

  • Michal Król

This paper examines a variant of the Hotelling two-stage mill-pricing duopoly game with “linear-quadratic” transport costs and the uniform customer distribution subject to a random shock. The demand is equally likely to be found anywhere in a fixed interval of feasible product characteristics, with the ex-post differentiation of tastes parametrized to reflect the degree of uncertainty. It turns out that, for uncertainty big enough, the presence of a linear component in the cost function no longer rules out an analytical solution to the game, which is a common problem in spatial competition models. In particular, a subgame-perfect equilibrium is shown to exist in which the firms’ locations approach the socially efficient ones as uncertainty further increases, regardless of the curvature of the cost function. When the demand uncertainty reaches maximum, mill-pricing is equivalent to spatial price discrimination under the most general conditions.

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Paper provided by Economics, The University of Manchester in its series The School of Economics Discussion Paper Series with number 1101.

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Date of creation: 2011
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Handle: RePEc:man:sespap:1101
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  1. Lederer, Phillip J & Hurter, Arthur P, Jr, 1986. "Competition of Firms: Discriminatory Pricing and Location," Econometrica, Econometric Society, vol. 54(3), pages 623-40, May.
  2. Aghion, Philippe & Espinosa, Maria Paz & Jullien, Bruno, 1993. "Dynamic Duopoly with Learning through Market Experimentation," Economic Theory, Springer, vol. 3(3), pages 517-39, July.
  3. F. Javier Casado-Izaga, 2000. "Location decisions: The role of uncertainty about consumer tastes," Journal of Economics, Springer, vol. 71(1), pages 31-46, February.
  4. Osborne, Martin J & Pitchik, Carolyn, 1987. "Equilibrium in Hotelling's Model of Spatial Competition," Econometrica, Econometric Society, vol. 55(4), pages 911-22, July.
  5. Balvers, Ronald & Szerb, Lazlo, 1996. "Location in the Hotelling duopoly model with demand uncertainty," European Economic Review, Elsevier, vol. 40(7), pages 1453-1461, August.
  6. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-50, September.
  7. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 27-41, January.
  8. Kieron Meagher & Klaus Zauner, 2005. "Location-then-price competition with uncertain consumer tastes," Economic Theory, Springer, vol. 25(4), pages 799-818, 06.
  9. 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.
  10. Mérel Pierre R & Sexton Richard J., 2010. "Kinked-Demand Equilibria and Weak Duopoly in the Hotelling Model of Horizontal Differentiation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-34, April.
  11. Anderson, Simon P, 1988. "Equilibrium Existence in the Linear Model of Spatial Competition," Economica, London School of Economics and Political Science, vol. 55(220), pages 479-91, November.
  12. Steffen Brenner, 2005. "Hotelling Games with Three, Four, and More Players," Journal of Regional Science, Wiley Blackwell, vol. 45(4), pages 851-864.
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