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Uncertainty in Spatial Duopoly with Possibly Asymmetric Distributions: a State Space Approach

  • Kieron J. Meagher
  • Klaus G. Zauner

In spatial competition firms are likely to be uncertain about consumer locations when launching products either because of shifting demograph- ics or of asymmetric information about preferences. Realistically distri- butions of consumer locations should be allowed to vary over states and need not be uniform. However, the existing literature models location uncertainty as an additive shock to a uniform consumer distribution. The additive shock restricts uncertainty to the mean of the consumers loca- tions. We generalize this approach to a state space model in which a vector of parameters gives rise to different distributions of consumer tastes in dif- ferent states, allowing other moments (besides the mean) of the consumer distribution to be uncertain. We illustrate our model with an asymmetric consumer distribution and obtain a unique subgame perfect equilibrium with an explicit, closed-form solution. An equilibrium existence result is then given for the general case. For symmetric distributions, the unique subgame perfect equilibrium in the general case can be described by a simple closed-form solution.

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Paper provided by Centre for Economic Policy Research, Research School of Economics, Australian National University in its series CEPR Discussion Papers with number 579.

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Date of creation: Apr 2008
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Handle: RePEc:auu:dpaper:579
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  1. Victor Ginsburgh & André De Palma & Yorgo Papageorgiou & Jacques-François Thisse, 1999. "The principle of minimum differentiation holds under sufficient heterogeneity," ULB Institutional Repository 2013/3319, ULB -- Universite Libre de Bruxelles.
  2. Jullien Bruno & Aghion Philippe & Paz Espinoza M, 1990. "Dynamic duopoly with learning through market experimentation," CEPREMAP Working Papers (Couverture Orange) 9012, CEPREMAP.
  3. Anderson, Simon P. & Goeree, Jacob K. & Ramer, Roald, 1997. "Location, Location, Location," Journal of Economic Theory, Elsevier, vol. 77(1), pages 102-127, November.
  4. Harrington Jr. , Joseph E., 1995. "Experimentation and Learning in a Differentiated-Products Duopoly," Journal of Economic Theory, Elsevier, vol. 66(1), pages 275-288, June.
  5. 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.
  6. 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.
  7. Tabuchi, Takatoshi & Thisse, Jacques-Francois, 1995. "Asymmetric equilibria in spatial competition," International Journal of Industrial Organization, Elsevier, vol. 13(2), pages 213-227.
  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. Asim Ansari & Nicholas Economides & Avijit Ghosh, 1994. "Competitive Positioning in Markets with Nonuniform Preferences," Marketing Science, INFORMS, vol. 13(3), pages 248-273.
  10. Boyan Jovanovic, 1981. "Entry With Private Information," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 649-660, Autumn.
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