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Sequential Location Equilibria Under Incomplete Information

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  • Marcel Boyer

    ()

  • Jean-Jacques Laffont
  • Philippe Mahenc
  • Michel Moreaux

    ()

Abstract

We consider a simple model of incomplete information in location theory. Two firms compete in a two stage framework: a sequential location stage and a price competition stage. Firm 1 knows both its own constant marginal cost technology and that of Firm 2, whereas the latter has incomplete information about firm 1's technology. The location stage turns out to be a monotonic signalling game and the unique D1 equilibrium is a pure strategy separating equilibrium if Firm 1's cost advantage is below some bound, and otherwise a pooling equilibrium if the prior probability that Firm 1 is of the low cost type is high, or a semi-pooling equilibrium if it is low. This surprising result is due to the fact that the location gap between the two types of Firm 1 is bounded because of natural economic reasons, which may prevent the separation of the two types. Hence, incomplete information matters: the equilibrium locations differ quite significantly from the full information equilibrium locations. Nous proposons ici un modèle simple d'information incomplète en théorie de la localisation. Deux entreprises s'affrontent dans un contexte à deux étapes : une étape de localisation séquentielle et un étape de concurrence en prix. La firme 1 connaît sa technologie à coût marginal constant et celle de la firme 20501s cette dernière n'a qu'une information imparfaite de la technologie de sa concurrente. La concurrence de première étape s'avère être un jeu de signal monotone et l'équilibre D1 unique est un équilibre séparateur en stratégies pures si l'avantage de coût de la firme 1 est relativement faible et sinon, un équilibre mélangeant, si la probabilité a priori que la firme 1 soit de type coût faible est élevée, ou un équilibre semi-mélangeant, si cette probabilité est faible. Ce résultat surprenant est dû au fait que l'écart de localisation entre les firmes est naturellement borné, ce qui peut empêcher la séparation des types. Ainsi, les localisations d'équilibre d'information incomplète diffèrent significativement des localisations d'équilibre d'information complète.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 94s-20.

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Date of creation: 01 Nov 1994
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Handle: RePEc:cir:cirwor:94s-20

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Keywords: Incomplete information model; Location theory; Sequential location; Price competition; Modèle d'information incomplète ; Théorie de la localisation ; Localisation séquentielle ; Concurrence en prix;

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  1. HAMILTON, John H. & MacLEOD, W. Bentley & THISSE, Jacques-François, . "Spatial competition and the core," CORE Discussion Papers RP -986, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Hobbs, Benjamin F, 1986. "Mill Pricing versus Spatial Price Discrimination under Bertrand and Cournot Spatial Competition," Journal of Industrial Economics, Wiley Blackwell, vol. 35(2), pages 173-91, December.
  3. Thisse, Jacques-Francois & Vives, Xavier, 1988. "On the Strategic Choice of Spatial Price Policy," American Economic Review, American Economic Association, vol. 78(1), pages 122-37, March.
  4. d'ASPREMONT, Claude & GABSZEWICZ, Jean J. & THISSE, Jacques-François, . "On Hotelling's "Stability in competition"," CORE Discussion Papers RP -385, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Anderson, Simon P & de Palma, Andre & Thisse, Jacques-Francois, 1989. "Spatial Price Policies Reconsidered," Journal of Industrial Economics, Wiley Blackwell, vol. 38(1), pages 1-18, September.
  6. Paul Milgrom & John Roberts, 1998. "Limit Pricing and Entry Under Incomplete Information: An Equilibrium Analysis," Levine's Working Paper Archive 245, David K. Levine.
  7. Cho, In-Koo & Sobel, Joel, 1990. "Strategic stability and uniqueness in signaling games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 381-413, April.
  8. Carlton, Dennis W, 1983. "A Reexamination of Delivered Pricing Systems," Journal of Law and Economics, University of Chicago Press, vol. 26(1), pages 51-70, April.
  9. Boyer, Marcel & Laffont, Jean-Jacques & Mahenc, Philippe & Moreaux, Michel, 1994. "Location distortions under incomplete information," Regional Science and Urban Economics, Elsevier, vol. 24(4), pages 409-440, August.
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Cited by:
  1. Margolis, D..N., 1995. "Firm Heterogeneity and Worker Self-Selection Bias Estimated Returns to Seniority," Cahiers de recherche 9502, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Boyer, Marcel & Mahenc, Philippe & Moreaux, Michel, 1995. "Entry Blockading Locations," IDEI Working Papers 53, Institut d'Économie Industrielle (IDEI), Toulouse.
  3. Marcel Boyer & Donatella Porrini, 2010. "The Impact of Court Errors on Liability Sharing and Safety Regulation for Environmental/Industrial Accidents," CIRANO Working Papers 2010s-48, CIRANO.
  4. Boyer, Marcel & Mahenc, Phillippe & Moreaux, Michel, 2003. "Asymmetric information and product differentiation," Regional Science and Urban Economics, Elsevier, vol. 33(1), pages 93-113, January.
  5. Andreea Cosnita-Langlais, 2014. "Where to locate to escape predation?," Economics Bulletin, AccessEcon, vol. 34(2), pages 614-626.
  6. Boyer, Marcel & Mahenc, Philippe & Moreaux, Michel, 2003. "Entry preventing locations under incomplete information," International Journal of Industrial Organization, Elsevier, vol. 21(6), pages 809-829, June.
  7. Kress, Dominik & Pesch, Erwin, 2012. "Sequential competitive location on networks," European Journal of Operational Research, Elsevier, vol. 217(3), pages 483-499.

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