IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/937.html
   My bibliography  Save this paper

Aggregation and Imperfect Competition: On the Existence of Equilibrium

Author

Listed:
  • Andrew Caplin

    (Columbia University)

  • Barry Nalebuff

    (Yale School of Management)

Abstract

We present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products. The central result provides general conditions under which there exists a pure strategy price equilibrium for any number of firms producing any set of products. This includes products with multi-dimensional attributes. In addition to the proof of existence, we provide conditions for uniqueness. Our analysis covers location models, the characteristic approach, and probabilistic choice together in a unified framework. To prove existence, we employ aggregation theorems due to Prekopa (1971) and Borell (1975). Our companion paper [CFDP 938] introduces these theorems and develops the application to super-majority voting rules.

Suggested Citation

  • Andrew Caplin & Barry Nalebuff, 1990. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Cowles Foundation Discussion Papers 937, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:937
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d09/d0937.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Michael Spence, 1976. "Product Selection, Fixed Costs, and Monopolistic Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(2), pages 217-235.
    2. Jeffrey M. Perloff & Steven C. Salop, 1985. "Equilibrium with Product Differentiation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 107-120.
    3. B. Curtis Eaton, 1972. "Spatial Competition Revisited," Canadian Journal of Economics, Canadian Economics Association, vol. 5(2), pages 268-278, May.
    4. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    5. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    6. Osborne, Martin J & Pitchik, Carolyn, 1987. "Equilibrium in Hotelling's Model of Spatial Competition," Econometrica, Econometric Society, vol. 55(4), pages 911-922, July.
    7. Simon P. Anderson & André De Palma & Jacques-François Thisse, 1989. "Demand for Differentiated Products, Discrete Choice Models, and the Characteristics Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(1), pages 21-35.
    8. de Palma, A, et al, 1985. "The Principle of Minimum Differentiation Holds under Sufficient Heterogeneity," Econometrica, Econometric Society, vol. 53(4), pages 767-781, July.
    9. Caplin, Andrew S & Nalebuff, Barry J, 1986. "Multi-dimensional Product Differentiation and Price Competition," Oxford Economic Papers, Oxford University Press, vol. 38(0), pages 129-145, Suppl. No.
    10. Robert C. Feenstra & James A. Levinsohn, 1989. "Distance, Demand, and Oligopoly Pricing," NBER Working Papers 3076, National Bureau of Economic Research, Inc.
    11. Levitan, Richard & Shubik, Martin, 1972. "Price Duopoly and Capacity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-122, February.
    12. W.J. Lane, 1980. "Product Differentiation in a Market with Endogenous Sequential Entry," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 237-260, Spring.
    13. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
    14. Kelvin J. Lancaster, 1966. "A New Approach to Consumer Theory," Journal of Political Economy, University of Chicago Press, vol. 74, pages 132-132.
    15. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    16. Hildegard DIERKER, 1989. "Existence of Nash Equilibrium in Pure Strategies in an Oligopoly With Price Setting Firms," Vienna Economics Papers vie8902, University of Vienna, Department of Economics.
    17. Jaskold Gabszewicz, J. & Thisse, J. -F., 1979. "Price competition, quality and income disparities," Journal of Economic Theory, Elsevier, vol. 20(3), pages 340-359, June.
    18. Simon P. Anderson & Andre de Palma & Jacques-Francois Thisse, 1987. "Demand for Differentiated Products," Discussion Papers 726, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. John R. Hauser, 1988. "Note—Competitive Price and Positioning Strategies," Marketing Science, INFORMS, vol. 7(1), pages 76-91.
    20. Lederer, Phillip J & Hurter, Arthur P, Jr, 1986. "Competition of Firms: Discriminatory Pricing and Location," Econometrica, Econometric Society, vol. 54(3), pages 623-640, May.
    21. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    22. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-383, June.
    23. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    24. Edward C. Prescott & Michael Visscher, 1977. "Sequential Location among Firms with Foresight," Bell Journal of Economics, The RAND Corporation, vol. 8(2), pages 378-393, Autumn.
    25. Schulz, Norbert & Stahl, Konrad, 1985. "On the non-existence of oligopolistic equilibria in differentiated products spaces," Regional Science and Urban Economics, Elsevier, vol. 15(2), pages 229-243, June.
    26. repec:ulb:ulbeco:2013/1759 is not listed on IDEAS
    27. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    28. G. C. Archibald & G. Rosenbluth, 1975. "The "New" Theory of Consumer Demand and Monopolistic Competition," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 89(4), pages 569-590.
    29. Hauser, John R., 1987. "Existence and uniqueness of price equilibria in Defender," Working papers 1878-87., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    30. repec:crs:wpaper:8801 is not listed on IDEAS
    31. Economides, Nicholas, 1989. "Symmetric equilibrium existence and optimality in differentiated product markets," Journal of Economic Theory, Elsevier, vol. 47(1), pages 178-194, February.
    32. Milgrom, Paul & Roberts, John, 1990. "The Economics of Modern Manufacturing: Technology, Strategy, and Organization," American Economic Review, American Economic Association, vol. 80(3), pages 511-528, June.
    33. Simon P. Anderson & André De Palma, 1988. "Spatial Price Discrimination with Heterogeneous Products," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 573-592.
    34. repec:fth:michin:245 is not listed on IDEAS
    35. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899, January.
    2. Auer, Raphael A. & Sauré, Philip, 2017. "Dynamic entry in vertically differentiated markets," Journal of Economic Theory, Elsevier, vol. 167(C), pages 177-205.
    3. Jean J. Gabszewicz & Jacques-François Thisse, 2000. "Microeconomic theories of imperfect competition," Cahiers d'Économie Politique, Programme National Persée, vol. 37(1), pages 47-99.
    4. Rhee, Byong-Duk, 2006. "First-mover disadvantages with idiosyncratic consumer tastes along unobservable characteristics," Regional Science and Urban Economics, Elsevier, vol. 36(1), pages 99-117, January.
    5. Simon P. Anderson & Andre de Palma, 1989. "The Logit as a Model of Product Differentiation: Further Results and Extensions," Discussion Papers 913, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Byong‐Duk Rhee & André de Palma & Claes Fornell & Jacques‐François Thisse, 1992. "Restoring The Principle Of Minimum Differentiation In Product Positioning," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 1(3), pages 475-505, September.
    7. Anderson, Simon P. & de Palma, Andre, 2000. "From local to global competition," European Economic Review, Elsevier, vol. 44(3), pages 423-448, March.
    8. Creane, Anthony & Manduchi, Agostino, 2022. "Informative advertising in monopolistically competitive markets," International Journal of Industrial Organization, Elsevier, vol. 83(C).
    9. Sällström, Susanna, 2009. "Functional Differentiation," CEPR Discussion Papers 7187, C.E.P.R. Discussion Papers.
    10. Ralph Braid, 2013. "The locations of firms on intersecting roadways," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 50(3), pages 791-808, June.
    11. Heritiana Ranaivoson, 2005. "The economic analysis of product diversity," Cahiers de la Maison des Sciences Economiques r05083, Université Panthéon-Sorbonne (Paris 1).
    12. Borenstein, Severin & Netz, Janet, 1999. "Why do all the flights leave at 8 am?: Competition and departure-time differentiation in airline markets," International Journal of Industrial Organization, Elsevier, vol. 17(5), pages 611-640, July.
    13. Ralph Braid, 2014. "The socially optimal and equilibrium locations of two stores or libraries with consumer search," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(1), pages 123-136, August.
    14. Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Documents de travail du Centre d'Economie de la Sorbonne 14033, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    15. MacLeod, W.B. & Norman, G. & Thisse, J.-F., 1988. "Price discrimination and equilibrium in monopolistic competition," International Journal of Industrial Organization, Elsevier, vol. 6(4), pages 429-446.
    16. Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    17. Ushchev, Philip & Zenou, Yves, 2018. "Price competition in product variety networks," Games and Economic Behavior, Elsevier, vol. 110(C), pages 226-247.
    18. Tauman, Yair & Urbano, Amparo & Watanabe, Junichi, 1997. "A Model of Multiproduct Price Competition," Journal of Economic Theory, Elsevier, vol. 77(2), pages 377-401, December.
    19. Lambertini, Luca, 2002. "Equilibrium locations in a spatial model with sequential entry in real time," Regional Science and Urban Economics, Elsevier, vol. 32(1), pages 47-58, January.
    20. Jan Witajewski-Baltvilks, 2018. "Green Growth and Taste Heterogeneity," IBS Working Papers 07/2018, Instytut Badan Strukturalnych.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:937. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.