IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20090072.html
   My bibliography  Save this paper

Selective Competition

Author

Listed:
  • Andrei Dubovik

    (Erasmus University Rotterdam)

  • Alexei Parakhonyak

    (Erasmus University Rotterdam)

Abstract

We consider a dynamic (differential) game with three players competing against each other. Each period each player can allocate his resources so as to direct his competition towards particular rivals -- we call such competition selective. The setting can be applied to a wide variety of cases: competition between firms, competition between political parties, warfare. We show that if the players are myopic, the weaker players eventually loose the game to their strongest rival. Vice versa, if the players value their future payoffs high enough, each player concentrates more on fighting his strongest opponent. Consequently, the weaker players grow stronger, the strongest player grows weaker and eventually all the players converge and remain in the game.

Suggested Citation

  • Andrei Dubovik & Alexei Parakhonyak, 2009. "Selective Competition," Tinbergen Institute Discussion Papers 09-072/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20090072
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/09072.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kelvin Lancaster, 1990. "The Economics of Product Variety: A Survey," Marketing Science, INFORMS, vol. 9(3), pages 189-206.
    2. Bailey, Elizabeth E & Friedlaender, Ann F, 1982. "Market Structure and Multiproduct Industries," Journal of Economic Literature, American Economic Association, vol. 20(3), pages 1024-1048, September.
    3. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    4. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    5. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
    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. Nan Xia & S. Rajagopalan, 2009. "Standard vs. Custom Products: Variety, Lead Time, and Price Competition," Marketing Science, INFORMS, vol. 28(5), pages 887-900, 09-10.
    2. Ulrich Doraszelski & Kenneth L. Judd, 2012. "Avoiding the curse of dimensionality in dynamic stochastic games," Quantitative Economics, Econometric Society, vol. 3(1), pages 53-93, March.
    3. Laussel, Didier & Resende, Joana, 2014. "Dynamic price competition in aftermarkets with network effects," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 106-118.
    4. Wang, Pengfei, 2019. "Price space and product demography: Evidence from the workstation industry, 1980–1996," Research Policy, Elsevier, vol. 48(9), pages 1-1.
    5. Dockner, Engelbert J. & Gaunersdorfer, Andrea, 2001. "On the profitability of horizontal mergers in industries with dynamic competition," Japan and the World Economy, Elsevier, vol. 13(3), pages 195-216, August.
    6. Andrew B. Bernard & Stephen J. Redding & Peter K. Schott, 2011. "Multiproduct Firms and Trade Liberalization," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(3), pages 1271-1318.
    7. Ekaterina Marova & Ekaterina Gromova & Polina Barsuk & Anastasia Shagushina, 2020. "On the Effect of the Absorption Coefficient in a Differential Game of Pollution Control," Mathematics, MDPI, vol. 8(6), pages 1-24, June.
    8. Bethmann, Dirk, 2008. "The open-loop solution of the Uzawa-Lucas model of endogenous growth with N agents," Journal of Macroeconomics, Elsevier, vol. 30(1), pages 396-414, March.
    9. Lalit Manral, 2010. "Demand competition and investment heterogeneity in industries based on systemic technologies: evidence from the US long-distance telecommunications services industry, 1984–1996," Journal of Evolutionary Economics, Springer, vol. 20(5), pages 765-802, October.
    10. Buechel, Berno & Roehl, Nils, 2015. "Robust equilibria in location games," European Journal of Operational Research, Elsevier, vol. 240(2), pages 505-517.
    11. Dubovik, Andrei & Parakhonyak, Alexei, 2014. "Drugs, guns, and targeted competition," Games and Economic Behavior, Elsevier, vol. 87(C), pages 497-507.
    12. Maican, Florin & Orth, Matilda, 2021. "Determinants of economies of scope in retail," International Journal of Industrial Organization, Elsevier, vol. 75(C).
    13. Hassan Benchekroun & Ngo Van Long, 2001. "Leader and Follower: A Differential Game Model," CIRANO Working Papers 2001s-08, CIRANO.
    14. Maican, Florin & Orth, Matilda, 2021. "Entry Regulations and Product Variety in Retail," CEPR Discussion Papers 15992, C.E.P.R. Discussion Papers.
    15. Taylor Randall & Karl Ulrich, 2001. "Product Variety, Supply Chain Structure, and Firm Performance: Analysis of the U.S. Bicycle Industry," Management Science, INFORMS, vol. 47(12), pages 1588-1604, December.
    16. Gagen, Michael & Nemoto, Kae, 2006. "Variational optimization of probability measure spaces resolves the chain store paradox," MPRA Paper 4778, University Library of Munich, Germany.
    17. Ulrich Doraszelski & Sarit Markovich, 2004. "Advertising Dynamics and Competitive Advantage," Computing in Economics and Finance 2004 61, Society for Computational Economics.
    18. Murray C. Kemp & Ngo Van Long, 2007. "Development Aid in the Presence of Corruption: Differential Games among Donors," CIRANO Working Papers 2007s-23, CIRANO.
    19. Ulrich Doraszelski & Sarit Markovich, 2007. "Advertising dynamics and competitive advantage," RAND Journal of Economics, RAND Corporation, vol. 38(3), pages 557-592, September.
    20. Michael Cohen & Rui Huang, 2012. "Corporate Social Responsibility for Kids’ Sake: A Dynamic Model of Firm Participation," Working Papers 12, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.

    More about this item

    Keywords

    selective competition; dynamic oligopolies; differential games;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

    Statistics

    Access and download statistics

    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:tin:wpaper:20090072. 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: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.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.