IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v159y2015ipap209-220.html
   My bibliography  Save this article

A theoretical foundation for the undercut-proof equilibrium

Author

Listed:
  • Byford, Martin C.

Abstract

This paper develops a theoretical foundation for the undercut-proof equilibrium (see Shy, 1996, 2002; Morgan and Shy, 2015). In a general spatial setting, the set of undercut-proof prices is equivalent to the core of a non-transferable utility coalitional-game, played on the set of outcomes that are feasible in Bertrand competition. The result depends critically on two conditions: First, firms must have unlimited capacity and constant marginal costs. Second, the goods produced by firms must only be differentiated by the spatial characteristics of the market. An application to network markets shows how the undercut-proof equilibrium can be used to describe stable price dispersion and persistent performance differences.

Suggested Citation

  • Byford, Martin C., 2015. "A theoretical foundation for the undercut-proof equilibrium," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 209-220.
    • Handle: RePEc:eee:jetheo:v:159:y:2015:i:pa:p:209-220
    DOI: 10.1016/j.jet.2015.06.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053115001064
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2015.06.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shy, Oz, 2002. "A quick-and-easy method for estimating switching costs," International Journal of Industrial Organization, Elsevier, vol. 20(1), pages 71-87, January.
    2. Jonathan H. Hamilton & W. Bentley MacLeod & Jacques-François Thisse, 1991. "Spatial Competition and the Core," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 925-937.
    3. Kujal, Praveen & Smith, Vernon L., 2008. "Fairness and Short Run Price Adjustment in Posted Offer Markets," Handbook of Experimental Economics Results, in: Charles R. Plott & Vernon L. Smith (ed.), Handbook of Experimental Economics Results, edition 1, volume 1, chapter 6, pages 55-61, Elsevier.
    4. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-659, September.
    5. Guesnerie, Roger & Oddou, Claude, 1981. "Second best taxation as a game," Journal of Economic Theory, Elsevier, vol. 25(1), pages 67-91, August.
    6. Kahneman, Daniel & Knetsch, Jack L & Thaler, Richard H, 1986. "Fairness and the Assumptions of Economics," The Journal of Business, University of Chicago Press, vol. 59(4), pages 285-300, October.
    7. Steven J. Davis & Kevin M. Murphy & Robert H. Topel, 2004. "Entry, Pricing, and Product Design in an Initially Monopolized Market," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 188-225, February.
    8. Iskakov, Mikhail & Iskakov, Alexey, 2012. "Solution of the Hotelling’s game in secure strategies," Economics Letters, Elsevier, vol. 117(1), pages 115-118.
    9. Corominas-Bosch, Margarida, 2004. "Bargaining in a network of buyers and sellers," Journal of Economic Theory, Elsevier, vol. 115(1), pages 35-77, March.
    10. Shilony, Yuval, 1977. "Mixed pricing in oligopoly," Journal of Economic Theory, Elsevier, vol. 14(2), pages 373-388, April.
    11. Lever Guzmán Carlos, 2011. "Price Competition on Network," Working Papers 2011-04, Banco de México.
    12. Stuart, Harborne Jr., 2004. "Efficient spatial competition," Games and Economic Behavior, Elsevier, vol. 49(2), pages 345-362, November.
    13. Rachel E. Kranton & Deborah F. Minehart, 2001. "A Theory of Buyer-Seller Networks," American Economic Review, American Economic Association, vol. 91(3), pages 485-508, June.
    14. 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.
    15. Daniel F. Spulber, 1986. "Second-Best Pricing and Cooperation," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 239-250, Summer.
    16. Oz Shy, 1996. "Industrial Organization: Theory and Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262691795, April.
    17. Kahneman, Daniel & Knetsch, Jack L & Thaler, Richard, 1986. "Fairness as a Constraint on Profit Seeking: Entitlements in the Market," American Economic Review, American Economic Association, vol. 76(4), pages 728-741, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Toraubally, Waseem A., 2024. "Quantity competition in Hotellings linear city," CRETA Online Discussion Paper Series 87, Centre for Research in Economic Theory and its Applications CRETA.
    2. Martin C. Byford, 2018. "Ex-post price stability with convex costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1065-1085, November.
    3. Christoph Graf & Viktor Zobernig & Johannes Schmidt & Claude Klockl, 2021. "Computational Performance of Deep Reinforcement Learning to find Nash Equilibria," Papers 2104.12895, arXiv.org.

    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. Martin C. Byford, 2018. "Ex-post price stability with convex costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1065-1085, November.
    2. repec:hal:spmain:info:hdl:2441/jeo70lroq9p9bmeio80mpgg5h is not listed on IDEAS
    3. Nermuth, Manfred & Pasini, Giacomo & Pin, Paolo & Weidenholzer, Simon, 2013. "The informational divide," Games and Economic Behavior, Elsevier, vol. 78(C), pages 21-30.
    4. Donna, Javier D. & Schenone, Pablo & Veramendi, Gregory F., 2020. "Networks, frictions, and price dispersion," Games and Economic Behavior, Elsevier, vol. 124(C), pages 406-431.
    5. Zakaria Babutsidze, 2017. "Duopolistic Price Competition with Captives," Metroeconomica, Wiley Blackwell, vol. 68(4), pages 903-926, November.
    6. Montez, João & Marxen, Annabelle, 2020. "Licensing at the patent cliff and market entry," CEPR Discussion Papers 14276, C.E.P.R. Discussion Papers.
    7. repec:spo:wpmain:info:hdl:2441/jeo70lroq9p9bmeio80mpgg5h is not listed on IDEAS
    8. Goyal, S., 2016. "Networks and Markets," Cambridge Working Papers in Economics 1652, Faculty of Economics, University of Cambridge.
    9. David Rea & Craig Froehle & Suzanne Masterson & Brian Stettler & Gregory Fermann & Arthur Pancioli, 2021. "Unequal but Fair: Incorporating Distributive Justice in Operational Allocation Models," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 2304-2320, July.
    10. Antonides, Gerrit & Kroft, Maaike, 2005. "Fairness judgments in household decision making," Journal of Economic Psychology, Elsevier, vol. 26(6), pages 902-913, December.
    11. Huang, Jen-Hung & Chang, Ching-Te & Chen, Cathy Yi-Hsuan, 2005. "Perceived fairness of pricing on the Internet," Journal of Economic Psychology, Elsevier, vol. 26(3), pages 343-361, June.
    12. Buechel, Berno & Krähenmann, Philemon, 2022. "Fixed price equilibria on peer‐to‐peer platforms: Lessons from time‐based currencies," Journal of Economic Behavior & Organization, Elsevier, vol. 195(C), pages 335-358.
    13. Sylvain Mignot & Stéphanie Saba & Annick Vignes, 2016. "To trust or to bid: an empirical analysis of social relationships on a fish market," Working Papers halshs-01298872, HAL.
    14. Bodo Schlegelmilch & Magdalena Oberseder, 2007. "Ethical Issues in Global Supply Chains," Symphonya. Emerging Issues in Management, Niccolò Cusano University, issue 2 Ethics .
    15. Blázquez de Paz, Mario, 2018. "Electricity auctions in the presence of transmission constraints and transmission costs," Energy Economics, Elsevier, vol. 74(C), pages 605-627.
    16. Bagwell, Kyle & Wolinsky, Asher, 2002. "Game theory and industrial organization," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 49, pages 1851-1895, Elsevier.
    17. Bester, Helmut & Petrakis, Emmanuel, 1995. "Price competition and advertising in oligopoly," European Economic Review, Elsevier, vol. 39(6), pages 1075-1088, June.
    18. Berck, Peter & Brown, Jennifer & Perloff, Jeffrey M. & Villas-Boas, Sofia Berto, 2008. "Sales: Tests of theories on causality and timing," International Journal of Industrial Organization, Elsevier, vol. 26(6), pages 1257-1273, November.
    19. Michael R. Baye & John Morgan & Patrick Scholten, 2004. "Price Dispersion In The Small And In The Large: Evidence From An Internet Price Comparison Site," Journal of Industrial Economics, Wiley Blackwell, vol. 52(4), pages 463-496, December.
    20. Sjur Didrik Flåm, 2013. "Reaching Market Equilibrium Merely by Bilateral Barters," CESifo Working Paper Series 4504, CESifo.
    21. Charness, Gary & Corominas-Bosch, Margarida & Frechette, Guillaume R., 2007. "Bargaining and network structure: An experiment," Journal of Economic Theory, Elsevier, vol. 136(1), pages 28-65, September.
    22. repec:zbw:bofrdp:2017_020 is not listed on IDEAS
    23. Joshua Sherman & Avi Weiss, 2017. "On Fruitful And Futile Tests Of The Relationship Between Search And Price Dispersion," Economic Inquiry, Western Economic Association International, vol. 55(4), pages 1898-1918, October.

    More about this item

    Keywords

    Bertrand–Nash equilibrium; Undercut-proof equilibrium; Non-transferable utility coalitional games; Core equivalence; Network markets;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative 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:eee:jetheo:v:159:y:2015:i:pa:p:209-220. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.