IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v102y2022ics0304406822000647.html
   My bibliography  Save this article

Spying in Bertrand markets under incomplete information: Who benefits and is it stable?

Author

Listed:
  • Fan, Cuihong
  • Jun, Byoung Heon
  • Wolfstetter, Elmar G.

Abstract

We analyze spying out a rival’s price in a general duopoly model with differentiated products where payoff functions are strictly supermodular and firms are subject to incomplete information about costs. Spying has two effects: it induces a sequential game and eliminates the spying firm’s uncertainty. In sharp contrast to the case of complete information, spying does not benefit both firms: it adversely affects the spied-at firm if its cost is low and may expose the spying firm to a negative value of information. We decompose the impact of spying into its sequential moves effect and its information effect and find conditions for profitable espionage. We also show that the spied-at firm cannot benefit from bypassing the spy if its cost is low by delaying its pricing decision (or firing the spy) because this would trigger a devastating cascade of belief changes.

Suggested Citation

  • Fan, Cuihong & Jun, Byoung Heon & Wolfstetter, Elmar G., 2022. "Spying in Bertrand markets under incomplete information: Who benefits and is it stable?," Journal of Mathematical Economics, Elsevier, vol. 102(C).
  • Handle: RePEc:eee:mateco:v:102:y:2022:i:c:s0304406822000647
    DOI: 10.1016/j.jmateco.2022.102722
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406822000647
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmateco.2022.102722?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. Amir, Rabah & Stepanova, Anna, 2006. "Second-mover advantage and price leadership in Bertrand duopoly," Games and Economic Behavior, Elsevier, vol. 55(1), pages 1-20, April.
    2. Esther Gal-or, 1986. "Information Transmission—Cournot and Bertrand Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 85-92.
    3. Bagwell, Kyle, 1995. "Commitment and observability in games," Games and Economic Behavior, Elsevier, vol. 8(2), pages 271-280.
    4. Arozamena, Leandro & Weinschelbaum, Federico, 2009. "The effect of corruption on bidding behavior in first-price auctions," European Economic Review, Elsevier, vol. 53(6), pages 645-657, August.
    5. Gal-Or, Esther, 1985. "First Mover and Second Mover Advantages," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 649-653, October.
    6. Burguet Roberto & Perry Martin K, 2007. "Bribery and Favoritism by Auctioneers in Sealed-Bid Auctions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-27, June.
    7. Kim, Jinwoo, 2008. "The value of an informed bidder in common value auctions," Journal of Economic Theory, Elsevier, vol. 143(1), pages 585-595, November.
    8. Giovanni Maggi, 1999. "The Value of Commitment with Imperfect Observability and Private Information," RAND Journal of Economics, The RAND Corporation, vol. 30(4), pages 555-574, Winter.
    9. Van Zandt, Timothy & Vives, Xavier, 2007. "Monotone equilibria in Bayesian games of strategic complementarities," Journal of Economic Theory, Elsevier, vol. 134(1), pages 339-360, May.
    10. van Damme, Eric & Hurkens, Sjaak, 1997. "Games with Imperfectly Observable Commitment," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 282-308, October.
    11. Solan, Eilon & Yariv, Leeat, 2004. "Games with espionage," Games and Economic Behavior, Elsevier, vol. 47(1), pages 172-199, April.
    12. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    13. Sakai, Yasuhiro, 1985. "The value of information in a simple duopoly model," Journal of Economic Theory, Elsevier, vol. 36(1), pages 36-54, June.
    14. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
    15. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    16. Barrachina, Alex & Tauman, Yair & Urbano, Amparo, 2014. "Entry and espionage with noisy signals," Games and Economic Behavior, Elsevier, vol. 83(C), pages 127-146.
    17. S. Ho, 2008. "Extracting the information: espionage with double crossing," Journal of Economics, Springer, vol. 93(1), pages 31-58, February.
    18. Steve Dowrick, 1986. "von Stackelberg and Cournot Duopoly: Choosing Roles," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 251-260, Summer.
    19. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
    20. Alex Barrachina & Yair Tauman & Amparo Urbano, 2021. "Entry with two correlated signals: the case of industrial espionage and its positive competitive effects," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 241-278, March.
    21. Xiaoshuai Fan & Ying‐Ju Chen & Christopher S. Tang, 2021. "To Bribe or Not in a Procurement Auction under Disparate Corruption Pressure," Production and Operations Management, Production and Operations Management Society, vol. 30(5), pages 1220-1245, May.
    22. Vives, Xavier, 1984. "Duopoly information equilibrium: Cournot and bertrand," Journal of Economic Theory, Elsevier, vol. 34(1), pages 71-94, October.
    23. Tao Wang, 2020. "Competitive Intelligence and Disclosure of Cost Information in Duopoly," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 57(3), pages 665-699, November.
    24. Konrad Podczeck, 2009. "On purification of measure-valued maps," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 399-418, February.
    25. Lengwiler, Yvan & Wolfstetter, Elmar, 2010. "Auctions and corruption: An analysis of bid rigging by a corrupt auctioneer," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 1872-1892, October.
    26. Kyung Hwan Baik & Shogren, Jason F., 1995. "Contests with spying," European Journal of Political Economy, Elsevier, vol. 11(3), pages 441-451, September.
    27. Raith, Michael, 1996. "A General Model of Information Sharing in Oligopoly," Journal of Economic Theory, Elsevier, vol. 71(1), pages 260-288, October.
    28. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    29. Sven Fischer & Werner Güth & Todd R. Kaplan & Ro'i Zultan, 2021. "Auctions With Leaks About Early Bids: Analysis And Experimental Behavior," Economic Inquiry, Western Economic Association International, vol. 59(2), pages 722-739, April.
    30. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    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. Cuihong Fan & Byoung Heon Jun & Elmar G. Wolfstetter, 2019. "Induced Price Leadership and (Counter-)Spying Rivals' Play under Incomplete Information," CESifo Working Paper Series 7476, CESifo.
    2. Cuihong Fan & Byoung Heon Jun & Elmar G. Wolfstetter, 2023. "Price leadership, spying, and secret price changes: a Stackelberg game with imperfect commitment," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 775-804, September.
    3. Arozamena, Leandro & Weinschelbaum, Federico, 2009. "Simultaneous vs. sequential price competition with incomplete information," Economics Letters, Elsevier, vol. 104(1), pages 23-26, July.
    4. Cuihong Fan & Byoung Heon Jun & Elmar G. Wolfstetter, 2023. "Spying and imperfect commitment in first-price auctions: a case of tacit collusion," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 255-275, October.
    5. Cumbul, Eray, 2021. "Stackelberg versus Cournot oligopoly with private information," International Journal of Industrial Organization, Elsevier, vol. 74(C).
    6. Tao Wang, 2020. "Competitive Intelligence and Disclosure of Cost Information in Duopoly," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 57(3), pages 665-699, November.
    7. Oriol Carbonell-Nicolau & Richard P. McLean, 2018. "On the Existence of Nash Equilibrium in Bayesian Games," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 100-129, February.
    8. Jonas Send, 2021. "Contest Copycats: Adversarial Duplication of Effort in Contests," Working Papers tax-mpg-rps-2021-17, Max Planck Institute for Tax Law and Public Finance.
    9. Camille Cornand & Rodolphe Dos Santos Ferreira, 2020. "The social value of information and the competition motive: price versus quantity games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1101-1137, November.
    10. Barrachina, Alex & Tauman, Yair & Urbano, Amparo, 2014. "Entry and espionage with noisy signals," Games and Economic Behavior, Elsevier, vol. 83(C), pages 127-146.
    11. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899, January.
    12. Chia-Hung Sun, 2020. "Simultaneous and sequential choice in a symmetric two-player game with canyon-shaped payoffs," The Japanese Economic Review, Springer, vol. 71(2), pages 191-219, April.
    13. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    14. Matsui, Kenji, 2017. "When should a manufacturer set its direct price and wholesale price in dual-channel supply chains?," European Journal of Operational Research, Elsevier, vol. 258(2), pages 501-511.
    15. Ilkka Leppänen, 2020. "Partial commitment in an endogenous timing duopoly," Annals of Operations Research, Springer, vol. 287(2), pages 783-799, April.
    16. Michael Kopel & Clemens Löffler, 2008. "Commitment, first-mover-, and second-mover advantage," Journal of Economics, Springer, vol. 94(2), pages 143-166, July.
    17. Haiyang Xia, 2021. "Price and quantity competition in a differentiated duopoly with heterogeneous beliefs," Manchester School, University of Manchester, vol. 89(1), pages 46-69, January.
    18. Junjie Zhou & Xiaoshuai Fan & Ying-Ju Chen & Christopher S. Tang, 2021. "Information Provision and Farmer Welfare in Developing Economies," Manufacturing & Service Operations Management, INFORMS, vol. 23(1), pages 230-245, 1-2.
    19. Matsui, Kenji, 2016. "Asymmetric product distribution between symmetric manufacturers using dual-channel supply chains," European Journal of Operational Research, Elsevier, vol. 248(2), pages 646-657.
    20. Magnus Hoffmann & Grégoire Rota‐Graziosi, 2020. "Endogenous timing in the presence of non‐monotonicities," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(1), pages 359-402, February.

    More about this item

    Keywords

    Bertrand games; Stackelberg games; Corporate espionage; Incomplete information; Value of information in games;
    All these keywords.

    JEL classification:

    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L41 - Industrial Organization - - Antitrust Issues and Policies - - - Monopolization; Horizontal Anticompetitive Practices
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:mateco:v:102:y:2022:i:c:s0304406822000647. 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/jmateco .

    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.