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Price leadership, spying, and secret price changes: a Stackelberg game with imperfect commitment

Author

Listed:
  • Cuihong Fan

    (Shanghai University of Finance and Economics)

  • Byoung Heon Jun

    (Korea University)

  • Elmar G. Wolfstetter

    (Humboldt-University at Berlin)

Abstract

We analyze price leadership in a Stackelberg game with incomplete information and imperfect commitment. Sequential play is induced by an information system, represented by a spy, that reports the price of one firm to its rival before the latter chooses its own price. However, the Stackelberg leader may secretly revise its price with some probability. Therefore, the spy’s message is only an imperfect signal. This gives rise to a complex signaling problem where both sender and receiver of messages have private information and the sender has a chance to take another action with some probability. We find partially separating and pooling equilibria that satisfy equilibrium refinements such as the intuitive criterion and support collusive outcomes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jogath:v:52:y:2023:i:3:d:10.1007_s00182-023-00840-9
    DOI: 10.1007/s00182-023-00840-9
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    References listed on IDEAS

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    1. Milgrom, Paul & Roberts, John, 1982. "Limit Pricing and Entry under Incomplete Information: An Equilibrium Analysis," Econometrica, Econometric Society, vol. 50(2), pages 443-459, March.
    2. Bagwell, Kyle, 1995. "Commitment and observability in games," Games and Economic Behavior, Elsevier, vol. 8(2), pages 271-280.
    3. van Damme, Eric & Hurkens, Sjaak, 1996. "Commitment Robust Equilibria and Endogenous Timing," Games and Economic Behavior, Elsevier, vol. 15(2), pages 290-311, August.
    4. 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.
    5. van Damme, Eric & Hurkens, Sjaak, 2004. "Endogenous price leadership," Games and Economic Behavior, Elsevier, vol. 47(2), pages 404-420, May.
    6. 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.
    7. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 179-221.
    8. Rotemberg, Julio J & Saloner, Garth, 1986. "A Supergame-Theoretic Model of Price Wars during Booms," American Economic Review, American Economic Association, vol. 76(3), pages 390-407, June.
    9. 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.
    10. Solan, Eilon & Yariv, Leeat, 2004. "Games with espionage," Games and Economic Behavior, Elsevier, vol. 47(1), pages 172-199, April.
    11. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
    12. Robert H. Porter, 1983. "A Study of Cartel Stability: The Joint Executive Committee, 1880-1886," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 301-314, Autumn.
    13. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
    14. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    15. Dmitry I. Ivanov & Alexander S. Nesterov, 2019. "Stealed-bid Auctions: Detecting Bid Leakage via Semi-Supervised Learning," Papers 1903.00261, arXiv.org, revised Nov 2020.
    16. Steve Dowrick, 1986. "von Stackelberg and Cournot Duopoly: Choosing Roles," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 251-260, Summer.
    17. 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.
    18. 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.
    19. Mouraviev, Igor & Rey, Patrick, 2011. "Collusion and leadership," International Journal of Industrial Organization, Elsevier, vol. 29(6), pages 705-717.
    20. 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.
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