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Impossibility of Collusion under Imperfect Monitoring with Flexible Production


  • Yuliy Sannikov
  • Andrzej Skrzypacz


We show that it is impossible to achieve collusion in a duopoly when (1) the prices depend only on the sum of the firms' supplies (2) firms are able to respond to new information quickly and (3) the likelihood ratio for detection of each deviation is a continuous process (so that new information does not arrive in jumps.) We prove this result in a discrete-time setting where prices are stationary normal random variables whose mean depends on the sum of produced quantities and the variance is inversely proportional to time interval over which the quantities are fixed. The length of this interval represents the flexibility of production. In this setting, we show that when the production is sufficiently flexible, so that firms can move sufficiently frequently, it is not possible to sustain payoffs better than in a static Nash equilibrium. This result is valid even when we allow asymmetric public perfect equilibria with the possibility of monetary transfers. We also discuss effects of product differentiation.

Suggested Citation

  • Yuliy Sannikov & Andrzej Skrzypacz, 2004. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," 2004 Meeting Papers 418, Society for Economic Dynamics.
  • Handle: RePEc:red:sed004:418

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    References listed on IDEAS

    1. Susan Athey & Kyle Bagwell & Chris Sanchirico, 2004. "Collusion and Price Rigidity," Review of Economic Studies, Oxford University Press, vol. 71(2), pages 317-349.
    2. Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-465, Autumn.
    3. Fudenberg, Drew & Levine, David I & Maskin, Eric, 1994. "The Folk Theorem with Imperfect Public Information," Econometrica, Econometric Society, vol. 62(5), pages 997-1039, September.
    4. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-1733, November.
    5. Joseph E. Harrington Jr. & Andrzej Skrzypacz, 2007. "Collusion under monitoring of sales," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 314-331, June.
    6. David A. Miller, 2012. "Robust Collusion with Private Information," Review of Economic Studies, Oxford University Press, vol. 79(2), pages 778-811.
    7. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    8. Skrzypacz, Andrzej & Hopenhayn, Hugo, 2004. "Tacit collusion in repeated auctions," Journal of Economic Theory, Elsevier, vol. 114(1), pages 153-169, January.
    9. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
    10. Andreas Blume & Paul Heidhues, 2008. "Modeling Tacit Collusion in Auctions," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 164(1), pages 163-184, March.
    11. Hay, George A & Kelley, Daniel, 1974. "An Empirical Survey of Price Fixing Conspiracies," Journal of Law and Economics, University of Chicago Press, vol. 17(1), pages 13-38, April.
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    More about this item


    repated games; imperfect monitoring; collusion;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory


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