Impossibility of Collusion under Imperfect Monitoring with Flexible Production

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Impossibility of Collusion under Imperfect Monitoring with Flexible Production

Author Info

Yuliy Sannikov
Andrzej Skrzypacz

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Andrzej Skrzypacz

Abstract

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.

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Paper provided by Society for Economic Dynamics in its series 2004 Meeting Papers with number 418.

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Date of creation: 2004
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Handle: RePEc:red:sed004:418

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Article
- Yuliy Sannikov & Andrzej Skrzypacz, 2007. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," American Economic Review, American Economic Association, vol. 97(5), pages 1794-1823, December. [Downloadable!]
Paper
- Skrzypacz, Andrzej & Sannikov, Yuliy, 2005. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," Research Papers 1887, Stanford University, Graduate School of Business. [Downloadable!]

Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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. [Downloadable!] (restricted)
Susan Athey & Kyle Bagwell & Chris Sanchirico, 1998. "Collusion and Price Rigidity," Working papers 98-23, Massachusetts Institute of Technology (MIT), Department of Economics.
Other versions:
- Susan Athey & Kyle Bagwell & Chris Sanchirico, 2002. "Collusion and price rigidity," Discussion Papers 0102-38, Columbia University, Department of Economics. [Downloadable!]
- Kyle Bagwell, 2004. "Collusion and Price Rigidity," Theory workshop papers 658612000000000081, UCLA Department of Economics. [Downloadable!]
- Susan Athey & Kyle Bagwell & Chris Sanchirico, 2004. "Collusion and Price Rigidity," Review of Economic Studies, Blackwell Publishing, vol. 71(2), pages 317-349, 04. [Downloadable!] (restricted)
Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-33, November. [Downloadable!] (restricted)
Other versions:
- Abreu, D. & Milgrom, P. & Pearce, D., 1990. "Information And Timing In Repeated Partnerships," Papers e-90-14, Stanford - Hoover Institution.
- David G. Pearce & Dilip Abreu & Paul R. Milgrom, 1988. "Information and Timing in Repeated Partnerships," Cowles Foundation Discussion Papers 875, Cowles Foundation, Yale University. [Downloadable!]
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. [Downloadable!] (restricted)
Joseph E Harrington & Jr Andrzej Skrzypacz, 2004. "Collusion under Monitoring of Sales," Economics Working Paper Archive 509, The Johns Hopkins University,Department of Economics, revised Mar 2005. [Downloadable!]
Other versions:
- Skrzypacz, Andrzej & Harrington, Joseph E., 2005. "Collusion under Monitoring of Sales," Research Papers 1885, Stanford University, Graduate School of Business. [Downloadable!]
Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January. [Downloadable!] (restricted)
Other versions:
- Green, Edward J. & Porter, Robert H., 1982. "Noncooperative Collusion Under Imperfect Price Information," Working Papers 367, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
Susan Athey & Kyle Bagwell, 1999. "Optimal Collusion with Private Information," Working papers 99-17, Massachusetts Institute of Technology (MIT), Department of Economics.
Other versions:
- Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-65, Autumn.
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. [Downloadable!] (restricted)
Other versions:
- Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 2058, David K. Levine. [Downloadable!]
- Fudenberg, D. & Levine, D.K. & Maskin, E., 1989. "The Folk Theorem With Inperfect Public Information," Working papers 523, Massachusetts Institute of Technology (MIT), Department of Economics.
- Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine. [Downloadable!]
Hay, George A & Kelley, Daniel, 1974. "An Empirical Survey of Price Fixing Conspiracies," Journal of Law & Economics, University of Chicago Press, vol. 17(1), pages 13-38, April.
David A. Miller, 2005. "The dynamic cost of ex post incentive compatibility in repeated games of private information," Game Theory and Information 0510002, EconWPA. [Downloadable!]
Skrzypacz, Andrzej & Hopenhayn, Hugo, 2004. "Tacit collusion in repeated auctions," Journal of Economic Theory, Elsevier, vol. 114(1), pages 153-169, January. [Downloadable!] (restricted)
Other versions:
- Hopenhayn, Hugo A. & Skrzypacz, Andrzej, 2001. "Tacit Collusion in Repeated Auctions," Research Papers 1698r2, Stanford University, Graduate School of Business. [Downloadable!]

Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

David A. Miller, 2005. "The dynamic cost of ex post incentive compatibility in repeated games of private information," Game Theory and Information 0510002, EconWPA. [Downloadable!]
Osório-Costa, António M., 2009. "Efficiency Gains in Repeated Games at Random Moments in Time," MPRA Paper 13105, University Library of Munich, Germany, revised 03 Feb 2009. [Downloadable!]
Drew Fudenberg & David K Levine, 2007. "Continuous Time Limits of Repeated Games with Imperfect Public Monitoring," Levine's Working Paper Archive 699152000000000028, David K. Levine. [Downloadable!]
Other versions:
- Drew Fudenberg & David Levine, 2007. "Continuous Time Limits of Repeated Games with Imperfect Public Monitoring," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(2), pages 173-192, April. [Downloadable!] (restricted)
Osório-Costa, António M., 2009. "Frequent Monitoring in Repeated Games under Brownian Uncertainty," MPRA Paper 13104, University Library of Munich, Germany. [Downloadable!]
Drew Fudenberg & David K Levine, 2007. "Repeated Games with Frequent Signals," Levine's Working Paper Archive 814577000000000009, David K. Levine. [Downloadable!]

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