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Costly Renegotiation in Repeated Bertrand Games

Author

Listed:
  • Andersson, Ola

    () (Dept. of Economics, Stockholm School of Economics)

  • Wengström, Erik

    () (Department of Economics, University of Copenhagen)

Abstract

This paper extends the concept of weak renegotiation-proof equilibrium (WRP) to allow for costly renegotiation and shows that even small renegotiation costs can have dramatic effects on the set of equilibria. More specifically, the paper analyzes the infinitely repeated Bertrand game. It is shown that for every level of renegotiation cost there exists a discount factor such that any collusive profit can be supported as an equilibrium outcome. Hence, any arbitrary small renegotiation cost will suffice to facilitate collusive outcomes for sufficiently patient firms. This result stands in stark contrast to the unique pure-strategy WRP equilibrium without renegotiation costs, which implies marginal-cost pricing in every period. Moreover, in comparison to the findings of McCutcheon (1997), who states that renegotiation costs have to be substantial to facilitate collusion, this result points to a quite different conclusion.

Suggested Citation

  • Andersson, Ola & Wengström, Erik, 2010. "Costly Renegotiation in Repeated Bertrand Games," SSE/EFI Working Paper Series in Economics and Finance 725, Stockholm School of Economics.
  • Handle: RePEc:hhs:hastef:0725
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    References listed on IDEAS

    as
    1. Motta,Massimo, 2004. "Competition Policy," Cambridge Books, Cambridge University Press, number 9780521016919, Fall.
    2. van Damme, Eric, 1989. "Renegotiation-proof equilibria in repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 47(1), pages 206-217, February.
    3. McCutcheon, Barbara, 1997. "Do Meetings in Smoke-Filled Rooms Facilitate Collusion?," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 330-350, April.
    4. David Genesove & Wallace P. Mullin, 2001. "Rules, Communication, and Collusion: Narrative Evidence from the Sugar Institute Case," American Economic Review, American Economic Association, vol. 91(3), pages 379-398, June.
    5. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December.
    6. Blume Andreas, 1994. "Intraplay Communication in Repeated Games," Games and Economic Behavior, Elsevier, vol. 6(2), pages 181-211, March.
    7. Goldlücke, Susanne & Kranz, Sebastian, 2013. "Renegotiation-proof relational contracts," Games and Economic Behavior, Elsevier, vol. 80(C), pages 157-178.
    8. Aramendia, Miguel & Larrea, Concepcion & Ruiz, Luis, 2005. "Renegotiation in the repeated Cournot model," Games and Economic Behavior, Elsevier, vol. 52(1), pages 1-19, July.
    9. Asheim, Geir B., 1991. "Extending renegotiation-proofness to infinite horizon games," Games and Economic Behavior, Elsevier, vol. 3(3), pages 278-294, August.
    10. Andersson, Ola & Wengstrom, Erik, 2007. "A note on renegotiation in repeated Bertrand duopolies," Economics Letters, Elsevier, vol. 95(3), pages 398-401, June.
    11. Kranz, Sebastian & Ohlendorf, Susanne, 2009. "Renegotiation-Proof Relational Contracts with Side Payments," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 259, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    12. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
    13. van Damme, Eric, 1989. "Renegotiation-proof equilibria in repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 47(1), pages 206-217, February.
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    More about this item

    Keywords

    Noncooperative game theory; Weak Renegotiation-proofness; Costly Renegotation; Repeated Bertrand games;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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