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Relational Contracting, Repeated Negotiations, and Hold-Up

  • Sebastian Kranz

    (Dept. of Mathematics and Economics, University of Ulm)

We propose a unified framework to study relational contracting and hold-up problems in infinite horizon stochastic games. We first illustrate that with respect to long run decisions, the common formulation of relational contracts as Pareto-optimal public perfect equilibria is in stark contrast to fundamental assumptions of hold-up models. We develop a model in which relational contracts are repeatedly newly negotiated during relationships. Negotiations take place with positive probability and cause bygones to be bygones. Traditional relational contracting and hold-up formulations are nested as opposite corner cases. Allowing for intermediate cases yields very intuitive results and sheds light on many plausible trade-offs that do not arise in these corner cases. We establish a general existence result and a tractable characterization for stochastic games in which money can be transferred. This paper formulates a theory of relational contracting in dynamic games. A crucial feature is that existing relational contracts can depreciate and ensuing negotiations then treat previous informal agreements as bygones. The model nests the traditional formulation of relational contracts as Pareto-optimal equilibria as a special case. In repeated games both formulations are always mathematically equivalent. We provide ample illustrations that in dynamic games the traditional formulation is restrictive in so far that it rules out by assumption many plausible hold-up problems -- even for small discount factors. Our model provides a framework that naturally unifies the analysis of relational contracting and hold-up problems.

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File URL: http://cowles.econ.yale.edu/P/cd/d18b/d1888.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1888.

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Length: 44 pages
Date of creation: Feb 2013
Date of revision:
Handle: RePEc:cwl:cwldpp:1888
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Web page: http://cowles.econ.yale.edu/

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  1. Sebastian Kranz, 2012. "Discounted Stochastic Games with Voluntary Transfers," Cowles Foundation Discussion Papers 1847, Cowles Foundation for Research in Economics, Yale University.
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  8. Goldluecke, Susanne & Kranz, Sebastian, 2010. "In?nitely Repeated Games with Public Monitoring and Monetary Transfers," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 332, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
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  13. Johannes Hörner & Takuo Sugaya & Satoru Takahashi & Nicolas Vieille, 2011. "Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem," Econometrica, Econometric Society, vol. 79(4), pages 1277-1318, 07.
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  19. Tore Ellingsen & Magnus Johannesson, 2004. "Is There a Hold-up Problem?," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 475-494, October.
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  23. Blonski, Matthias & Spagnolo, Giancarlo, 2002. "Relational Contracts and Property Rights," CEPR Discussion Papers 3460, C.E.P.R. Discussion Papers.
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  28. Asheim, Geir B., 1991. "Extending renegotiation-proofness to infinite horizon games," Games and Economic Behavior, Elsevier, vol. 3(3), pages 278-294, August.
  29. Goldlücke, Susanne & Kranz, Sebastian, 2013. "Renegotiation-proof relational contracts," Games and Economic Behavior, Elsevier, vol. 80(C), pages 157-178.
  30. 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.
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