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Cooperative production under diminishing marginal returns: Interpreting fixed-path methods

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Abstract

Fixed-path methods (FPMs) were introduced to manage situations where several individuals jointly operate a single technology (see [4]). In the production context, they consist in allocating marginal increments of output according to a proportions vector which changes along an arbitrary path. While very appealing from an incentives viewpoint under diminishing marginal returns, the asymmetry of these methods lacks solid economic interpretation. We provide such an interpretation by considering a situation where the technology to be shared results from the aggregation of private production processes. We propose a group-strategyproof mechanism under which no single agent wishes to secede from the partnership: the inverse marginal product proportions mechanism. It is the only FPM satisfying autarkic individual rationality; its path is uniquely determined by the technological contributions of the agents.

Suggested Citation

  • Justin Leroux, 2006. "Cooperative production under diminishing marginal returns: Interpreting fixed-path methods," Cahiers de recherche 06-10, HEC Montréal, Institut d'économie appliquée.
    • Handle: RePEc:iea:carech:0610
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    1. Shin, Sungwhee & Suh, Sang-Chul, 1997. "Double Implementation by a Simple Game Form in the Commons Problem," Journal of Economic Theory, Elsevier, vol. 77(1), pages 205-213, November.
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    9. Friedman, Eric J., 2002. "Strategic properties of heterogeneous serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 145-154, November.
    10. Eric Friedman, 2004. "Strong monotonicity in surplus sharing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 643-658, March.
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    Cited by:

    1. Kumar, Rajnish, 2013. "Secure implementation in production economies," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 372-378.
    2. Trudeau, Christian, 2009. "Cost sharing with multiple technologies," Games and Economic Behavior, Elsevier, vol. 67(2), pages 695-707, November.
    3. Chatterjee, Siddhartha & Ertemel, Sinan & Kumar, Rajnish, 2021. "Parametric Rules for State Contingent Claims," QBS Working Paper Series 2021/03, Queen's University Belfast, Queen's Business School.
    4. Moulin, Hervé, 2010. "An efficient and almost budget balanced cost sharing method," Games and Economic Behavior, Elsevier, vol. 70(1), pages 107-131, September.
    5. Leroux, Justin, 2008. "Profit sharing in unique Nash equilibrium: Characterization in the two-agent case," Games and Economic Behavior, Elsevier, vol. 62(2), pages 558-572, March.

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    More about this item

    Keywords

    Autarky; incentive compatibility; cooperative production; surplus sharing; serial rule; path methods.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D23 - Microeconomics - - Production and Organizations - - - Organizational Behavior; Transaction Costs; Property Rights
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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