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Assignment of Heterogeneous Agents in Trees under the Permission Value


  • Chakrabarti, Subhadip
  • Ghintran, Amandine


We investigate assignment of heterogeneous agents in trees where the allocation rule is given by the permission value. We focus on efficient hierarchies,namely those, for which the payoff of the top agent is maximized. For additive games, such hierarchies are always cogent, namely, more productive agents occupy higher positions. The result can be extended to non-additive games with appropriate restrictions on the value function. Finally, we consider auctions where agents bid for positions in a two agent vertical hierarchy. Under simultaneous bidding, an equilibrium does not exist while sequential bidding always results in a non-cogent hierarchy.

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  • Chakrabarti, Subhadip & Ghintran, Amandine, 2013. "Assignment of Heterogeneous Agents in Trees under the Permission Value," MPRA Paper 49115, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:49115

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    References listed on IDEAS

    1. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    2. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    3. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    4. Oliver E. Williamson, 1967. "Hierarchical Control and Optimum Firm Size," Journal of Political Economy, University of Chicago Press, vol. 75, pages 123-123.
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    More about this item


    permission value; hierarchies;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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