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Assignment of heterogeneous agents in trees under the permission value

Author

Listed:
  • Subhadip Chakrabarti

    (Queen’s University Belfast)

  • Amandine Ghintran

    (LEM, University of Lille)

  • Rajnish Kumar

    (Queen’s University Belfast)

Abstract

We investigate assignment of heterogeneous agents in trees where the payoff is given by the permission value. We focus on optimal 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. Next, we consider auctions where agents bid for positions in a vertical hierarchy of depth 2 . Under standard auctions, usually this results in a non-cogent hierarchy.

Suggested Citation

  • Subhadip Chakrabarti & Amandine Ghintran & Rajnish Kumar, 2019. "Assignment of heterogeneous agents in trees under the permission value," Review of Economic Design, Springer;Society for Economic Design, vol. 23(3), pages 155-188, December.
  • Handle: RePEc:spr:reecde:v:23:y:2019:i:3:d:10.1007_s10058-019-00226-y
    DOI: 10.1007/s10058-019-00226-y
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    References listed on IDEAS

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    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. Gilles, R.P. & Owen, G., 1999. "Cooperative Games and Disjunctive Permission Structures," Discussion Paper 1999-20, Tilburg University, Center for Economic Research.
    4. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    5. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 754-778, August.
    6. Stole, Lars A & Zwiebel, Jeffrey, 1996. "Organizational Design and Technology Choice under Intrafirm Bargaining," American Economic Review, American Economic Association, vol. 86(1), pages 195-222, March.
    7. René Brink & Pieter Ruys, 2008. "Technology driven organizational structure of the firm," Annals of Finance, Springer, vol. 4(4), pages 481-503, October.
    8. René Brink & Chris Dietz & Gerard Laan & Genjiu Xu, 2017. "Comparable characterizations of four solutions for permission tree games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(4), pages 903-923, April.
    9. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    10. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
    11. Oliver E. Williamson, 1967. "Hierarchical Control and Optimum Firm Size," Journal of Political Economy, University of Chicago Press, vol. 75, pages 123-123.
    12. René Brink, 2008. "Vertical wage differences in hierarchically structured firms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 225-243, February.
    13. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
    14. Gilles, R.P. & Owen, G., 1999. "Cooperative Games and Disjunctive Permission Structures," Other publications TiSEM 4f162187-3069-4cb5-8353-5, Tilburg University, School of Economics and Management.
    15. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    16. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 249-266.
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    More about this item

    Keywords

    Permission value; Hierarchies; Auctions;
    All these keywords.

    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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