Abstract
The manipulation of the Shapley-value, when used as a resource allocation mechanism, is examined. First, the extent to which an individual can, by unilaterally misrepresenting his utility function, affect the value allocation in his favor, is evaluated. When all agents attempt to manipulate, a game results, whose equilibrium allocations can be described as follows. At an equilibrium, the initial allocation appears to be Pareto-efficient. Any equilibrium allocation is also an equilibrium allocation of the analogously defined Walrasian manipulation game. The true (constrained) Walrasian allocations are equilibrium allocations. Under two slight respecifications of the value, there are no other equilibrium allocations.
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This is a revised version of a University of Minnesota discussion paper (September 1979). The author thanks L. Hurwicz, T. Ikeda, T. Ito, J. Jordan, and particularly A. Mas-Colell for their comments. Assistance from NSF, under grant No 8006482, and from the Sloan Foundation, is gratefully acknowledged.
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Thomson, W. The manipulability of the Shapley-value. Int J Game Theory 17, 101–127 (1988). https://doi.org/10.1007/BF01254542
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DOI: https://doi.org/10.1007/BF01254542