Abstract
For a transferable utility game the convex hull of the Weber allocations contains the core as a subset. A proof of this result normally involves an induction hypothesis to the number of players. We will give here a short proof based on a well known result in convex analysis.
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References
Derks JJM, Gilles RP (1992) Hierarchical Organization Structures and Constraints in Coalition Formation. Working Paper, Department of Economics, Virginia State University, Blacksburg.
Weber RJ (1988) Probabilistic values for games. In: The Shapley Value, edited by A. E. Roth, Cambridge University Press, 101–119.
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Derks, J.J.M. A short proof of the inclusion of the core in the Weber set. Int J Game Theory 21, 149–150 (1992). https://doi.org/10.1007/BF01245457
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DOI: https://doi.org/10.1007/BF01245457