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The core of large differentiable TU games. (English) Zbl 1005.91014
The authors show that for non-atomic TU games under certain conditions, the core can be determined by computing appropriate derivatives of the characteristic function $$v$$. The computations yield either the core of $$v$$ is empty or it consists of a single measure. If the latter case happens, the core measure can be expressed explicitly in terms of the derivatives of $$v$$. Then the core theory for a class of non-atomic TU games may be reduced to calculus.

MSC:
 91A12 Cooperative games 91A13 Games with infinitely many players (MSC2010)
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References:
 [1] Aumann, R.; Dreze, J., Co-operative games with coalition structures, Int. J. game theory, 3, 217-237, (1974) · Zbl 0313.90074 [2] Aumann, R.; Shapley, L., Values of non-atomic games, (1974), Princeton Univ. Press Princeton · Zbl 0311.90084 [3] Einy, E.; Moreno, D.; Shitovitz, B., The core of a class of non-atomic games which arise in economic applications, Int. J. game theory, 28, 1-14, (1999) · Zbl 0960.91010 [4] Epstein, L.G., A definition of uncertainty aversion, Rev. econ. stud., 66, 579-608, (1999) · Zbl 0953.91002 [5] Hart, S.; Neyman, A., Values of non-atomic vector measure games, J. math. econ., 17, 31-40, (1988) · Zbl 0662.90100 [6] M. Machina, Local probabilistic sophistication, mimeo, UC, San Diego, 1992. [7] Mertens, J.F., Values and derivatives, Math. oper. res., 5, 523-552, (1980) · Zbl 0448.90079 [8] Phelps, R.P., Convex functions, monotone operators, and differentiability, Lecture notes in mathematics, 1364, (1989), Springer-Verlag New York [9] Rao, B.; Rao, B., Theory of charges, (1983), Academic Press New York [10] Rockafellar, R.T., Convex analysis, (1970), Princeton Univ. Press Princeton · Zbl 0229.90020 [11] Rosenmuller, J., Some properties of convex set functions, part II, Math. oper. res., 17, 277-307, (1972) [12] Schmeidler, D., Cores of exact games, J. math. anal. appl., 40, 214-225, (1972) · Zbl 0243.90071 [13] Schmeidler, D., Subjective probability and expected utility without additivity, Econometrica, 57, 571-587, (1989) · Zbl 0672.90011 [14] Wasserman, L.A.; Kadane, J., Symmetric upper probabilities, Ann. stat., 20, 1720-1736, (1992) · Zbl 0767.60001
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