Bargaining Solutions via Surface Measures

Joachim Rosenmüller
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Joachim Rosenmüller: Center for Mathematical Economics, Bielefeld University

No 658, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We introduce a generalization of the Maschler--Perles bargaining solution to smooth bargaining problems for $n$ players. We proceed by the construction of measures on the Pareto surface of a convex body. The MP surface measure is defined for Cephoids, i.e., Minkowski sums of simplices (see [14] for a coherent description); this measure cannot directly be extended to a smooth Pareto surface. Therefore, we introduce a further extension of the Maschler--Perles idea to Pareto surfaces of convex bodies. This extension is suggested by the density $\sqrt[n]{n_1\cdots n_n }$ of normals in coordinate directions -- a term generalizing the Maschler--Perles line integral of $\sqrt{-dx_1 dx_2}$ -- the "donkey cart" in their interpretation. The "deGua'' measure defined this way, is then verified to be the limiting measure of the MP measures along the filter of convergent Cephoids as established in [15].

Pages: 43
Date: 2021-11-22
New Economics Papers: this item is included in nep-gth
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