Bargaining solutions via surface measures - Joachim Rosenmüller (Bielefeld University, Center for Mathematical Economics (IMW), 2021)
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 [n]n_1… n_n of normals in coordinate directions – a term generalizing the Maschler–Perles line integral of -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].
urn:nbn:de:0070-pub-29594673
Keywords: 330