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Obligation rules for minimum cost spanning tree situations and their monotonicity properties

Institution:	1. Department of Mathematics, University of Genoa, Italy and CentER and Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands;2. Faculty of Computer Science, “Alexandru Ioan Cuza” University, Carol I Bd., 11, 6600 Iasi, Romania;3. Unit of Molecular Epidemiology, National Cancer Research Institute of Genoa and Department of Mathematics, University of Genoa, Via Dodecaneso, 35, 16146 Genoa, Italy;4. CentER and Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands;1. Perm State University, Russia;2. ICREA-Barcelona Supercomputing Centre, Spain;1. Department of Business and Management Science, NHH Norwegian School of Economics, N-5045 Bergen, Norway;2. Département de génie mécanique, Université Laval, Québec, G1V 0A6, Canada;1. Tecnológico de Monterrey (ITESM), Campus Monterrey, Mexico;2. Central Economics and Mathematics Institute (CEMI), Moscow, Russia;3. Sumy State University, Sumy, Ukraine;4. ICREA-BSC, C/Jordi Girona 29, Barcelona, Spain;5. Universidad Autónoma de Nuevo León (UANL), Monterrey, Mexico

Abstract:	We consider the class of Obligation rules for minimum cost spanning tree situations. The main result of this paper is that such rules are cost monotonic and induce also population monotonic allocation schemes. Another characteristic of Obligation rules is that they assign to a minimum cost spanning tree situation a vector of cost contributions which can be obtained as product of a double stochastic matrix with the cost vector of edges in the optimal tree provided by the Kruskal algorithm. It turns out that the Potters value (P-value) is an element of this class.

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