Characterization of the painting rule for multi-source minimal cost spanning tree problems

Bergantiños, Gustavo and Navarro, Adriana (2019): Characterization of the painting rule for multi-source minimal cost spanning tree problems.

Abstract

In this paper we provide an axiomatic characterization of the painting rule for minimum cost spanning tree problems with multiple sources. The properties we need are: cone-wise additivity, cost monotonicity, symmetry, isolated agents, and equal treatment of source costs.

• Item Type: MPRA Paper
• Language: English
• Keywords: minimum cost spanning tree problems with multiple sources, painting rule, axiomatic characterization.
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games

References

G. Bergantinos and L. Lorenzo. Cost additive rules in minimum cost spanning tree problems with multiple sources. Mimeo, Universidade de Vigo, 2019.

G. Bergantinos and A. Navarro-Ramos. The folk rule through a painting procedure for minimum cost spanning tree problems with multiple sources. Mathematical Social Sciencies, 99: 43-48, 2019.

G. Bergantinos, M. Gomez-Rua, N. Llorca, M. Pulido, and J. Sanchez-Soriano. A new rule for source connection problems. European Journal of Operational Research, 234(3):780-788, 2014.

G. Bergantinos, Y. Chun, E. Lee, and L. Lorenzo. The folk rule for minimum cost spanning tree problems with multiple sources. Mimeo, Universidade de Vigo, 2019.

C. G. Bird. On cost allocation for a spanning tree: a game theoretic approach. Networks, 6(4):335-350, 1976.

B. Dutta and A. Kar. Cost monotonicity, consistency and minimum cost spanning tree games. Games and Economic Behavior, 48(2):223-248, 2004.

J. B. Kruskal. On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical society, 7(1): 48-50, 1956.

H. Norde, S. Moretti, and S. Tijs. Minimum cost spanning tree games and population monotonic allocation schemes. European Journal of Operational Research, 154(1):84-97, 2004.

R. C. Prim. Shortest connection networks and some generalizations. Bell Labs Technical Journal, 36(6):1389-1401, 1957.