论文信息 - Bird's tree allocations revisited

Bird's tree allocations revisited

Minimum cost spanning tree (mcst) construction and cost allocation problems have been studied extensively in the literature, though usually not together. Bird (1976) proposes an allocation rule of which Granot and Huberman (1981) prove that it lies in the core of the associated mcst game. We show that the problems of finding an mcst and allocating its cost can be integrated. Furthermore, we provide an axiomatic characterization of the set of all Bird’s tree allocations using consistency, converse consistency, non-emptyness and efficiency, and give a strategic form game of which the set of Nash equilibria contains Bird’s tree allocations.

Shigeo Muto | Vincent Feltkamp | Stef Tijs

[1] Daniel J. Kleitman,et al. Cost allocation for a spanning tree , 1973, Networks.

[2] C. G. Bird,et al. On cost allocation for a spanning tree: A game theoretic approach , 1976, Networks.

[3] J. Kruskal. On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[4] R. Prim. Shortest connection networks and some generalizations , 1957 .

[5] Daniel Granot,et al. Minimum cost spanning tree games , 1981, Math. Program..

[6] Henricus F.M. Aarts. Marginal allocations in the core of minimal chain-games , 1992 .

[7] Ronald L. Graham,et al. On the History of the Minimum Spanning Tree Problem , 1985, Annals of the History of Computing.

[8] Theo S. H. Driessen,et al. The irreducible Core of a minimum cost spanning tree game , 1993, ZOR Methods Model. Oper. Res..

[9] Daniel Granot,et al. On the core and nucleolus of minimum cost spanning tree games , 1984, Math. Program..

[10] Jeroen Kuipers. On the core of information graph games , 1993 .

[11] Edsger W. Dijkstra,et al. A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[12] Daniel Granot,et al. The Relationship Between Convex Games and Minimum Cost Spanning Tree Games: A Case for Permutationally Convex Games , 1982 .