Summary
A new way is presented to define for minimum cost spanning tree (mcst) games the irreducible core, which is introduced by Bird in 1976. The Bird core correspondence turns out to have interesting monotonicity and additivity properties and each stable cost monotonic allocation rule for mcst-problems is a selection of the Bird core correspondence. Using the additivity property an axiomatic characterization of the Bird core correspondence is obtained.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
H. Aarts. Minimum cost spanning tree games and set games. PhD Dissertation, Univ. of Twente, The Netherlands, 1994.
G. Bergañtinos and J.J. Vidal-Puga. Defining rules in cost spanning tree problems through the canonical form. EconPapers (RePEc:wpa:wuwpga 0402004), 2004.
C.G. Bird. On cost allocation for a spanning tree: a game theoretic approach. Networks 6:335–350, 1976.
R. Branzei, S. Moretti, H. Norde, and S. Tijs. The P-value for cost sharing in minimum cost spanning tree situations. Theory and Decision 56:47–61, 2004.
R. Branzei, T. Solymosi, and S. Tijs. Type monotonic allocation schemes for multi-glove games. CentER DP 2002-117, Tilburg Univ., The Netherlands, 2002.
R. Branzei and S. Tijs. Additivity regions for solutions in cooperative game theory. Libertas Mathematics 21:155–167, 2001.
R. Branzei, S. Tijs, and J. Timmer. Information collecting situations and bimonotonic allocation schemes. Math. Meth. Oper. Res., 54:303–313, 2001.
A. Claus and D.J. Kleitman. Cost allocation for a spanning tree. Networks 3:289–304, 1973.
I. Dragan, J. Potters, and S. Tijs. Superadditivity for solutions of coalitional games. Libertas Mathematics 9:101–110, 1989.
B. Dutta and A. Kar. Cost monotonicity, consistency and minimum cost spanning tree games. Games and Economic Behavior, 48:223–248, 2004.
V. Feltkamp. Cooperation in controlled network structures. PhD Dissertation, Tilburg Univ., The Netherlands, 1995.
V. Feltkamp, S. Tijs, and S. Muto. On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems. CentER DP 1994 nr.106, Tilburg Univ., The Netherlands, 1994.
D. Granot and A. Claus. Game theory application to cost allocation for a spanning tree. Working Paper 402, Fac. of Commerce and Business Administration, Univ. of British Columbia, 1976.
D. Granot and G. Huberman. On minimum cost spanning tree games. Mathematical Programming 21:1–18, 1981.
T. Ichiishi. Super-modularity: applications to convex games and the greedy algorithm for LP. Journal of Economic Theory 25:283–286, 1981.
J.B. Kruskal. On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Amer. Math. Soc., 7:48–50, 1956.
S. Moretti, H. Norde, K.H. Pham Do, and S. Tijs. Connection problems in mountains and monotonic allocation schemes. Top 10:83–99, 2002.
S. Moretti, S. Tijs, R. Branzei, H. Norde. Cost monotonic’ construct and charge’ rules for connection situations. Working Paper, 2005.
H. Norde, S. Moretti, and S. Tijs. Minimum cost spanning tree games and population monotonic allocation schemes. European J. Oper. Res. 154:84–97, 2004.
R.C. Prim. Shortest connection networks and some generalizations. Bell Systems Technical Journal 36:1389–1401, 1957.
Y. Sprumont. Population monotonic allocation schemes for cooperative games with transferable utility. Games and Economic Behavior 2:378–394, 1990.
S. Tijs and R. Branzei. Additive stable solutions on perfect cones of cooperative games. Int. J. Game Theory 31:469–474, 2002.
S. Tijs, R. Branzei, S. Moretti and H. Norde. Obligation rules for minimum cost spanning tree situations and their monotonicity properties. CentER DP 2004-53, Tilburg Univ., The Netherlands, 2004 (to appear in European J. Oper. Res.).
M. Voorneveld, S. Tijs, and S. Grahn. Monotonic allocation schemes in clan games. Math. Meth. Oper. Res., 56:439–449, 2002.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tijs, S., Moretti, S., Branzei, R., Norde, H. (2006). The Bird Core for Minimum Cost Spanning Tree Problems Revisited: Monotonicity and Additivity Aspects. In: Seeger, A. (eds) Recent Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28258-0_19
Download citation
DOI: https://doi.org/10.1007/3-540-28258-0_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28257-0
Online ISBN: 978-3-540-28258-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)