Minimum incoming cost rules for arborescences

Minimum incoming cost rules for arborescences The paper examines minimum cost arborescence (mca) problems, which generalize the well-known minimum cost spanning tree (mcst) problems by allowing the cost to depend on the direction of the flow. We propose a new family of cost sharing methods that are easy to compute, as they closely relate to the network-building algorithm. These methods are called minimum incoming cost rules for arborescences (MICRAs). They include as a particular case the extension of the folk solution introduced by Dutta and Mishra [Games Econ Behav 74(1):120–143, 2012], providing a simple procedure for its computation. We also provide new axiomatizations of (a) the set of stable and symmetric MICRAs and (b) the Dutta–Mishra solution. Finally, we closely examine two MICRAs that (unlike the Dutta–Mishra rule) compensate agents who help others connect at a lower cost. The first of these two rules relates to the cycle-complete solution for mcst problems introduced by Trudeau [Games Econ Behav 75(1):402–412, 2012]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Social Choice and Welfare Springer Journals

Minimum incoming cost rules for arborescences

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Economics; Economic Theory/Quantitative Economics/Mathematical Methods; Public Finance; International Political Economy; Game Theory, Economics, Social and Behav. Sciences; Social Policy
ISSN
0176-1714
eISSN
1432-217X
D.O.I.
10.1007/s00355-017-1061-9
Publisher site
See Article on Publisher Site

Abstract

The paper examines minimum cost arborescence (mca) problems, which generalize the well-known minimum cost spanning tree (mcst) problems by allowing the cost to depend on the direction of the flow. We propose a new family of cost sharing methods that are easy to compute, as they closely relate to the network-building algorithm. These methods are called minimum incoming cost rules for arborescences (MICRAs). They include as a particular case the extension of the folk solution introduced by Dutta and Mishra [Games Econ Behav 74(1):120–143, 2012], providing a simple procedure for its computation. We also provide new axiomatizations of (a) the set of stable and symmetric MICRAs and (b) the Dutta–Mishra solution. Finally, we closely examine two MICRAs that (unlike the Dutta–Mishra rule) compensate agents who help others connect at a lower cost. The first of these two rules relates to the cycle-complete solution for mcst problems introduced by Trudeau [Games Econ Behav 75(1):402–412, 2012].

Journal

Social Choice and WelfareSpringer Journals

Published: May 31, 2017

References

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