# Random reduction consistency of the Weber set, the core and the anti-core

Random reduction consistency of the Weber set, the core and the anti-core In this paper we introduce a new consistency condition and provide characterizations for several solution concepts in TU cooperative game theory. Our new consistency condition, which we call the random reduction consistency, requires the consistency of payoff vectors assigned by a solution concept when one of the players is removed with some probability. We show that the random reduction consistency and other standard properties characterize the Weber set, the convex hull of the marginal contribution vectors. Another salient feature of random reduction consistency is that, by slightly changing its definition, we can characterize the core and the anti-core in a parallel manner. Our result enables us to compare the difference between the three solution concepts from the viewpoint of consistency. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Methods of Operations Research Springer Journals

# Random reduction consistency of the Weber set, the core and the anti-core

, Volume 85 (3) – Feb 13, 2017
17 pages

/lp/springer_journal/random-reduction-consistency-of-the-weber-set-the-core-and-the-anti-PiBeEoXNWP
Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Operations Research/Decision Theory; Business and Management, general
ISSN
1432-2994
eISSN
1432-5217
D.O.I.
10.1007/s00186-017-0575-3
Publisher site
See Article on Publisher Site

### Abstract

In this paper we introduce a new consistency condition and provide characterizations for several solution concepts in TU cooperative game theory. Our new consistency condition, which we call the random reduction consistency, requires the consistency of payoff vectors assigned by a solution concept when one of the players is removed with some probability. We show that the random reduction consistency and other standard properties characterize the Weber set, the convex hull of the marginal contribution vectors. Another salient feature of random reduction consistency is that, by slightly changing its definition, we can characterize the core and the anti-core in a parallel manner. Our result enables us to compare the difference between the three solution concepts from the viewpoint of consistency.

### Journal

Mathematical Methods of Operations ResearchSpringer Journals

Published: Feb 13, 2017

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