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- Title
Stable sets in one-seller assignment games.
- Authors
Bednay, Dezső
- Abstract
We consider von Neumann-Morgenstern stable sets in assignment games with one seller and many buyers. We prove that a set of imputations is a stable set if and only if it is the graph of a certain type of continuous and monotone function. This characterization enables us to interpret the standards of behavior encompassed by the various stable sets as possible outcomes of well-known auction procedures when groups of buyers may form bidder rings. We also show that the union of all stable sets can be described as the union of convex polytopes all of whose vertices are marginal contribution payoff vectors. Consequently, each stable set is contained in the Weber set. The Shapley value, however, typically falls outside the union of all stable sets.
- Subjects
COOPERATIVE game theory; GAME theory; CONTINUOUS functions; CONVEX polytopes; SET theory
- Publication
Annals of Operations Research, 2014, Vol 222, Issue 1, p143
- ISSN
0254-5330
- Publication type
Article
- DOI
10.1007/s10479-013-1439-8