Stable sets in one-seller assignment games

Bednay, Dezső (2013) Stable sets in one-seller assignment games. Manual. Annals of Operation Research. (In Press)

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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.

Item Type:Monograph (Manual)
Subjects:Mathematics, Econometrics
Projects:OTKA K72856
ID Code:1322
Deposited By: Dezső Bednay
Deposited On:12 Aug 2013 07:29
Last Modified:12 Aug 2013 07:29

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