Von Neumann–Morgenstern solutions in the assignment market

The existence of von Neumann–Morgenstern solutions (stable sets) for assignment games has been an unsolved question since Shapley and Shubik (1972) [11]. For each optimal matching between buyers and sellers, Shubik (1984) [12] proposed considering the union of the core of the game and the core of th...

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Bibliographic Details
Published in:Journal of economic theory 2013-05, Vol.148 (3), p.1282-1291
Main Authors: Núñez, Marina, Rafels, Carles
Format: Article
Language:English
Subjects:
Assignment game
Assignment problem
Compatibility
Core
Econometria
Econometrics
Economic behaviour
Economic theory
Economics
Experimental methods
Game theory
Games
Lattice theory
Lattices
Management science
Markets
Matching
Optimization
Optimization techniques
Payments
Studies
Teoria de jocs
Third party
Third-party intervention
Unions
Von Neumann algebras
Von Neumann–Morgenstern stable set
Àlgebres de Von Neumann
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Summary:The existence of von Neumann–Morgenstern solutions (stable sets) for assignment games has been an unsolved question since Shapley and Shubik (1972) [11]. For each optimal matching between buyers and sellers, Shubik (1984) [12] proposed considering the union of the core of the game and the core of the subgames that are compatible with this matching. We prove in the present paper that this set is the unique stable set for the assignment game that excludes third-party payments with respect to a fixed optimal matching. Moreover, the stable sets that we characterize, as well as any other stable set of the assignment game, have a lattice structure with respect to the same partial order usually defined on the core.
ISSN:0022-0531
1095-7235
DOI:10.1016/j.jet.2012.10.002