Article1982

Generalized Network Problems Yielding Totally Balanced Games

177 citations0/0 files storedOperations Research

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Game Theory and Voting Systems Complexity and Algorithms in Graphs Game Theory and Applications

Abstract

A class of multiperson mathematical optimization problems is considered and is shown to generate cooperative games with nonempty cores. The class includes, but is not restricted to, numerous versions of network flow problems. It was shown by Owen that for games generated by linear programming optimization problems, optimal dual solutions correspond to points in the core. We identify a special class of network flow problems for which the converse is true, i.e., every point in the core corresponds to an optimal dual solution.

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References

1969The Nucleolus of a Characteristic Function Game 1967On balanced sets and cores 1975On the core of linear production games 1969On market games 1982Totally Balanced Games and Games of Flow

Cited by

2011Computational Aspects of Cooperative Game Theory 1986A generalized linear production model: A unifying model 1984Totally balanced games arising from controlled programming problems 1984On the Core and Dual Set of Linear Programming Games 1991On the core of network synthesis games 2008Mechanism design for a multicommodity flow game in service network alliances 2009Collaboration in Cargo Transportation 1995Chapter 9 Network models in economics

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