Holger Ingmar Meinhardt's Books

The Pre-Kernel as a Tractable Solution for Cooperative Games

An Exercise in Algorithmic Game Theory

By: Holger Ingmar Meinhardt

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The Pre-Kernel as a Tractable Solution for Cooperative Games

An Exercise in Algorithmic Game Theory

By: Holger Ingmar Meinhardt

This present book provides an alternative approach to study the pre-kernel solution of transferable utility games based on a generalized conjugation theory from convex analysis. Although the pre-kernel solution possesses an appealing axiomatic foundation that lets one consider this solution concept as a standard of fairness, the pre-kernel and its related solutions are regarded as obscure and too technically complex to be treated as a real alternative to the Shapley value. Comprehensible and efficient computability is widely regarded as a desirable feature to qualify a solution concept apart from its axiomatic foundation as a standard of fairness. We review and then improve an approach to compute the pre-kernel of a cooperative game by the indirect function. The indirect function is known as the Fenchel-Moreau conjugation of the characteristic function. Extending the approach with the indirect function, we are able to characterize the pre-kernel of the grand coalition simply by the solution sets of a family of quadratic objective functions.

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Page Count

270

Publisher

Springer Science & Business Media

Published Date

ISBN 10

364239549X

ISBN 13

9783642395499

Cooperative Decision Making in Common Pool Situations

By: Holger I. Meinhardt

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Cooperative Decision Making in Common Pool Situations

By: Holger I. Meinhardt

The monograph gives a theoretical explanation of observed cooperative behavior in common pool situations. The incentives for cooperative decision making are investigated by means of a cooperative game theoretical framework. In a first step core existence results are worked out. Whereas general core existence results provide us with an answer for mutual cooperation, nothing can be said how strong these incentives and how stable these cooperative agreements are. To clarify these questions the convexity property for common pool TU-games in scrutinized in a second step. It is proved that the convexity property holds for a large subclass of symmetrical as well as asymmetrical cooperative common pool games. Core existence and the convexity results provide us with a theoretical explanation to bridge the gap between the observation in field studies for cooperation and the noncooperative prediction that the common pool resource will be overused and perhaps endangered.

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Page Count

212

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642561365

ISBN 13

9783642561368

The Pre-Kernel as a Tractable Solution for Cooperative Games

An Exercise in Algorithmic Game Theory

By: Holger Ingmar Meinhardt

Write a review Read reviews Take a Quiz Solve Book Puzzle

The Pre-Kernel as a Tractable Solution for Cooperative Games

An Exercise in Algorithmic Game Theory

By: Holger Ingmar Meinhardt

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

270

Publisher

Springer Science & Business Media

Published Date

ISBN 10

364239549X

ISBN 13

9783642395499

Book's by Holger Ingmar Meinhardt

The Pre-Kernel as a Tractable Solution for Cooperative Games

The Pre-Kernel as a Tractable Solution for Cooperative Games

Cooperative Decision Making in Common Pool Situations

Cooperative Decision Making in Common Pool Situations

The Pre-Kernel as a Tractable Solution for Cooperative Games

The Pre-Kernel as a Tractable Solution for Cooperative Games

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