Meinhardt, Holger Ingmar. <br/><br/>
The Pre-Kernel as a Tractable Solution for Cooperative Games  An Exercise in Algorithmic Game Theory /  [electronic resource] : 
by Holger Ingmar Meinhardt. 
 - XXXIII, 242 p. 8 illus., 3 illus. in color.  online resource. 
 - Theory and Decision Library C, Game Theory, Social Choice, Decision Theory, and Optimization,  45  0924-6126 ; .
 - Theory and Decision Library C, Game Theory, Social Choice, Decision Theory, and Optimization,  45 .
<br/><br/>Introduction -- Some Solution Schemes and Game Properties -- The Shapley Value and (Pre-Kernel) as a Fairness Concept -- Fair Division in Cournot Markets -- Some Preliminary Results -- A Pre-Kernel Characterization and Orthogonal Projection -- Characterization of the Pre-Kernel by Solution Sets -- Algorithms for Computing the Pre-Kernel -- An Upper Dimension Bound of the Pre-Kernel -- Concluding Remarks. 
<br/><br/> 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. 
<br/><br/><label>ISBN: </label>9783642395499 
<br/><br/><label>Standard No.: </label>10.1007/978-3-642-39549-9  doi 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Computer science--Mathematics.<br/>Game theory.<br/>Economic theory.<br/>Economics.<br/>Game Theory.<br/>Game Theory, Economics, Social and Behav. Sciences.<br/>Economic Theory/Quantitative Economics/Mathematical Methods.<br/>Math Applications in Computer Science.
<br/><br/><label>LC Class. No.: </label>HB144 
<br/><br/><label>Dewey Class. No.: </label>519.3