02809nmm a2200349 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002900139245015800168250001700326260006300343300006400406505041100470653001600881653002100897653004200918653001600960653002000976653006400996653001601060653005501076710003401131041001901165989003601184490009701220856007201317082001001389520106001399EB000421316EBX0100000000000000027439800000000000000.0cr|||||||||||||||||||||131104 ||| eng a97836423954991 aMeinhardt, Holger Ingmar00aThe Pre-Kernel as a Tractable Solution for Cooperative GameshElektronische RessourcebAn Exercise in Algorithmic Game Theorycby Holger Ingmar Meinhardt a1st ed. 2014 aBerlin, HeidelbergbSpringer Berlin Heidelbergc2014, 2014 aXXXIII, 242 p. 8 illus., 3 illus. in colorbonline resource0 aIntroduction -- 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 aGame Theory aComputer science aMath Applications in Computer Science aGame theory aEconomic theory aEconomic Theory/Quantitative Economics/Mathematical Methods aMathematics aGame Theory, Economics, Social and Behav. Sciences2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aTheory and Decision Library C, Game Theory, Social Choice, Decision Theory, and Optimization uhttps://doi.org/10.1007/978-3-642-39549-9?nosfx=yxVerlag3Volltext0 a519.3 aThis 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