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008 131023s2014 gw | s |||| 0|eng d
020 _a9783642395499
_9978-3-642-39549-9
024 7 _a10.1007/978-3-642-39549-9
_2doi
050 4 _aHB144
072 7 _aPBUD
_2bicssc
072 7 _aKCH
_2bicssc
072 7 _aBUS069000
_2bisacsh
072 7 _aMAT011000
_2bisacsh
082 0 4 _a330.0151
_223
082 0 4 _a330
_223
100 1 _aMeinhardt, Holger Ingmar.
_eauthor.
245 1 4 _aThe Pre-Kernel as a Tractable Solution for Cooperative Games
_h[electronic resource] :
_bAn Exercise in Algorithmic Game Theory /
_cby Holger Ingmar Meinhardt.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2014.
300 _aXXXIII, 242 p. 8 illus., 3 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTheory and Decision Library C, Game Theory, Social Choice, Decision Theory, and Optimization,
_x0924-6126 ;
_v45
505 0 _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.
520 _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.
650 0 _aEconomics.
650 0 _aComputer science.
650 0 _aMathematics.
650 0 _aEconomics, Mathematical.
650 1 4 _aEconomics/Management Science.
650 2 4 _aGame Theory/Mathematical Methods.
650 2 4 _aGame Theory, Economics, Social and Behav. Sciences.
650 2 4 _aEconomic Theory.
650 2 4 _aMath Applications in Computer Science.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642395482
830 0 _aTheory and Decision Library C, Game Theory, Social Choice, Decision Theory, and Optimization,
_x0924-6126 ;
_v45
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-39549-9
912 _aZDB-2-SBE
942 _2ddc
_cEBOOK
999 _c3243
_d3243