Del i serien Theory and Decision Library C

Cooperative Games on Combinatorial Structures

Häftad, Engelska, 2012

AvJesús Mario Bilbao

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This book will be of interest to graduate students with some experience in game theory or mathematical programming and professional researchers in game theory, operational research and its applications in economic theory, and the political and social sciences.

Produktinformation

Utgivningsdatum2012-10-12
Mått155 x 235 x 19 mm
Vikt522 g
FormatHäftad
SpråkEngelska
SerieTheory and Decision Library C
Antal sidor326
FörlagSpringer-Verlag New York Inc.
ISBN9781461369769

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1 Structures.- 1.1 Cooperative games.- 1.2 Graph theory.- 1.3 Examples of cooperative games.- 1.4 Closure spaces and convex geometries.- 1.5 Matroids, greedoids and antimatroids.- 1.6 Project: Bicooperative games.- 2 Linear optimization methods.- 2.1 Polyhedra.- 2.2 Linear programming.- 2.3 Integer and combinatorial optimization.- 2.4 Balanced games.- 2.5 The greedy algorithm.- 2.6 Polymatroids.- 3 Discrete convex analysis.- 3.1 Fenchel conjugation.- 3.2 Subgradients and subdifferentials.- 3.3 Indirect functions of cooperative games.- 3.4 The least increment function.- 3.5 The Lovasz extension of games.- 4 Computational complexity.- 4.1 Models of computation.- 4.2 The complexity classes P and NP.- 4.3 NP-completeness and #P-completeness.- 4.4 Complexity in cooperative game theory.- 4.5 Project: Locally concave (convex) games.- 5 Restricted games by partition systems.- 5.1 Partition systems.- 5.2 F-restricted games.- 5.3 The core of restricted games.- 5.4 Hart and Mas-Colell potential.- 5.5 The Shapley and Banzhaf values.- 6 Restricted games by union stable systems.- 6.1 Union stable systems.- 6.2 Components of sets.- 6.3 The Myerson value.- 6.4 The position value.- 6.5 Convexity of the conference game.- 6.6 Project: Solution continuation games.- 7 Values for games on convex geometries.- 7.1 Games on convex geometries.- 7.2 Probabilistic values for games.- 7.3 Efficiency and compatible-order values.- 7.4 Axioms for the Shapley value.- 7.5 Axioms for the Banzhaf index.- 7.6 Project: Maxginalist and efficient values.- 8 Values for games on matroids.- 8.1 The rank game.- 8.2 The Shapley value for games on matroids.- 8.3 Quasi-probabilistic values.- 8.4 The probabilistic Shapley value.- 9 The core, the selectope and the Weber set.- 9.1 The core.- 9.2 The selectope.- 9.3 TheWeber set.- 9.4 Convex and quasi-convex games.- 9.5 Marginal operators.- 10 Simple games on closure spaces.- 10.1 Minimal winning coalitions.- 10.2 The core.- 10.3 The Weber set.- 10.4 Stable sets.- 10.5 Bargaining sets.- 11 Voting power.- 11.1 Weighted voting games.- 11.2 Generating functions.- 11.3 Computational complexity.- 11.4 Algorithms with Mathematica.- 11.5 Power in 2-weighted voting games.- 12 Computing values with Mathematica.- 12.1 Computing values of restricted games.- 12.2 Computing convex Shapley values.- 12.3 Computing convex Banzhaf indices.- 12.4 The Banzhaf power in the European Union.- 12.5 Computing the number of subtrees.- 12.6 The Myerson value in the European Union.