Models in Cooperative Game Theory (Google eBook)

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Springer Science & Business Media, Mar 8, 2008 - Mathematics - 215 pages
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This book investigates models in cooperative game theory in which the players have the possibility to cooperate partially. In a crisp game the agents are either fully involved or not involved at all in cooperation with some other agents, while in a fuzzy game players are allowed to cooperate with infinite many different participation levels, varying from non-cooperation to full cooperation. A multi-choice game describes the intermediate case in which each player may have a fixed number of activity levels. Different set and one-point solution concepts for these games are presented. The properties of these solution concepts and their interrelations on several classes of crisp, fuzzy, and multi-choice games are studied. Applications of the investigated models to many economic situations are indicated as well. The second edition is highly enlarged and contains new results and additional sections in the different chapters as well as one new chapter.
  

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Contents

Preliminaries
5
Cores and Related Solution Concepts
13
22 The Core Cover the Reasonable Set and the Weber Set
20
The Shapley Value the τvalue and the Average Lexicographic Value
25
32 The τvalue
31
33 The Average Lexicographic Value
33
Egalitarianismbased Solution Concepts
36
42 The Equal SplitOff Set
38
74 The Shapley Value and the Weber Set
94
75 Path Solutions and the Path Solution Cover
96
76 Compromise Values
100
Convex Fuzzy Games
103
82 Egalitarianism in Convex Fuzzy Games
110
83 Participation Monotonic Allocation Schemes
116
84 Properties of Solution Concepts
119
Fuzzy Clan Games
127

421 The Equal SplitOff Set for General Games
39
422 The Equal SplitOff Set for Superadditive Games
41
Classes of Cooperative Crisp Games
43
512 Totally Balanced Games and Population Monotonic Allocation Schemes
45
52 Convex Games
46
522 Convex Games and Population Monotonic Allocation Schemes
49
523 The Constrained Egalitarian Solution for Convex Games
50
524 Properties of Solution Concepts
53
53 Clan Games
59
532 Total Clan Games and Monotonic Allocation Schemes
62
54 Convex Games versus Clan Games
65
541 Characterizations via Marginal Games
66
542 Dual Transformations
68
543 The Core versus the Weber Set
70
Preliminaries
77
Solution Concepts for Fuzzy Games
82
72 Cores and Stable Sets
85
73 Generalized Cores and Stable Sets
89
92 Cores and Stable Sets for Fuzzy Clan Games
131
93 BiMonotonic Participation Allocation Rules
135
Preliminaries
142
Solution Concepts for MultiChoice Games
149
112 Marginal Vectors and the Weber Set
155
113 Shapleylike Values
159
114 The Equal SplitOff Set for MultiChoice Games
163
Classes of MultiChoice Games
165
122 Convex MultiChoice Games
170
1222 Monotonic Allocation Schemes
173
1223 The Constrained Egalitarian Solution
174
1224 Properties of Solution Concepts
180
123 MultiChoice Clan Games
182
1232 BiMonotonic Allocation Schemes
186
References
193
Index
200
Copyright

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Page vii - MP was supported by a Marie Curie Fellowship of the European Community Programme Improving the Human Research Potential and the Socio-economic Knowledge Base under contract number HPMT-CT-2001-00364 and by the grant GACR 201/03/0946.
Page 199 - R. (1988): Probabilistic values for games, in: Roth, AE (Ed.), The Shapley Value: Essays in Honour of Lloyd S. Shapley, Cambridge University Press, Cambridge, pp.
Page 4 - It is concerned primarily with "coalitions" groups of players who coordinate their actions and perhaps even pool their winnings. A cooperative game can often be put into the form of a characteristic function, v(S), which expresses for each set of players 5 the amount they can get if they form a coalition excluding the other players. In an economic context, v(S) might represent the gross product...
Page 199 - S. and FAS Lipperts (1982): The hypercube and the core cover of n-person cooperative games, Cahiers du Centre d'Etudes de Researche Operationelle 24, 27-37.

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