## Models in Cooperative Game TheoryCooperative game theory is a booming research area with many new developments in the last few years. So, our main purpose when prep- ing the second edition was to incorporate as much of these new dev- opments as possible without changing the structure of the book. First, this o?ered us the opportunity to enhance and expand the treatment of traditional cooperative games, called here crisp games, and, especially, that of multi-choice games, in the idea to make the three parts of the monograph more balanced. Second, we have used the opportunity of a secondeditiontoupdateandenlargethelistofreferencesregardingthe threemodels of cooperative games. Finally, we have bene?ted fromthis opportunity by removing typos and a few less important results from the ?rst edition of the book, and by slightly polishing the English style and the punctuation, for the sake of consistency along the monograph. The main changes are: (1) Chapter 3 contains an additional section, Section 3. 3, on the - erage lexicographic value, which is a recent one-point solution concept de?ned on the class of balanced crisp games. (2) Chapter 4 is new. It o?ers a brief overview on solution c- cepts for crisp games from the point of view of egalitarian criteria, and presents in Section 4. 2 a recent set-valued solution concept based on egalitarian considerations, namely the equal split-o? set. (3)Chapter5isbasicallyanenlargedversionofChapter4ofthe?rst edition because Section 5. 4 dealing with the relation between convex games and clan games with crisp coalitions is new. |

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### Contents

5 | |

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 |

200 | |

### Other editions - View all

Models in Cooperative Game Theory: Crisp, Fuzzy, And Multi-Choice Games Rodica Brânzei,Dinko Dimitrov,Stef Tijs No preview available - 2005 |

### Common terms and phrases

a e I(v Aubin core bi-monotonic big boss CFGN characteristic function clan members constrained egalitarian solution convex combination convex fuzzy games convex games convex set cooperative crisp games cooperative games core element corresponding cr(v crisp coalition DC(v defined Definition denote Div(e EDC(v equal split-off set Example fuzzy clan game fuzzy coalitions Game Theory game v e game ve G game with clan grand coalition Hence hypercube i e car(s implies inequality follows introduced Journal of Game Lemma Let a e Let v e G marginal contribution marginal vectors MCN,m monotonic allocation schemes non-clan members non-empty Note obtain ordered partition p-core participation level payoff vector player set pmas Proof Proposition prove satisfies Shapley value solution concepts stable set subgame superadditive supermodularity Suppose Theorem total clan games unanimity game union property Weber set XDeN XDies zero-normalized

### Popular passages

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.

### References to this book

The Social Science Jargon Buster: The Key Terms You Need to Know Zina O'Leary Limited preview - 2007 |