INSEAD Library

Includes bibliographical references and index

Digitized

Models in Cooperative Game Theory Crisp, Fuzzy, and Multi-Choice Games Contents Part I Cooperative Games with Crisp Coalitions 1 Preliminaries ............................................................................ 5 2 Cores and Related Solution Concepts....................................... 13 2.1 Imputations, Cores and Stable Sets ........................................... 13 2.2 1 The Core Cover, the Reasonable Set and the Weber Set ........... 18 3 The Shapley Value and the r-Value........................................... 23 3.1 The Shapley Value ..................................................................... 23 3.2 The r-Value ................................................................................ 28 4 Classes of Cooperative Crisp Games......................................... 31 4.1 Totally Balanced Games.............................................................. 4.1.1 Basic Characterizations ................................................... 4.1.2 Totally Balanced Games and Population Monotonic Allocation Schemes ........................................................ 4.2 Convex Games............................................................................ 4.2.1 Basic Characterizations ................................................... 4.2.2 Convex Games and Population Monotonic Allocation Schemes......................................................................... 4.2.3 The Constrained Egalitarian Solution for Convex Games 4.3 Clan Games ............................................................................... 4.3.1 Basic Characterizations ................................................... 4.3.2 Total Clan Games and Monotonic Allocation Schemes ..... 31 31 32 33 33 36 37 40 40 41 Part II Cooperative Games with Fuzzy Coalitions 5 Preliminaries .......................................................................... 49 6 Solution Concepts for Fuzzy Games ............................................. 53 6.1 6.2 6.3 6.4 6.5 Imputations and the Aubin Core ................................................ Other Cores and Stable Sets ...................................................... The Shapley Value and the Weber Set ........................................ Path Solutions and the Path Solution Cover ............................... Compromise Values..................................................................... 53 54 59 61 64 7 Convex Fuzzy Games....................................................................... 67 7.1 7.2 7.3 7.4 Basic Characterizations .............................................................. Properties of Solution Concepts .................................................. Participation Monotonic Allocation Schemes .............................. Egalitarianism in Convex Fuzzy Games....................................... 67 74 80 82 89 89 92 96 8 Fuzzy Clan Games................................................................................ 8.1 The Cone of Fuzzy Clan Games .................................................. 8.2 Cores and Stable Sets for Fuzzy Clan Games.............................. 8.3 Bi-Monotonic Participation Allocation Rules................................ Part III Multichoice Games 9 Preliminaries .................................................................................... 105 10 Solution Concepts for Multichoice Games................................. 109 10.1 Imputations, Cores and Stable Sets ......................................... 109 10.2 Marginal Vectors, Shapley Values and the Weber Set................ 113 11 Classes of Multichoice Games...................................................... 121 11.1 Balanced Multichoice Games.....................................................121 11.2 Convex Multichoice Games .......................................................125 References............................................................................................ 129 Index...................................................................................................... 133