<p><strong><font size="3"><span id="btAsinTitle">Models in Cooperative Game Theory (Hardcover)</span><!--Element not supported - Type: 8 Name: #comment--><br/></font></strong>by <a href="http://www.amazon.com/exec/obidos/search-handle-url?%5Fencoding=UTF8&search-type=ss&index=books&field-author=Rodica%20Branzei"><font color="#003399">Rodica Branzei</font></a> (Author), <a href="http://www.amazon.com/exec/obidos/search-handle-url?%5Fencoding=UTF8&search-type=ss&index=books&field-author=Dinko%20Dimitrov"><font color="#003399">Dinko Dimitrov</font></a> (Author), <a href="http://www.amazon.com/exec/obidos/search-handle-url?%5Fencoding=UTF8&search-type=ss&index=books&field-author=Stef%20Tijs"><font color="#003399">Stef Tijs</font></a> (Author) </p><p><a href="http://www.amazon.com/gp/product/images/3540779531/sr=11-1/qid=1205251203/ref=dp_image_0?ie=UTF8&n=283155&s=books&qid=1205251203&sr=11-1" target="AmazonHelp"><img id="prodImage" height="240" alt="Models in Cooperative Game Theory" src="http://ecx.images-amazon.com/images/I/51Nm96KjCOL._AA240_.jpg" width="240" border="0"/></a></p><li><b>Hardcover:</b> 203 pages </li><li><b>Publisher:</b> Springer; 2nd ed. edition (April 1, 2008) </li><li><b>Language:</b> English </li><div class="content"><b>Review</b><br/><p>From the reviews of the first edition:</p><p></p><p>"This small book can be very interesting for readers who want to study further generalizations of the classical topic on cooperative games. It investigates the classical cooperative games with transferable utility and some game models in which the players have the possibility to cooperate partially, that is, fuzzy games and multichoice games. The book is written very clearly, being a rich review of the most essential notions and theorems (with proofs) in these topics." (Tadeusz Radzik, Zentralblatt MATH, Vol. 1079, 2006)</p><br/><br/><b>Book Description</b><br/><p>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.</p><p><strong><font size="4">Contents</font></strong><br/><strong>Part I Cooperative Games with Crisp Coalitions<br/>1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5<br/>2 Cores and Related Solution Concepts . . . . . . . . . . . . . . . . 13</strong><br/>2.1 Imputations, Cores and Stable Sets . . . . . . . . . . . . . . . . . . . 13<br/>2.2 The Core Cover, the Reasonable Set and the Weber Set . 20<br/><strong>3 The Shapley Value, the τ -value, and the Average</strong><br/><strong>Lexicographic Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25</strong><br/>3.1 The Shapley Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25<br/>3.2 The τ-value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31<br/>3.3 The Average Lexicographic Value . . . . . . . . . . . . . . . . . . . . 33<br/><strong>4 Egalitarianism-based Solution Concepts . . . . . . . . . . . . . . 37</strong><br/>4.1 Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37<br/>4.2 The Equal Split-Off Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38<br/>4.2.1 The Equal Split-Off Set for General Games . . . . . . 39<br/>4.2.2 The Equal Split-Off Set for Superadditive Games . 41<br/><strong>5 Classes of Cooperative Crisp Games . . . . . . . . . . . . . . . . . 43</strong><br/>5.1 Totally Balanced Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43<br/>5.1.1 Basic Characterizations and Properties of<br/>Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43<br/>5.1.2 Totally Balanced Games and Population<br/>Monotonic Allocation Schemes . . . . . . . . . . . . . . . . . 45<br/>5.2 Convex Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46<br/>5.2.1 Basic Characterizations . . . . . . . . . . . . . . . . . . . . . . . 46<br/>5.2.2 Convex Games and Population Monotonic<br/>Allocation Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 49<br/>5.2.3 The Constrained Egalitarian Solution for Convex<br/>Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50<br/>5.2.4 Properties of Solution Concepts . . . . . . . . . . . . . . . . 53<br/>5.3 Clan Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59<br/>5.3.1 Basic Characterizations and Properties of<br/>Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59<br/>5.3.2 Total Clan Games and Monotonic Allocation<br/>Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62<br/>5.4 Convex Games versus Clan Games . . . . . . . . . . . . . . . . . . . 65<br/>5.4.1 Characterizations via Marginal Games . . . . . . . . . . 66<br/>5.4.2 Dual Transformations . . . . . . . . . . . . . . . . . . . . . . . . . 68<br/>5.4.3 The Core versus the Weber Set . . . . . . . . . . . . . . . . . 70<br/><strong>Part II Cooperative Games with Fuzzy Coalitions</strong><br/><strong>6 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77<br/>7 Solution Concepts for Fuzzy Games . . . . . . . . . . . . . . . . . . 83</strong><br/>7.1 Imputations and the Aubin Core . . . . . . . . . . . . . . . . . . . . . 83<br/>7.2 Cores and Stable Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85<br/>7.3 Generalized Cores and Stable Sets . . . . . . . . . . . . . . . . . . . . 89<br/>7.4 The Shapley Value and the Weber Set . . . . . . . . . . . . . . . . 94<br/>7.5 Path Solutions and the Path Solution Cover . . . . . . . . . . . 96<br/>7.6 Compromise Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100<br/><strong>8 Convex Fuzzy Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103</strong><br/>8.1 Basic Characterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103<br/>8.2 Egalitarianism in Convex Fuzzy Games . . . . . . . . . . . . . . . 110<br/>8.3 Participation Monotonic Allocation Schemes . . . . . . . . . . . 116<br/>8.4 Properties of Solution Concepts . . . . . . . . . . . . . . . . . . . . . . 119<br/><strong>9 Fuzzy Clan Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127</strong><br/>9.1 The Cone of Fuzzy Clan Games . . . . . . . . . . . . . . . . . . . . . . 127<br/>9.2 Cores and Stable Sets for Fuzzy Clan Games . . . . . . . . . . 131<br/>9.3 Bi-Monotonic Participation Allocation Rules . . . . . . . . . . . 135<br/>Contents XI<br/><strong>Part III Multi-Choice Games<br/>10 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145</strong><br/><strong>11 Solution Concepts for Multi-Choice Games . . . . . . . . . . 149</strong><br/>11.1 Imputations, Cores and Stable Sets . . . . . . . . . . . . . . . . . . . 149<br/>11.2Marginal Vectors and the Weber Set . . . . . . . . . . . . . . . . . . 155<br/>11.3 Shapley-like Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159<br/>11.4 The Equal Split-Off Set for Multi-Choice Games . . . . . . . 163<br/><strong>12 Classes of Multi-Choice Games . . . . . . . . . . . . . . . . . . . . . . 165</strong><br/>12.1 Balanced Multi-Choice Games . . . . . . . . . . . . . . . . . . . . . . . 165<br/>12.1.1 Basic Characterizations . . . . . . . . . . . . . . . . . . . . . . . 165<br/>12.1.2 Totally Balanced Games and Monotonic<br/>Allocation Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 169<br/>12.2 Convex Multi-Choice Games . . . . . . . . . . . . . . . . . . . . . . . . . 170<br/>12.2.1 Basic Characterizations . . . . . . . . . . . . . . . . . . . . . . . 170<br/>12.2.2 Monotonic Allocation Schemes . . . . . . . . . . . . . . . . . 173<br/>12.2.3The Constrained Egalitarian Solution . . . . . . . . . . . 174<br/>12.2.4 Properties of Solution Concepts . . . . . . . . . . . . . . . . 180<br/>12.3Multi-Choice Clan Games . . . . . . . . . . . . . . . . . . . . . . . . . . . 182<br/>12.3.1 Basic Characterizations . . . . . . . . . . . . . . . . . . . . . . . 182<br/>12.3.2 Bi-Monotonic Allocation Schemes . . . . . . . . . . . . . . . 186<br/><strong>References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193<br/>Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201</strong></p></div><p></p><p><br/></p>