<p><br/>Springer&nbsp;&nbsp;2008<br/>Models in Cooperative Game Theory (Hardcover)<br/>by Rodica Branzei (Author), Dinko Dimitrov (Author), Stef Tijs (Author)&nbsp;<br/><font style="FONT-SIZE: 0px; COLOR: #fff;">f7 P</font><br/>Hardcover: 203 pages <font style="FONT-SIZE: 0px; COLOR: #fff;">2 j; n/ n0 L8 I! ]6 z! [</font><br/>Publisher: Springer; 2nd ed. edition (April 1, 2008) <br/>Language: English</p><p>Contents<br/><span style="DISPLAY: none;">&nbsp;</span>Part I Cooperative Games with Crisp Coalitions<font style="FONT-SIZE: 0px; COLOR: #fff;">&amp; K$ I&nbsp;&nbsp;o7 r, r</font><br/>1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5<font style="FONT-SIZE: 0px; COLOR: #fff;">' M2 s$ i3 F&nbsp;&nbsp;e+ \7 L+ _' G5 R</font><br/>2 Cores and Related Solution Concepts . . . . . . . . . . . . . . . . 13<font style="FONT-SIZE: 0px; COLOR: #fff;">% Z+ |. c1 i* G* G# U# e# y0 a</font><br/>2.1 Imputations, Cores and Stable Sets . . . . . . . . . . . . . . . . . . . 13<br/>2.2 The Core Cover, the Reasonable Set and the Weber Set . 20<br/>The Shapley Value, the τ -value, and the Average<br/>Lexicographic Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25<br/>3.1 The Shapley Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25<br/>3.2 The τ-value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31<br/>3.3 The Average Lexicographic Value . . . . . . . . . . . . . . . . . . . . 33<font style="FONT-SIZE: 0px; COLOR: #fff;">8 o% ?. ?/ L! n% v+ p1 ^, q" |6 N</font><br/>4 Egalitarianism-based Solution Concepts . . . . . . . . . . . . . . 37<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<font style="FONT-SIZE: 0px; COLOR: #fff;">7 ]- X* I# D) P; L</font><br/>5 Classes of Cooperative Crisp Games . . . . . . . . . . . . . . . . . 43<font style="FONT-SIZE: 0px; COLOR: #fff;">3 T' M5 ^# ]) O$ \</font><br/>5.1 Totally Balanced Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43<font style="FONT-SIZE: 0px; COLOR: #fff;">5 Z&nbsp;&nbsp;~7 |, d&amp; k</font><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<font style="FONT-SIZE: 0px; COLOR: #fff;">2 R4 p% T&amp; x+ S- h&amp; H* X/ j, L" {</font><br/>5.2.1 Basic Characterizations . . . . . . . . . . . . . . . . . . . . . . . 46<font style="FONT-SIZE: 0px; COLOR: #fff;">/ X; g. A6 e3 j' o</font><br/>5.2.2 Convex Games and Population Monotonic<font style="FONT-SIZE: 0px; COLOR: #fff;">0 w9 S' @, Q# `</font><br/>Allocation Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 49<font style="FONT-SIZE: 0px; COLOR: #fff;">7 h$ Z9 O4 E4 h8 h4 K( |</font><br/>5.2.3 The Constrained Egalitarian Solution for Convex<font style="FONT-SIZE: 0px; COLOR: #fff;"># N( a4 S: u" s</font><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<font style="FONT-SIZE: 0px; COLOR: #fff;">" f0 G% Z$ |3 h3 G! D</font><br/>Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62<font style="FONT-SIZE: 0px; COLOR: #fff;">3 L' Z5 ~: P$ H&nbsp;&nbsp;d4 q) B</font><br/>5.4 Convex Games versus Clan Games . . . . . . . . . . . . . . . . . . . 65<font style="FONT-SIZE: 0px; COLOR: #fff;">* {. c9 e3 z9 g, S- |</font><br/>5.4.1 Characterizations via Marginal Games . . . . . . . . . . 66<font style="FONT-SIZE: 0px; COLOR: #fff;">1 B5 @5 y: H) z! \2 J3 v- ^</font><br/>5.4.2 Dual Transformations . . . . . . . . . . . . . . . . . . . . . . . . . 68<font style="FONT-SIZE: 0px; COLOR: #fff;">9 G. |" j# X6 X</font><br/>5.4.3 The Core versus the Weber Set . . . . . . . . . . . . . . . . . 70<br/>Part II Cooperative Games with Fuzzy Coalitions<br/>6 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77<font style="FONT-SIZE: 0px; COLOR: #fff;">+ z&amp; G! D5 b9 k" J6 G) V7 C</font><br/>7 Solution Concepts for Fuzzy Games . . . . . . . . . . . . . . . . . . 83<br/><span style="DISPLAY: none;">8 X9 O1 h( }! i</span>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<font style="FONT-SIZE: 0px; COLOR: #fff;">. W" U# [3 [1 S, ^</font><br/>7.4 The Shapley Value and the Weber Set . . . . . . . . . . . . . . . . 94<font style="FONT-SIZE: 0px; COLOR: #fff;">5 R% U$ k&amp; c) t8 A! V) O7 O% I</font><br/>7.5 Path Solutions and the Path Solution Cover . . . . . . . . . . . 96<br/>7.6 Compromise Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100<font style="FONT-SIZE: 0px; COLOR: #fff;">2 R% e- n) v- V+ F&nbsp;&nbsp;q8 \1 l</font><br/>8 Convex Fuzzy Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103<font style="FONT-SIZE: 0px; COLOR: #fff;">( O( \. e; B7 o</font><br/>8.1 Basic Characterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103<font style="FONT-SIZE: 0px; COLOR: #fff;">5 O- m% x) x&amp; L) j; w&nbsp;&nbsp;w' M. C0 U, Y</font><br/>8.2 Egalitarianism in Convex Fuzzy Games . . . . . . . . . . . . . . . 110<font style="FONT-SIZE: 0px; COLOR: #fff;">9 c&amp; V5 W9 b* G</font><br/>8.3 Participation Monotonic Allocation Schemes . . . . . . . . . . . 116<font style="FONT-SIZE: 0px; COLOR: #fff;">+ i* |: H&nbsp;&nbsp;n&nbsp;&nbsp;q</font><br/>8.4 Properties of Solution Concepts . . . . . . . . . . . . . . . . . . . . . . 119<br/>9 Fuzzy Clan Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127<br/>9.1 The Cone of Fuzzy Clan Games . . . . . . . . . . . . . . . . . . . . . . 127<font style="FONT-SIZE: 0px; COLOR: #fff;"># g0 R$ [7 @2 p/ h</font><br/>9.2 Cores and Stable Sets for Fuzzy Clan Games . . . . . . . . . . 131<font style="FONT-SIZE: 0px; COLOR: #fff;">6 h; l! A! a&nbsp;&nbsp;{&amp; z) ^&amp; A2 _</font><br/>9.3 Bi-Monotonic Participation Allocation Rules . . . . . . . . . . . 135<br/>Part III Multi-Choice Games<font style="FONT-SIZE: 0px; COLOR: #fff;">4 q3 V, z2 a% H9 c5 v</font><br/>10 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145<br/>11 Solution Concepts for Multi-Choice Games . . . . . . . . . . 149<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<font style="FONT-SIZE: 0px; COLOR: #fff;">; _1 n&nbsp;&nbsp;c. ~) T# T! z</font><br/>12 Classes of Multi-Choice Games . . . . . . . . . . . . . . . . . . . . . . 165<br/>12.1 Balanced Multi-Choice Games . . . . . . . . . . . . . . . . . . . . . . . 165<font style="FONT-SIZE: 0px; COLOR: #fff;">, \&amp; @&amp; }' a: c3 c' o5 g</font><br/>12.1.1 Basic Characterizations . . . . . . . . . . . . . . . . . . . . . . . 165<font style="FONT-SIZE: 0px; COLOR: #fff;">) O9 ^6 u: a6 v" W0 X5 r</font><br/>12.1.2 Totally Balanced Games and Monotonic<font style="FONT-SIZE: 0px; COLOR: #fff;">7 N7 u/ f, o3 V5 s5 Z</font><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<font style="FONT-SIZE: 0px; COLOR: #fff;">; |5 l&nbsp;&nbsp;i" T' a/ h# i% m</font><br/>12.3Multi-Choice Clan Games . . . . . . . . . . . . . . . . . . . . . . . . . . . 182<font style="FONT-SIZE: 0px; COLOR: #fff;">" r$ o% N: e7 ?0 m</font><br/>12.3.1 Basic Characterizations . . . . . . . . . . . . . . . . . . . . . . . 182<br/>Bi-Monotonic Allocation Schemes . . . . . . . . . . . . . . . 186<font style="FONT-SIZE: 0px; COLOR: #fff;">&nbsp;&nbsp;r0 d1 o. }+ n, u</font><br/>References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193<font style="FONT-SIZE: 0px; COLOR: #fff;">5 g9 }' a+ a$ W. c</font><br/>Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201</p><p></p><br/>