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Resolving conflicts with mathematica: algorithms for two-person games

Author: Canty, Morton John Publisher: Academic Press, 2003.Language: EnglishDescription: 327 p. : Graphs ; 25 cm. includes CD-ROM / DVDISBN: 0121588556Type of document: BookBibliography/Index: Includes bibliographical references and indexContents Note: CD available inside back cover
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA269 .C36 2003
(Browse shelf)
001266894
Available 001266894
Total holds: 0

Includes bibliographical references and index

CD available inside back cover

Digitized

Resolving Conflicts with Mathematica® Algorithms for Two-Person Games Contents 1. Non-Cooperative Games 1.1 The battle of the sexes 1.1.1 Extensive form: Ladies first 1.1.2 Normal form: Bimatrix games 1.1.3 Mixed strategies 1.2 Rationality 1.3 The shape of things to conic 1.3.1 A spectrum auction 1.3.2 Attack and defense 1.3.3 Customs and smugglers 1.4 Nash equilibrium 1.1.1 Games in extensive form 1.1.2 Normal form and mixed strategies 1.4.3 Dominance 1.4.4 More definitions 1.4.5 An existence theorem 1.5 Exercises 2 Linear Complementarity 2.1 Solving bimatrix games 2.1.1 An equivalent representation of equilibrium 2.1.2 An equivalence theorem 2.1.3 Enumerating the equilibria 2.1.4 Degeneracy and a Mathematica program 2.1.5 Symbolic solutions and NashEquilibria 2.2 Examples 2.2.1 Todd's game 2.2.2 Von Stengel's game 2.2.3 Winkels' game 2.3 Exercises 3 Zero-Sum Games 3.1 Matrix games 3.1.1 Maxmin strategies 3.1.2 Solving matrix games 1 3 3 3 7 10 13 13 17 19 23 23 25 26 27 34 38 43 43 45 47 49 51 55 57 57 59 60 61 65 65 66 68 3.1.3 Five Finger Morra 3.2 Linear programming 3.2.1 Duality 3.2.2 Simplex 3.3 Strategy domination 3.4 Simplified poker 3.5 Exercises 4 Degenerate Games 4.1 Linear complementarily revisited 4.2 Extreme equilibria 4.3 Vertex enumeration 4.4 Maximal Nash subsets 4.5 Exercises 5 Inspection Games 5.1 Controlling several locations 5.1.1 Solution with Mathematica 5.1.2 Formalities 5.1.3 Legal behavior 70 72 74 81 93 102 108 111 111 113 119 125 129 131 131 134 138 139 140 143 151 151 152 154 158 162 163 165 166 168 169 173 174 176 180 183 184 186 186 192 196 5.2 Periodic inspections 5.2.1 Solution with Mathematica 5.2.2 Legal behavior 5.3 Playing for time 5.3.1 Discrete solutions 5.3.2 Solutions on the unit square 5.4 Detection probability 5.5 A final remark 5.6 Exercises 6 Evolutionary Games 6.1 Symmetric bimatrix games 6.2 Evolutionary stability 6.2.1 Hawks and doves 6.2.2 Childsplay 6.2.3 Negative definiteness and eigenvalues 6.2.4 Haigh's criterion and an algorithm 6.2.5 Bullies and retaliators 6.2.6 Attrition or dove meets dove 6.2.7 Asymmetric conflicts 6.3 Behavior dynamics 6.3.1 Dynamical stability 6.3.2 An ESS becomes a limit, cycle 6.4 Exercises 7 Games in Extensive Form 7.1 Games of perfect information 7.1.1 Backward induction 7.1.2 Minimax and alpha-beta pruning 7.1.3 Othello 7.2 Games of imperfect information 7.2.1 Subgame perfection 7.2.2 Cooperation 7.2.3 Behavior strategies, sequences and perfect recall 7.3 Perfect equilibrium 7.3.1 To err is human 7.3.2 Perfection in context 7.4 A sequential inspection game 7.5 Exercises A Lemke and Howson A.1 Complementary pivoting A.2 Existence, degeneracy and a Mathematica program B GameTheory `Bimatrix` B.1 Installation B.2 Functions B.3 Symbolic solutions C Solutions to the Exercises C.1 Non-Cooperative Games C.2 Linear Complementarity C.3 Zero-Sum Games C.4 Degenerate Games C.5 Inspection Games C.6 Evolutionary Gaines C.7 Games in Extensive Form Mathematical Notation Bibliography Index 199 199 200 203 207 210 211 213 216 220 220 226 231 241 245 245 251 255 255 255 257 259 259 268 275 283 289 297 307 319 321 325

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