Standards of Excellence-Alto-sax Book 1.pdf
Practice the difficult spots in your lesson assignment and band music over and over at a Thank you! KJOS NEIL A. KJOS MUSIC COMPANY PUBLISHER. PW21XE ...
Turing Tumble Educators Guide
and white to make it easy for you to print or copy. This version of the 21. Turing Tumble Educator's Guide 1.0. Computer Logic Lesson #3: Crossovers.
English Grammar Test Package
I .... attentively to the lecture on philosophy but I still didn't understand much of ... English Grammar / Incomplete Sentences / Elementary level # 21.
vail.com
16 nov. 2018 Vail's most beginner-friendly park offers an assortment of features designed ... 21. 20. FULL-DAY: LESSON & LIFT TICKET WITH LUNCH (L/L/L).
GUIDE CALENDAR
Pre-registration is required for all classes to ensure class minimums are met Recreation Center during the 17th annual show on September 21
Game Theory Through Examples
the book which is undergraduates who take a mathematics class to fulfill general letters between Pascal and Fermat
8n8AA
21 Avoiding dangerous drugs and medications If so this can be the beginning of your recovery.) ... As a class
Korg Micro Arranger Manual
DJ Skills Stephen Webber 2012-08-21 DJ Skills: The Essential Guide to Beginner Guitar Lessons for Kids Book with Online Video and Audio Access Jay ...
Fall Holiday Class Schedule
hydrate 21g (Dietary Fiber 2g Sugars 11g); Protein 2g Driving through the City of Hurst it's easy ... joyed hamburger sliders
2021 MAJOR COUNTY FREE FAIR
1 sept. 2021 Open Class Dairy Sheep
PRISNER
GameCLASSROOM RESOURCE MATERIALS
Alles" 2014/5/8 11:19 page i #1?Game Theory
Through Examples
"Alles" - 2014/5/8 - 11:36 - page ii - #2? c?2014 by the Mathematical Association of America, Inc.Electronic edition ISBN 978-1-61444-115-1
Alles" 2014/5/8 11:19 page iii #3?Game Theory
Through Examples
Erich Prisner
Franklin University Switzerland
Published and Distributedby
The Mathematical Association of America
Alles" 2014/5/8 11:19 page iv #4?Council on Publications and Communications
Frank Farris,Chair
Committee on Books
Fernando Gouvˆea,Chair
Classroom Resource Materials Editorial Board
Susan G Staples,Editor
Michael Bardzell
Jennifer Bergner
Caren L Diefenderfer
ChristopherHallstrom
Cynthia J Huffman
Paul R Klingsberg
Brian Lins
Mary Morley
Philip P Mummert
Barbara E Reynolds
Darryl Yong
Alles" 2014/5/8 11:19 page v #5?CLASSROOM RESOURCE MATERIALS
Classroom Resource Materials is intended to provide supplementary classroom material for students
laboratoryexercises, projects, historical information,textbooks withunusual approaches for presenting math-
ematical ideas, career information, etc.101 Careers in Mathematics,3rd edition edited by Andrew Sterrett
Archimedes: What Did He Do Besides Cry Eureka?,Sherman SteinCalculus: An Active Approach with Projects,Stephen Hilbert, Diane Driscoll Schwartz, Stan Seltzer, John
Maceli, and Eric Robinson
Calculus Mysteries and Thrillers,R. Grant Woods
Conjecture and Proof,Mikl´os Laczkovich
Counterexamples in Calculus,Sergiy Klymchuk
Creative Mathematics,H. S. Wall
Environmental Mathematics in the Classroom,edited by B. A. Fusaro and P. C. Kenschaft Excursions in Classical Analysis: Pathways to Advanced Problem Solving and Undergraduate Research,byHongwei Chen
Explorations in Complex Analysis,Michael A. Brilleslyper, Michael J. Dorff, Jane M. McDougall, James S.
Rolf, Lisbeth E. Schaubroeck, Richard L. Stankewitz, and Kenneth Stephenson Exploratory Examples for Real Analysis,Joanne E. Snow and Kirk E. Weller Exploring Advanced Euclidean Geometry with GeoGebra, Gerard A. VenemaGame Theory Through Examples, Erich Prisner
Geometry From Africa: Mathematical and Educational Explorations,Paulus Gerdes Historical Modules for the Teaching and Learning of Mathematics(CD), edited by Victor Katz and KarenDee Michalowicz
IdentificationNumbers and Check Digit Schemes,Joseph Kirtland Interdisciplinary Lively ApplicationProjects,edited by Chris Arney Inverse Problems: Activities for Undergraduates,Charles W. Groetsch Keeping it R.E.A.L.: Research Experiences for All Learners,Carla D. Martin and Anthony Tongen Laboratory Experiences in Group Theory,Ellen Maycock Parker Learn from the Masters,Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, andVictor Katz Math Made Visual: Creating Images for UnderstandingMathematics,Claudi Alsina and Roger B. Nelsen MathematicsGalore!: The First Five Years of the St. Marks Institute of Mathematics,James Tanton Methods for Euclidean Geometry,Owen Byer, Felix Lazebnik, and Deirdre L. Smeltzer Ordinary Differential Equations: A Brief Eclectic Tour,David A. S´anchez Oval Track and Other Permutation Puzzles,John O. Kiltinen Paradoxes and Sophisms in Calculus,Sergiy Klymchuk and Susan StaplesA Primer of Abstract Mathematics,Robert B. Ash
Proofs WithoutWords,Roger B. Nelsen
Proofs WithoutWords II,Roger B. Nelsen
Rediscovering Mathematics: You Do the Math,Shai Simonson Alles" 2014/5/8 11:19 page vi #6?She Does Math!,edited by Marla Parker
Solve This: Math Activities for Students and Clubs,James S. Tanton Student Manual for Mathematics for Business Decisions Part1: Probability and Simulation,David Williamson, Marilou Mendel, Julie Tarr, and Deborah Yoklic Student Manual for Mathematics for Business Decisions Part2: Calculus and Optimization,David Williamson, Marilou Mendel, Julie Tarr, and Deborah YoklicTeaching StatisticsUsing Baseball,Jim Albert
Visual Group Theory,Nathan C. Carter
Which Numbers are Real?,Michael Henle
Writing Projects for Mathematics Courses: Crushed Clowns,Cars, and Coffee to Go,Annalisa Crannell,Gavin LaRose, Thomas Ratliff, and Elyn Rykken
MAA Service Center
P.O. Box 91112
Washington, DC 20090-1112
1-800-331-1MAA FAX: 1-301-206-9789
Alles" 2014/5/8 11:19 page vii #7?Contents
Prefacexvi
1 Theory 1: Introduction1
1.1 What"s a Game?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Game, Play, Move: Some Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Classification of Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Theory 2: Simultaneous Games4
2.1 Normal FormBimatrixDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Two Players. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 Two Players, Zero-sum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.3 Three or More Players. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.4 Symmetric Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Which Option to Choose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Maximin Move and Security Level. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Dominated Moves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.3 Best Response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.4 Nash Equilibria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Additional Topics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 Best Response Digraphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 2-Player Zero-sum Symmetric Games. . . . . . . . . . . . . . . . . . . . . . . . . . 14
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Project 1: Reacting fast or slow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3 Example: Selecting a Class19
3.1 Three Players, Two Classes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 I like you both". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.2 Dislikingthe Rival. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.3 Outsider. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Larger Cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Project 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Project 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Project 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
vii Alles" 2014/5/8 11:19 page viii #8? viiiContents4 Example: Doctor Location Games25
4.1 Doctor Location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.1.1 An Example Graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1.2 No (Pure) Nash Equilibrium?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.3 How Good are the Nash Equilibriafor the Public?. . . . . . . . . . . . . . . . . . . 28
4.2 Trees. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3 More than one Office (optional). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Project 5: Doctor location on MOPs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Project 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Project 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5 Example: Restaurant Location Games34
5.1 A First Graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2 A Second Graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.3 Existence of Pure Nash Equilibria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.4 More than one Restaurant (optional). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6 Using Excel42
6.1 Spreadsheet Programs like Excel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6.2 Two-Person Simultaneous Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.3 Three-Person Simultaneous Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Project 8: Simultaneous Quatro-Uno. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Project 9: Restaurant Location Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Project 10: 5 Knights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Project 11: 5 Cardinals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
7 Example: Election I47
7.1 First Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7.2 Second Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
7.3 The General Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
7.4 Third Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
7.5 The Eight Cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
7.6 Voting Power Indices (optional). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
8 Theory 3: Sequential Games I: Perfect Information and no Randomness53
8.1 Extensive Form: Game Tree and Game Digraph. . . . . . . . . . . . . . . . . . . . . . . . . 53
8.2 Analyzing the Game: Backward Induction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
8.2.1 Finite Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
8.2.2 The Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
8.2.3 Zermelo"s Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
8.3 Additional Topics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
8.3.1 Reality Check. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
8.3.2 Playing it SafeGuaranteed Payoffs. . . . . . . . . . . . . . . . . . . . . . . . . . 61
8.3.3 Two-person Zero-sum Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Alles" 2014/5/8 11:19 page ix #9?Contentsix
8.3.4 Breaking Ties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
8.3.5 Existing Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
8.3.6 Greedy Strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Project 12: TAKE SOME. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Project 13: WHO"s NEXT(n). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Project 14: LISA"s GAME. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Project 15: 2-AUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Project 16: 3-AUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
9 Example: Dividing A Few Items I70
9.1 Greedy Strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
9.2 Backward Induction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
9.2.1 Game Tree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
9.2.2 Game Digraph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
9.2.3 Example: Game Digraph for ABBAB. . . . . . . . . . . . . . . . . . . . . . . . . . 72
9.3 An Abbreviated Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
9.3.1 Why it Matters: Complexity (optional). . . . . . . . . . . . . . . . . . . . . . . . . 74
9.4 Bottom-Up Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
9.5 Interdependencies between the Items (optional). . . . . . . . . . . . . . . . . . . . . . . . . 76
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
10 Example: Shubik Auction I77
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Project 17: SHUBIK AUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7911 Example: Sequential Doctor and Restaurant Location80
11.1 General Observations for Symmetric Games. . . . . . . . . . . . . . . . . . . . . . . . . . . 80
11.2 Doctor Location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
11.3 Constant-Sum Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
11.4 Restaurant Location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
11.5 Nash Equilibriaand First Mover Advantage for Symmetric Games. . . . . . . . . . . . . . . 84
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Project 18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Project 19: Hostile versus Friendly Play. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
12 Theory 4: Probability86
12.1 Terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
12.2 Computing Probabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
12.2.1 Equally Likely Simple Events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
12.2.2 Simple Events not Equally Likely. . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
12.3 Expected Value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
12.4 Multistep Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
12.4.1 ProbabilityTrees. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
12.4.2 Conditional Probabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
12.4.3 ProbabilityDigraphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
12.5 Randomness in Simultaneous Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
12.6 Countingwithout Counting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Alles" 2014/5/8 11:19 page x #10? xContentsExercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Project 20: Tennis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Project 21: Final Exam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
13 France 165499
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
14 Example: DMA Soccer I102
14.1 1-Round 2-Step Experiment for Given Player Distributions. . . . . . . . . . . . . . . . . . . 103
14.2 Expected Goal Difference for the One-Round Game. . . . . . . . . . . . . . . . . . . . . . . 104
14.3 3-Rounds Experiment for Given Player Distributions. . . . . . . . . . . . . . . . . . . . . . 105
14.4 Static Three-round Game. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
14.5 Static Nine-round DMA Soccer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Project 22: DMA6* Soccer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Project 23: DMA7* Soccer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
15 Example: Dividing A Few Items II110
15.1 Goals of Fairness and Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
15.1.1 Fairness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
15.1.2 Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
15.1.3 Three Additional Features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
15.1.4 Mechanism Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
15.2 Some Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
15.2.1 Selecting one by one Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
15.2.2 Cut and Choose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
15.2.3 Random and Exchange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
15.3 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
15.4 Comparison of the Games for Seven Items and Complete Information. . . . . . . . . . . . . 115
15.4.1 Opposing or Similar Preferences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
15.5 Incomplete Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Project 24: Dividingfive items A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Project 25: Dividingfive items B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
16 Theory 5: Sequential Games with Randomness121
16.1 Extensive Form Extended. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
16.2 Analyzing the Game: Backward Inductionagain. . . . . . . . . . . . . . . . . . . . . . . . . 121
16.3 Decision Theory: Alone against Nature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Project 26: Job Interviews. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Project 27: 5 Envelopes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Project 28: Oh-No or Oh-No6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Project 29:3?4version of PolyominoREC THE SQUARE with randomness. . . . . . . . . . . . 12817 Example: Sequential Quiz Show I129
17.1 Candidates with Little Knowledge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
17.1.1 More May be Less. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Alles" 2014/5/8 11:19 page xi #11?Contentsxi
quotesdbs_dbs27.pdfusesText_33[PDF] Beginner1. Lesson #49. Au restaurant 3
[PDF] Beginner2. Lesson #17. Au bois de Boulogne - France
[PDF] Beginner2. Lesson #39. Week-end en amoureux - Anciens Et Réunions
[PDF] beginners` vinyasa
[PDF] Beginner`s Jig - Anciens Et Réunions
[PDF] Beginning a Life in Australia - English - Assurance
[PDF] Beginning algebra lial hornsby mcginnis 11th
[PDF] Beglaubigter Auszug aus dem Sitzungsbuch des Kreisausschusses
[PDF] Begleitbericht: Verordnung zum Bundesegsetz über den Konsumkredit
[PDF] Begleiten Sie - Wacker Burghausen
[PDF] Begleiten Sie uns auf dem Weg zur globalen Nr. 1
[PDF] Begleitende Folien zur Vorlesung
[PDF] Begleiterkrankungen bei Morbus Crohn
[PDF] Begleitete Gruppenreise Schottland Auf den Spuren der Highlander