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CS599: Algorithm Design in Strategic Settings Fall 2012 Lecture 2: Game Theory Preliminaries
CS599: Algorithm Design in Strategic Settings Fall 2012 Lecture 2: Game Theory Preliminaries Instructor: Shaddin Dughmi Administrivia Website: http://www-bcf.usc.edu/~shaddin/cs599fa12 Or go to www.cs.usc.edu/people/shaddin and follow link Emails? Registration Outline 1 Games of Complete Information 2 Games of Incomplete Information Prior-free Games Bayesian Games Outline 1 Games of Complete Information 2 Games of Incomplete Information Prior-free Games Bayesian Games Example: Rock, Paper, Scissors Figure: Rock, Paper, Scissors Games of Complete Information 2/23 Rock, Paper, Scissors is an example of the most basic type of game. Simultaneous move, complete information games Players act simultaneously Each player incurs a utility, determined only by the players’ (joint) actions. Equivalently, player actions determine “state of the world” or “outcome of the game”. The payoff structure of the game, i.e. the map from action vectors to utility vectors, is common knowledge Games of Complete Information 3/23 Typically thought of as an n-dimensional matrix, indexed by a 2 A, with entry (u1(a); : : : ; un(a)). Also useful for representing more general games, like sequential and incomplete information games, but is less natural there. Figure: Generic Normal Form Matrix Standard mathematical representation of such games: Normal Form A game in normal form is a tuple (N; A; u), where N is a finite set of players. Denote n = jNj and N = f1; : : : ; ng. A = A1 × :::An, where Ai is the set of actions of player i. Each ~a = (a1; : : : ; an) 2 A is called an action profile. u = (u1; : : : un), where ui : A ! R is the utility function of player i. -
2021-2022 Prefect Board Introduced - - - Times
Westminster School Simsbury, CT 06070 www.westminster-school.org Saturday, May 8, 2021 Vol. 110 No. 8 2021-2022 Prefect Board Introduced COMPILED BY ALEYNA BAKI ‘21, MATTHEW PARK ‘21 & HUDSON STEDMAN ‘21 CO-EDITORS-IN-CHIEF, 2020-2021 Head Prefect Junior Prefect Cooper Kistler is a boarder from Bella Tawney is a day student Tiburon, CA. He is a member of John Hay, from Simsbury, CT. She is a member of Black & Gold, First Boys’ Basketball, and John Hay, Black & Gold, the SAC Board, a Captain of First Boys’ lacrosse. As the new Captain of First Girls’ Basketball and First Head Prefect, Cooper aims to be the voice Girls’ Cross Country, as well as a Horizons of everyone in the community to cultivate a volunteer, the Co-President of AWARE, and culture of growth by celebrating the diver- a HOTH board member. In her final year sity of perspectives in the community. on the Hill, she is determined to create an In his own words: “I want to be the environment, where each and every member middleman between the Students and the of the school community feels accepted. Administration. I want to share the new In her own words: “The past year has perspective that we have all established dur- posed a number of difficulties, and it is ing the pandemic, and use it for the better. hard to adapt, but we should take this as an I want to UNITE the NEW school com- opportunity to teach our community and munity." continue to make it our Westminster." Priscilla Ameyaw is a Sung Min Cho is a Margot Douglass is a boarder from Ghana. -
North Shore Secondary School Fair
NORTH SECONDARY SHORE SCHOOL FAIR The Academy at Penguin Hall Lexington Christian Academy TUESDAY Avon Old Farms School Lincoln Academy TH Belmont Hill School Linden Hall SEPTEMBER 26 Berkshire School Loomis Chaffee School Berwick Academy Marianapolis Preparatory School 6:00-8:30 PM Bishop Fenwick High School Marvelwood School Boston University Academy Middlesex School Brewster Academy Millbrook School FREE & OPEN Brooks School Milton Academy The Cambridge School of Weston Miss Hall’s School TO THE PUBLIC Cate School Miss Porter’s School *Meet representatives CATS Academy New Hampton School Chapel Hill-Chauncy Hall School Noble and Greenough School and gather information Cheshire Academy Northfield Mount Hermon School Choate Rosemary Hall Phillips Academy from day, boarding Christ School Phillips Exeter Academy Clark School Pingree School and parochial schools. Commonwealth School Pomfret School Concord Academy Portsmouth Abbey School Covenant Christian Academy Proctor Academy Cushing Academy The Putney School HOSTED BY: Dana Hall School Saint Mary’s School Deerfield Academy Salisbury School BROOKWOOD SCHOOL Dublin School Shore Country Day School ONE BROOKWOOD ROAD Eaglebrook School Sparhawk School Emma Willard School St. Andrew’s School MANCHESTER, MA 01944 The Ethel Walker School St. George’s School 978-526-4500 Fay School St. John’s Preparatory School brookwood.edu/ssfair The Fessenden School St. Mark’s School Foxcroft Academy St. Mary’s School, Lynn Fryeburg Academy St. Paul’s School Garrison Forest School Stoneleigh-Burnham School -
2019 CAROLINA HURRICANES DRAFT GUIDE Rogers Arena • Vancouver, B.C
2019 CAROLINA HURRICANES DRAFT GUIDE Rogers Arena • Vancouver, B.C. Round 1: Friday, June 21 – 8 P.M. ET (NBCSN) Hurricanes pick: 28th overall Rounds 2-7: Saturday, June 22 – 1 P.M. ET (NHL Network) Hurricanes picks: Round 2: 36th overall (from BUF), 37th overall (from NYR) and 59th overall; Round 3: 90th overall; Round 4: 121st overall; Round 5: 152nd overall; Round 6: 181st overall (from CGY) and 183rd overall; Round 7: 216th overall (from BOS via NYR) The Carolina Hurricanes hold ten picks in the 2019 NHL Draft, including four in the first two rounds. The first round of the NHL Draft begins on Friday, June 21 at Rogers Arena in Vancouver and will be televised on NBCSN at 8 p.m. ET. Rounds 2-7 will take place on Saturday, June 22 at 1 p.m. ET and will be televised on NHL Network. The Hurricanes made six selections in the 2018 NHL Draft in Dallas, including second-overall pick Andrei Svechnikov. HURRICANES ALL-TIME FIRST HURRICANES DRAFT NOTES ROUND SELECTIONS History of the 28th Pick – Carolina’s first selection in the 2019 NHL Draft will be 28th overall in the first round. Hurricanes captain Justin Williams was taken 28th overall by Year Overall Player Philadelphia in the 2000 NHL Draft, and his 786 career points (312g, 474a) are the most 2018 2 Andrei Svechnikov, RW all-time by a player selected 28th. Other notable active NHL players drafted 28th overall 2017 12 Martin Necas, C include Cory Perry, Nick Foligno, Matt Niskanen, Charlie Coyle, and Brady Skjei. -
School Brochure
Bring Global Diversity to Your Campus with ASSIST 52 COUNTRIES · 5,210 ALUMNI · ONE FAMILY OUR MISSION ASSIST creates life-changing opportunities for outstanding international scholars to learn from and contribute to the finest American independent secondary schools. Our Vision WE BELIEVE that connecting future American leaders with future “Honestly, she made me think leaders of other nations makes a substantial contribution toward about the majority of our texts in brand new ways, and increasing understanding and respect. International outreach I constantly found myself begins with individual relationships—relationships born taking notes on what she through a year of academic and cultural immersion designed would say, knowing that I to affect peers, teachers, friends, family members and business would use these notes in my teaching of the course associates for a lifetime. next year.” WE BELIEVE that now, more than ever, nurturing humane leaders “Every time I teach this course, there is at least one student through cross-cultural interchange affords a unique opportunity in my class who keeps me to influence the course of future world events in a positive honest. This year, it’s Carlota.” direction. “Truly, Carlota ranks among the very best of all of the students I have had the opportunity to work with during my nearly 20 years at Hotchkiss.” ASSIST is a nonprofit organization that works closely with American independent secondary Faculty members schools to achieve their global education and diversity objectives. We identify, match The Hotchkiss School and support academically talented, multilingual international students with our member Connecticut schools. During a one-year school stay, an ASSIST scholar-leader serves as a cultural ambassador actively participating in classes and extracurricular activities. -
20021 Food Number and Item GI 2 Serve GL 3 Glucose S
REVISED INTERNATIONAL TABLE OF GLYCEMIC INDEX (GI) AND GLYCEMIC LOAD (GL)—20021 Food Number and Item GI 2 Serve GL 3 glucose size per =100 grams serve BAKERY PRODUCTS Cakes 1 Angel food cake (Loblaw's, Toronto, Canada) 67 50 19 2 Banana cake, made with sugar 47±8 80 18 3 Banana cake, made without sugar 55±10 80 16 Chocolate cake made from packet mix with chocolate frosting (Betty Crocker, General 4 38±3 111 20 Mills Inc., Minneapolis, MN, USA) Cupcake, strawberry-iced (Squiggles, Farmland, Grocery Holdings, Tooronga, Vic, 5 73±12 38 19 Australia) Lamingtons (sponge dipped in chocolate and coconut) (Farmland, Grocery Holdings, 6 87±17 50 25 Australia) 7 Pound cake (Sara Lee Canada, Bramalea, Canada) 54 53 15 8 Sponge cake, plain 46±6 63 17 9 Vanilla cake made from packet mix with vanilla frosting (Betty Crocker, USA) 42±4 111 24 10 Croissant (Food City, Toronto, Canada) 67 57 17 11 Crumpet (Dempster's Corporate Foods Ltd., Etobicoke, Canada) 69 50 13 12 Doughnut, cake type (Loblaw's, Canada) 76 47 17 13 Flan cake (Weston's Bakery, Toronto, Canada) 65 70 31 14 Muffins Apple, made with sugar4 44±6 60 13 Apple, made without sugar4 48±10 60 9 Apple, oat, sultana, made from packet mix (Defiance Milling Co., Acacia Ridge, Qld, 54±4 50 14 Australia) Apricot, coconut and honey, made from packet mix (Defiance Milling Co., Australia) 60±4 50 16 Banana, oat and honey, made from packet mix (Defiance Milling Co., Australia) 65±11 50 17 Bran (Culinar Inc., Grandma Martin's Muffins, Aurora, Canada) 60 57 15 Blueberry (Culinar Inc., Canada) 59 57 17 Carrot (Culinar Inc., Canada) 62 57 20 Chocolate butterscotch, made from packet mix (Defiance Milling Co., Australia) 53±5 50 15 Corn muffin, low-amylose5 102 57 30 Corn muffin, high-amylose5 49 Oatmeal, muffin, made from mix (Quaker Oats Co. -
Chapter 16 Oligopoly and Game Theory Oligopoly Oligopoly
Chapter 16 “Game theory is the study of how people Oligopoly behave in strategic situations. By ‘strategic’ we mean a situation in which each person, when deciding what actions to take, must and consider how others might respond to that action.” Game Theory Oligopoly Oligopoly • “Oligopoly is a market structure in which only a few • “Figuring out the environment” when there are sellers offer similar or identical products.” rival firms in your market, means guessing (or • As we saw last time, oligopoly differs from the two ‘ideal’ inferring) what the rivals are doing and then cases, perfect competition and monopoly. choosing a “best response” • In the ‘ideal’ cases, the firm just has to figure out the environment (prices for the perfectly competitive firm, • This means that firms in oligopoly markets are demand curve for the monopolist) and select output to playing a ‘game’ against each other. maximize profits • To understand how they might act, we need to • An oligopolist, on the other hand, also has to figure out the understand how players play games. environment before computing the best output. • This is the role of Game Theory. Some Concepts We Will Use Strategies • Strategies • Strategies are the choices that a player is allowed • Payoffs to make. • Sequential Games •Examples: • Simultaneous Games – In game trees (sequential games), the players choose paths or branches from roots or nodes. • Best Responses – In matrix games players choose rows or columns • Equilibrium – In market games, players choose prices, or quantities, • Dominated strategies or R and D levels. • Dominant Strategies. – In Blackjack, players choose whether to stay or draw. -
Pepsico Pledges $650,000 to Help Clean up Australia
MEDIA RELEASE 25 February 2020 PepsiCo pledges $650,000 to help Clean Up Australia PepsiCo and Clean Up Australia, together with REDcycle and Replas aim to build a circular economy initiative for sporting facilities Today, PepsiCo and Clean Up Australia have announced a new partnership to launch a three-year program called, Greening the Green, aimed at educating consumers on soft plastic recovery and increasing soft plastic recycling across Australia. Despite Australia’s recycling rate growing by over 50 per cent since 1996, waste to landfill has not decreased. According to the Australian Plastics Recycling Survey from 2017 – 2018, of the 3.4million tonnes of plastics consumed in Australia, less than 10 per cent was recycled. PepsiCo has pledged $650,000 (AUD) to support Greening the Green, which will see Clean Up Australia, PepsiCo and REDcycle (with support from Replas) partner with 110 local sporting facilities across the country. Greening the Green will consist of a 12-week module program to improve existing waste management and resource recovery by changing behaviour and providing better waste management resources. Upon successful completion of the 12-week program, each sporting facility that takes part will receive recycled plastic equipment such as table settings and benches made by Replas, one of Australia’s leading manufacturers of products made from soft plastics. The program aims to restore confidence in recycling across the country and support a circular economy for plastics by showing Australians that what they put in the bin, can be transformed into items the community can use. Danny Celoni, CEO PepsiCo Australia and New Zealand, says, “We are thrilled to partner with Clean Up Australia and REDcycle to launch Greening the Green and create a program that will work towards our goal of building a world where plastics never become waste. -
Mccarren Park Uart View All Monuments in NYC Parks, As Well As Temporary Public Art Installations on Our NYC Public Art Map and Guide I Map)
BOARD MEETING AFFIRMATION OF NEW MEMBERS Chairperson Ms. Fuller requested the new members to come forward to be affirmed. Mr. Solomon Green, Ms. Dana Rachlin, Mr. Michael Gary Schlesinger ROLL CALL Chairperson Ms. Fuller requested District Manager Mr. Esposito to call the roll. He informed the Chairperson that there were 39 members present, a sufficient quorum to call the meeting to order. MOMENT OF SILENCE Chairperson Ms. Fuller called for a moment of silence dedicated to Mr. Weidberg and his family, for the passing of Mr. Weidberg’s brother. ELECTIONS At 8:00 PM, Chairperson Ms. Fuller announced that it was time for elections. She requested the Elections Committee members [Ms. Barros; Ms. Foster; Mr. Torres] to come forward. Ballots were distributed and collected. The meeting continued while the Elections Committee convened in the other room to count the ballots. The committee reported the following regarding the elections: EXECUTIVE COMMITTEE POSITION CANDIDATE TALLY OF VOTES Chairperson Dealice Fuller 38 votes __________________________________________________________________________________ First Vice Chairperson Simon Weiser 23 votes. Karen Nieves 14 votes. __________________________________________________________________________________ Second Vice Chairperson Del Teague 38 votes. __________________________________________________________________________________ Third Vice Chairperson Stephen J. Weidberg 38 votes. __________________________________________________________________________________ Financial Secretary Maria Viera -
Guiding Mathematical Discovery How We Started a Math Circle
Guiding Mathematical Discovery How We Started a Math Circle Jackie Chan, Tenzin Kunsang, Elisa Loy, Fares Soufan, Taylor Yeracaris Advised by Professor Deanna Haunsperger Illustrations by Elisa Loy Carleton College, Mathematics and Statistics Department 2 Table of Contents About the Authors 4 Acknowledgments 6 Preface 7 Designing Circles 9 Leading Circles 11 Logistics & Classroom Management 14 The Circles 18 Shapes and Patterns 20 Penny Shapes 21 Polydrons 23 Knots and What-Not 25 Fractals 28 Tilings and Tessellations 31 Graphs and Trees 35 The Four Islands Problem (Königsberg Bridge Problem) 36 Human Graphs 39 Map Coloring 42 Trees: Dots and Lines 45 Boards and Spatial Reasoning 49 Filing Grids 50 Gerrymandering Marcellusville 53 Pieces on a Chessboard 58 Games and Strategy 63 Game Strategies (Rock/Paper/Scissors) 64 Game Strategies for Nim 67 Tic-Tac-Torus 70 SET 74 KenKen Puzzles 77 3 Logic and Probability 81 The Monty Hall Problem 82 Knights and Knaves 85 Sorting Algorithms 87 Counting and Combinations 90 The Handshake/High Five Problem 91 Anagrams 96 Ciphers 98 Counting Trains 99 But How Many Are There? 103 Numbers and Factors 105 Piles of Triangular Numbers 106 Cup Flips 108 Counting with Cups — The Josephus Problem 111 Water Cups 114 Guess What? 116 Additional Circle Ideas 118 Further Reading 120 Keyword Index 121 4 About the Authors Jackie Chan Jackie is a senior computer science and mathematics major at Carleton College who has had an interest in teaching mathematics since an early age. Jackie’s interest in mathematics education stems from his enjoyment of revealing the intuition behind mathematical concepts. -
A Centennial History of the U.S. Commission of Fine Arts
CIVIC ART A Centennial History of the U.S. Commission of Fine Arts . . . , · Published by the U.S. Commission of Fine Arts · mmxiii United States Commission of Fine Arts 401 F Street, NW, Suite 312 Washington, D.C. 20001-2728 Telephone: 202-504-2260 www.cfa.gov The U.S. Commission of Fine Arts offers broad public access to its resources—including photographs, drawings, and official govern- ment documents—as a contribution to education, scholarship, and public information. The submission of documents to the Commis- sion of Fine Arts for review constitutes permission to use the documents for purposes related to the activities of the commission, including display, reproduction, publication, or distribution. printed and bound in the united states of america 16 15 14 13 4 3 2 1 U.S. Government Printing Office Cataloging-in-Publication Data Civic art : a centennial history of the U.S. Commission of Fine Arts / edited by Thomas E. Luebke. Washington, D.C. : [U.S. Commission of Fine Arts], 2013. p. cm. Supt. of Docs. no: FA 1.2: C 87 ISBN: 978-0-160897-02-3 1. Washington (D.C.)—Buildings, structures, etc. 2. U.S Commission of Fine Arts—History. 3. Public architecture—United States. 4. Architecture--Washington (D.C.)—History. I. Luebke, Thomas E. II. U.S. Commission of Fine Arts. Editor and Project Director: Thomas E. Luebke, FAIA Managing Editor: Mary M.Konsoulis Historian: Kathryn Fanning, PhD Architectural Historian: Eve Barsoum Illustration Editor: Sarah Batcheler Manuscript Editor: Beth Carmichael Meadows Design Office, Inc., Washington, D.C. Art Director and Designer: Marc Alain Meadows Assistant Editor: Caroline Taylor Imaging Assistant: Nancy Bratton : Michael Lantz, Man Controlling Trade, Federal Trade Commission building, 1937–42 (CFA collection). -
Milestones 1914
.'-BE-LmOMT 511V! LLE- V^vjJU^ Al „.,,„- "v^^o ^ ^a^>kJ ? ^ t , u gfommtsitratiott anb Jfacultp Ira Landrith, D.D., LL.D. John Diell Blanton, LL.D. Mrs. J. D. Blanton President Vice-President and Chairman of Faculty Principal Home Department Emma Elizabeth McClure Martha Annette Cason Assembly Hall Superintendent Latin Graduate Pea body College; A.M. University of Nashville; Student University A.B. University of Chicago; Graduate Student Columbia University of Arkansas Ruby E. C. Mason Helen Atwood Thach Psychology, Education, Sociology Latin Graduate Webb School; Special Student University of Chicago A.B. and A.M. University of Toronto; Post-graduate Student Universities of Oxford and Paris Richard Garfield Cox Olive Carter Ross Mathematics English, Art History A.B. Hiram College; A.M. Columbia University of Nashville; Special Student Vanderbilt University; A.M. Columbia University Mary Laura Sheppe Anna H. Lewis Mathematics English Graduate Peabody College; Special Student University of Chicago and Harvard University Special Student U of North Carolina; Ph.B. and A.M. Univ Gladys Earle Bertha Cornelia Norris Science English, Greek . and A.M. Bryn Mawr College; Special Student Yale University Theodora Coolev Scruggs Elisa Cuendet English, History French A.B. Wellesley College; Special Student Chicago University Diploma from College Vinet, Lausanne Edith Collin Lawrence Germaine Frederikka Sansot English, History French A.B. Smith College; Student Wooster University College de Bagnares de Bigorre, Universite de Lille Universite de la Sorbonne Rcth K. Clarke, A.B. Laure Marie Schoeni English -German, French University of Cincinnati; Special Student Le Brun Sumn r School of French Ecole Secondaire, St.