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### 102Syll0809Spring

Course: MATH 102, Fall 2008
School: Duke
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Word Count: 380

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for Syllabus Math 102, Spring '08-'09, Clark Bray Mathematics for Economists, Simon and Blume; Notes on Integrals for Math 102, Bray (Note: New homework problems will be added throughout semester; be sure you are looking at a current version!) Linear Algebra (S&amp;B) 7.1 - Gaussian and Gauss-Jordan Elimination 7.2 - Elementary Row Operations 7.3 - Systems With Many or No Solutions 7.4 - Rank - The...

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Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
for Syllabus Math 102, Spring '08-'09, Clark Bray Mathematics for Economists, Simon and Blume; Notes on Integrals for Math 102, Bray (Note: New homework problems will be added throughout semester; be sure you are looking at a current version!) Linear Algebra (S&B) 7.1 - Gaussian and Gauss-Jordan Elimination 7.2 - Elementary Row Operations 7.3 - Systems With Many or No Solutions 7.4 - Rank - The Fundamental Criterion 7.5 - Linear Implicit Function Theorem 8.1 - Matrix Algebra 8.2 - Special Kinds of Matrices 8.3 - Elementary Matrices 8.4 - Algebra of Square Matrices 9.1 - Determinant of a Matrix 9.2 - Uses of the Determinant 9.3 - IS-LM Analysis via Cramer's Rule 10.1 - Points and Vectors in Euclidean Space 10.2 - Vectors 10.3 - Algebra of Vectors 10.4 - Length and Inner Product in R^n 10.5 - Lines 10.6 - Planes 10.7 - Economic Applications 11.1 - Linear Independence 11.2 - Spanning Sets 11.3 - Basis and Dimension in R^n Exercises: 3, 7, 8 Exercises: 9, 10, 11, 12 Exercises: 15, 16, 17, 18, 19 Exercises: 21, 23, 24 Exercises: 25, 29, 30 Exercises: 1, 3, 4(once), 5b Exercises: 7, 9, 10 Exercises: 12, 14 Exercises: 18, 19ad, 20c, 21, 23, 28 Exercises: 5, 6, 9 Exercises: 11, 13b, 14b Exercises: 17 Exercises: Exercises: 3, 4 Exercises: 8, 9 Exercises: 10a, 11b, 13, 19, 20, 24, 25, 26 Exercises: 27, 29, 31 Exercises: 32, 34, 37, 39, 40, 41 Exercises: Exercises: 1, 3, 4, 5b, 6, 7, 8 Exercises: 9, 10 Exercises: 14 Exercises: Exercises: 1, 2, 3, 6, 9, 10, AHP(1,2) Exercises: 11, 12, 14, 15, AHP(3) Exercises: Exercises: 22, 23(largest possible domain; let range = R^1), 24 Exercises: 1, 2 Exercises: Exercises: 3, 4, 5a Exercises: 7, 8, 9, 10 Exercises: 11, 12, 13, 14, 15, 16, 17 Exercises: 18, 19, 20 Exercises: 21(error in solutions), 22 Exercises: 1, 2, 5, 6, 7, 9 Exercises: 11, 10, 12, 13 Exercises: 15, 16, 17, 18, 19, 20, 21, 24 Exercises: 31 Exercises: 35, 36, 37, 38, 39 Exercises: Exercises: 1, 2, 3, 4 Exercises: 6c Exercises: Exercises: Exercises: Exercises: 4, 6, 7, 8, 11 Exercises: Exercises: 2, 4, 5, 6, 7, 8 Exercises: 10, 11, 14 Exercises: 15 (`<=37' not `>=37') Exercises: BEW(1,2) Exercises: ALJ(1, 2, 10, 11, 15, 23, 24), BEW(1, 3) Exercises: ALJ(1, 2, 3, 6, 10, 19, 20, 23, 24), BEW(1, 3) Exercises: ALJ(2, 3, 4, 6, 7, 10, 11, 15, 16, 17) Exercises: BEW(2, 3, 5, 6, 7, 9, 10, 11, 13, 14) Exercises: BEW(1, 2, 5, 7, 8, 11, 12, 13, 15, 16, 17) Calculus of Several Variables (S&B) 13.1 - Functions Between Euclidean Spaces 13.2 - Geometric Representations of Functions 13.3 - Special Kinds of Functions 13.4 - Continuous Functions 13.5 - Vocabulary of Functions 14.1 - Definitions and Examples 14.2 - Economic Interpretation 14.3 - Geometric Interpretation 14.4 - Total Derivative 14.5 - Chain Rule 14.6 - Directional Derivatives and Gradients 14.7 - Explicit Functions From R^n To R^m 15.1 - Implicit Functions a...

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Duke - MATH - 290
[ 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 34, 35, 37, 42, 58, 93, 110, 145, 203, 290]
Duke - MATH - 290
&lt; minimal [ 2, 0, -1, 0 ; 0, 4, 2, 0 ; -1, 2, 10, 3 ; 0, 0, 3, 28 ] &lt; 0 ; [ 128 , 12008989 ] ; [ ] ; [ ] &gt; [ [ [ 4, 4, 0 ; 4, 38, 6 ; 0, 6, 28 ] ] , [ [ 2, -2, 0 ; -2, 36, 6 ; 0, 6, 28 ] ] , [ [ 12, 0, 0 ; 0, 34, 6 ; 0,
Duke - MATH - 290
&lt; minimal [ 2, 0, -1, -1 ; 0, 4, 2, 0 ; -1, 2, 10, 7 ; -1, 0, 7, 28 ] &lt; 0 ; [ 64 , 56181887 ] ; [ ] ; [ ] &gt; [ [ [ 4, 4, 0 ; 4, 38, 26 ; 0, 26, 110 ] ] , [ [ 2, -2, -1 ; -2, 36, 14 ; -1, 14, 28 ] ] ] [ [ &lt; 0 ; [ 128
Duke - MATH - 290
&lt; minimal [ 2, 0, -1, 0 ; 0, 4, 2, -2 ; -1, 2, 10, 4 ; 0, -2, 4, 28 ] &lt; 0 ; [ 32 , 68417929 ] ; [ 2 ] ; [ ] &gt; [ [ [ 4, 4, -2 ; 4, 38, 8 ; -2, 8, 28 ] ] , [ [ 2, -2, 0 ; -2, 36, 20 ; 0, 20, 108 ] ] ] [ [ &lt; 0 ; [ 64 ,
Duke - MATH - 290
&lt; minimal [ 2, 0, -1, -1 ; 0, 4, 2, 0 ; -1, 2, 10, 8 ; -1, 0, 8, 28 ] &lt; 0 ; [ 64 , 125 , 357911 ] ; [ ] ; [ ] &gt; [ [ [ 4, 4, 0 ; 4, 38, 30 ; 0, 30, 110 ] ] , [ [ 2, -2, -1 ; -2, 36, 16 ; -1, 16, 28 ] ] ] [ [ &lt; 0 ; [
Duke - MATH - 290
&lt; minimal [ 2, 0, -1, -2 ; 0, 4, 2, -4 ; -1, 2, 10, 0 ; -2, -4, 0, 28 ] &lt; 0 ; [ 128 , 27 , 29791 ] ; [ ] ; [ ] &gt; [ [ [ 4, 4, -4 ; 4, 38, -2 ; -4, -2, 26 ] ] , [ [ 2, -2, -2 ; -2, 36, 4 ; -2, 4, 24 ] ] ] [ [ &lt; 0 ; [
Duke - MATH - 290
&lt; minimal [ 2, 0, -1, -1 ; 0, 4, 2, -1 ; -1, 2, 10, 0 ; -1, -1, 0, 28 ] &lt; 0 ; [ 32 , 4913 , 1295029 ] ; [ ] ; [ ] &gt; [ [ [ 4, 4, -2 ; 4, 38, -2 ; -2, -2, 110 ] ] , [ [ 2, -2, -4 ; -2, 36, 4 ; -4, 4, 444 ] ] , [ [ 12, 0,
Duke - MATH - 290
&lt; minimal [ 2, 0, -1, -2 ; 0, 4, 2, -2 ; -1, 2, 10, 0 ; -2, -2, 0, 28 ] &lt; 0 ; [ 32 , 625 , 4913 ] ; [ 2 ] ; [ ] &gt; [ [ [ 4, 4, -2 ; 4, 38, -2 ; -2, -2, 26 ] ] , [ [ 2, -2, -4 ; -2, 36, 4 ; -4, 4, 108 ] ] , [ [ 12, 0, -6 ;
Duke - PSY - 367
1 M 2 2.50000 3.1 2 F 7 1.50000 2.7 3 M 22 3.50000 3.8 4 F 11 3.83333 3.4 5 F 7 4.16667 2.6 6 F 7 4.00000 4.2 7 M 5 3.50000
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The Art of Graphical Presentation Types of Variables Guidelines for Good Graphics Charts Common Mistakes in Graphics Pictorial Games Special-Purpose Charts 1998, Geoff KuenningTypes of Variables Qualitative Ordered (e.g., modem, Ethernet,
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Common Mistakes in Graphics Excess information Multiple scales Using symbols in place of text Poor scales Using lines incorrectly 1998, Geoff KuenningExcess Information Sneaky trick to meet length limits Rules of thumb: 6 curves on line c
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General 2k Factorial Designs Used to explain the effects of k factors, each with two alternatives or levels 22 factorial designs are a special case Methods developed there extend to the more general case But many more possible interactions betwee
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Simulation Techniques OverviewSimulation environmentsWorkload parametersemulationSystem Config parametersexecdriven simDiscrete eventsResult DataFactor levelstracedriven sim stochastic sim 2003, Carla EllisThe End Game: When to S
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Simulation Techniques OverviewSimulation environmentsemulation/ execdriven eventdriven simWorkload parametersSystem Config parametersResult Datatracedriven sim stochastic simFactor levelsWhy Simulate System to be tested is not (yet)
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Exper i mentati on i n Computer Systems Resear chWhy: &quot;It doesn't matter how beautiful your theory is, it doesn't matter how smart you are if it doesn't agree with the experiment, it's wrong.&quot; R. Feynman 2003, Carla EllisWhy?W. Tichy in &quot;Shoul
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Parallel Discrete Event SimulationRichard Fujimoto CACM, Oct. 1990Still relevant after all these years? 2003, Carla EllisStructure of Discrete Event SimulationeventQschedulerState varEvent handlers results 2003, Carla ElliseventQPar
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Strong InferenceJ. Pratt Progress in science advances by excluding among alternate hypotheses. Experiments should be designed to disprove a hypothesis. A hypothesis which is not subject to being falsified doesn't lead anywhere meaningful Any con
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Automatically Characterizing Large Scale Program BehaviorTimothy Sherwood Erez Perelman Greg Hamerly Brad CalderUsed with permission of authorCharacterizing Program Behavior Ideal: To understand the effects of cycle-level events on full progra
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Comparison Methodology Meaning of a sample Confidence intervals Making decisions and comparing alternatives Special considerations in confidence intervals Sample sizes 1998, Geoff KuenningEstimating Confidence Intervals Two formulas for con
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Market Opportunity &amp; Analysis Part 2CPS 181s Jan 21, 2003Future Case Studies500words initial post and each response Raise questions, point out contradictions What was fascinating, what did you struggle to understand? Extrapolate future areas of
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Databases &amp; Data MiningCPS 181s April 3, 2003Databases in eCommerceThe move to eCommerce is in part driven by the ability to gather data that benefits the businessWhat is a Database?What is a Database?Asystem that stores data &quot;Persistent&quot;
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Random Number Generatorsxn = f ( xn-1, xn-2) where x0 is seed Pseudo-random since, given the same seed, the sequence is repeatable and deterministic Cycle length length of repeating sequence Example: xn = a xn-1 + b mod mseed cycle period 2003
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Fine-Grained Network Time Synchronization Using Reference BroadcastsJeremy Elson, Lew Girod, and Deborah Estrin University of California, Los AngelesOS 2002 - Boston, MA DIUsed with permission of authorThe bigger picture Isn't this a solved pr
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ImplementationCPS 181s Feb 20, 2003Questions What is online implementation? Why does implementation matter? What is the deliver system? What are the categories of offline innovation? What is the offline innovation process? What is the new lo
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For Discussion Today (when the alarm goes off) Survey your proceedings for just one paper in which factorial design has been used or, if none, one in which it could have been used effectively. 2003, Carla EllisFor Discussion Today?Project Propo
Duke - CPS - 108
&quot;C:\Program Files\JCreator Pro\MyProjects\Basic\HTMLAlternateView.java&quot;&quot;C:\Program Files\JCreator Pro\MyProjects\Basic\myprojects\basic\StreamBookSource.java&quot;&quot;C:\Program Files\JCreator Pro\MyProjects\Basic\myprojects\basic\DOMBookSource.java&quot;&quot;C:\P
Duke - CPS - 006
10120103581298014061148631579216222171381793718441185781981720035206692249524485250752548927598295103153832636331143331134455356183807338307399594015041630425944351644775448154803048172501235018950212502165082
Duke - CPS - 006
Grade Sheet03/171. adc3 Adam Chandler ams23 Andrew Stephens2. brs5 Brian Sellers ajw11 Ade Wise3. ajb21 Ashley Burns ddd7 Daniel Dwyer4. dgr2 Denise Rotatori js44 Jennika Suero5. dkb4 David Barker jmg24 Jessica Gallegos6. e
Duke - CPS - 006
Fundamentals of RecursionqqBase case (aka exit case) Simple case that can be solved with no further computation Does not make a recursive call Reduction step (aka Inductive hypothesis) Reduce the problem to another smaller one of the same str
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Grade Sheet24/21. adc3 Adam Chandler bjt2 Benjamin Tripp2. ajb21 Ashley Burns ajw11 Ade Wise3. ams23 Andrew Stephens brs5 Brian Sellers5. ddd7 Daniel Dwyer tjf7 Thomas Fernandez6. det2 Devon Taurman dgr2 Denise Rotatori7. d
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1)void doPath(Tree * t, tvector&lt;int&gt;&amp; path){ if (t = 0) { for(int k=0; k &lt; path.size(); k+) { cout &lt; path[k] &lt; &quot; &quot;; } cout &lt; endl; } path.push_back(t-&gt;info); doPath(t-&gt;left,path); doPath(t-&gt;r
Duke - WEEK - 100
1)void doPath(Tree * t, tvector&lt;int&gt;&amp; path){ if (t = 0) { for(int k=0; k &lt; path.size(); k+) { cout &lt; path[k] &lt; &quot; &quot;; } cout &lt; endl; } path.push_back(t-&gt;info); doPath(t-&gt;left,path); doPath(t-&gt;r
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Baring It All to Software: Raw Machines E. Waingold, M. Taylor, D. Srikrishna, V. (Presented by Linda Deng)Sarkar, W. Lee, V. Lee, J. Kim, M. Frank, P. Finch, R. Barua, J. Babb, S. Amarasinghe, A. AgarwalHitting a wall Already in 1997? As
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http:/www.icsb-2009.org/http:/www.icsb-2008.org/http:/www.icsb-2007.org/http:/www.icsb-2006.org/http:/www.icsb-2005.org/ICSB 2004: summarized in schuster.2006.pdfhttp:/meetings.cshl.edu/meetings/network09.shtmlhttp:/meetings.cshl.edu/meetings
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Outline for Today Announcements How office hours for UTAs work: announced around Nachos assignments. Those who didn't get your photo taken last time, we will do it again next time (or you can provide a picture jpg, 216x216 px) Groups - if you ha
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CPS 110 F08 Practice Problems for Discussions the Week of 9/8/08Problem 1) You have been hired by an airline company and asked to design a Monitor solution to handle seat reservations on a flight. The flight has MAX seats, initially all a
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Cube Computation and Indexes for Data WarehousesCPS 196.03 Notes 71ProcessingROLAP servers vs. MOLAP servers q Index Structures q Cube computation q What to Materialize? q AlgorithmsqClient Query &amp; Analysis Metadata Warehouse IntegrationCli
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CPS 196.03: Information Management and Mining Association Rules and Frequent Itemsets1Improvements to APrioriParkChenYu Algorithm Multistage Algorithm Savasere, Omiecinski, and Navathe Algorithm2PCY Algorithmx Hashbased improvement to APri
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CPS 196.03: Information Management and Mining Association Rules and Frequent Itemsets1Let Us Begin with an Examplex A common marketing problem: examine what people buy together to discover patterns.1. What pairs of items are unusually often
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CPS 196.03: Information Management and MiningShivnath BabuOutline for Today Logistics What this class is aboutInstructor Shivnath Babu, http:/www.cs.duke.edu/~shivnath Office hours: TBA Research interests: Database systems Simplifying sys
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Multi-way Algorithm for Cube ComputationCPS 196.03 Notes 81First Programming Projectq qIndividual project, 15 Points in final grade Sales(customer_id, item_id, item_group, item_price, purchase_date)xWill be provided as a file during demo a
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CPS 170: Artificial Intelligencehttp:/www.cs.duke.edu/courses/spring09/cps170/First-Order LogicInstructor: Vincent ConitzerLimitations of propositional logic So far we studied propositional logic Some English statements are hard to model in
Duke - CPS - 170
CPS 170: Artificial Intelligencehttp:/www.cs.duke.edu/courses/spring09/cps170/Two-player, zero-sum, perfect-informationGamesInstructor: Vincent ConitzerGame playing Rich tradition of creating game-playing programs in AI Many similarities to
Duke - CPS - 104
1. d2. a3. d4. c5. c d6. LRUFIFO0xFFFFEE44mm0xA10C0450mm0xFFFFEE88mm0xC4444464mm0xA10C0440hh0x77777770mm0xFFFFEE7Chh0xBA000440mm0xFFFFEE68hm0xA10C046ChmMiss ratio60%80%
Duke - CPS - 104
1. a2. b3. b4. d5. b6. tagindexblock offset 18 bits9 bits5 bits7. 60%
Duke - CPS - 104
1. b2. c3. a4. a5. b6. a7. b
Duke - CPS - 104
Datapath and Related Stuff1. Which of the following is not a stage of the &quot;Fetch-Execute&quot; cycle ?a. Instruction Fetchb. Executec. Find Next Instructiond. Check for User Input2. Which is not a part of the &quot;Register Transfer Language (RTL)&quot; for
Duke - CPS - 104
1. a2. b3. c4.func: subu \$sp, \$sp, 32 # create frame sw \$ra, 20(\$sp) # save return address sgt \$t0, \$a0, 1 bnez \$t0, recursion # if k &gt; 0, make recursive call
Duke - CPS - 104
A= 0xFADEB= 0xDEAF1. What is A &amp; Ba. 0xDA8Eb. 0xFADEc. 0xDEAFd. 0xFFFF2. What is A | Ba. 0xFFEFb. 0xFFFFc. 0xFEDFd. 0xFEFF3. What is (A &lt; 4)a. 0xFAD0b. 0x0ADEc. 0xADE0d. 0xFADE4. If an address is &quot;word aligned&quot;, it is divisible b
Duke - CPS - 104
Virtual Memory 1. Which of the following is NOT a true reason for using virtual memorya. More memory as seen by the userb. User can map a program to any part of the logical address space withoutworrying about the actual physical addressc. It pr
Duke - CPS - 104
I/O and Misc1. Which of the following is NOT a potential storage devicea. DRAMb. CD-ROMc. Tape Drived. ALU 2. Which of the following is not a component of disk access time ?a. Seek Timeb. Rotational Delay (or Rotational Latency)c. Head S
Duke - CPS - 104
More Cache Stuff 1. Which is NOT a reason for using a set-associative cache, as compared toa direct mapped cache ?a. Higher Hit Rateb. Fewer Conflict Missesc. Fewer bits required to index the cached. Faster hit detection 2. What is &quot;Write-Th
Duke - CPS - 104
1. What does the &quot;Hit Ratio&quot; measure ?a. Number of hits per accessb. Number of misses per accessc. Number of hits per missd. None of the above2. Consider the following piece of codefor(i=0;i&lt;100000;i+) Data[i]+;What kind of localit
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=CPS 1: Computer Science FundamentalsSample Lab Final=Be sure to read the WHOLE handout before starting and follow all ofthe directions. You should do this program in stepsThe goal of this lab is to make an applet that will tell youeverythi
Duke - CPS - 100
=The Sorting Cheat Sheetby: J. Forbes=This handout is intended as a very rough guide. It's for those of youwho want the quick and dirty answers to what how does sorting algorithm&quot;x&quot; work and how does it compare to the other ones we've learned.
Duke - CPS - 001
Today's topicsNetworks &amp; the Internet Basic HTML The basis for web pages &quot;Almost&quot; programming Upcoming Connections Algorithms Reading Internet history readings Great Ideas Chapters 1 Computer Science, Chapter 4CompSci 001 2.1Networksqqq
Duke - CPS - 296
CPS 296.2 Computational Game Theory and Mechanism DesignInstructor: Vincent Conitzer Assistant Professor of Computer Science Assistant Professor of Economics conitzer@cs.duke.edu Course web page: http:/www.cs.duke.edu/courses/fall06/cps296.2/What
Duke - CPS - 296
Automated mechanism designVincent Conitzer conitzer@cs.duke.eduGeneral vs. specific mechanisms Mechanisms such as Clarke (VCG) mechanism are very general. . but will instantiate to something specific in any specific setting This is what we car
Duke - CPS - 296
Risk attitudes, normal-form games, dominance, iterated dominanceVincent Conitzer conitzer@cs.duke.edu Which would you prefer?Risk attitudes A lottery ticket that pays out \$10 with probability .5 and \$0 otherwise, or A lottery ticket that pay
Duke - CPS - 296
Concise representations of gamesVincent Conitzer conitzer@cs.duke.eduGames with many agents How do we represent a (say, normal-form) game with n agents? Even with only 2 actions (pure strategies) per player, there are 2n possible outcomes Impr
Duke - CPS - 296
Learning in gamesVincent Conitzer conitzer@cs.duke.eduLearning in (normal-form) games Approach we have taken so far when playing a game: just compute an optimal/equilibrium strategy Another approach: learn how to play a game by playing it many