Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

1 Page

Lecture15-new

Course: CS 6.254, Spring 2010
School: MIT
Rating:

Word Count: 2474

Document Preview

: 6.254 Game Theory with Engineering Applications Lecture 15: Repeated Games Asu Ozdaglar MIT April 1, 2010 1 Game Theory: Lecture 15 Introduction Outline Repeated Games (perfect monitoring) The problem of cooperation Finitely-repeated prisoner's dilemma Infinitely-repeated games and cooperation Folk Theorems Reference: Fudenberg and Tirole, Section 5.1. 2 Game Theory: Lecture 15 Introduction Prisoners'...

Register Now

Unformatted Document Excerpt

Coursehero >> Massachusetts >> MIT >> CS 6.254

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.

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.
: 6.254 Game Theory with Engineering Applications Lecture 15: Repeated Games Asu Ozdaglar MIT April 1, 2010 1 Game Theory: Lecture 15 Introduction Outline Repeated Games (perfect monitoring) The problem of cooperation Finitely-repeated prisoner's dilemma Infinitely-repeated games and cooperation Folk Theorems Reference: Fudenberg and Tirole, Section 5.1. 2 Game Theory: Lecture 15 Introduction Prisoners' Dilemma How to sustain cooperation in the society? Recall the prisoners' dilemma, which is the canonical game for understanding incentives for defecting instead of cooperating. Cooperate 1, 1 2, -1 Defect -1, 2 0, 0 Cooperate Defect Recall that the strategy profile (D, D ) is the unique NE. In fact, D strictly dominates C and thus (D, D ) is the dominant equilibrium. In society, we have many situations of this form, but we often observe some amount of cooperation. Why? 3 Game Theory: Lecture 15 Introduction Repeated Games In many strategic situations, players interact repeatedly over time. Perhaps repetition of the same game might foster cooperation. By repeated games, we refer to a situation in which the same stage game (strategic form game) is played at each date for some duration of T periods. Such games are also sometimes called "supergames". We will assume that overall payoff is the sum of discounted payoffs at each stage. Future payoffs are discounted and are thus less valuable (e.g., money and the future is less valuable than money now because of positive interest rates; consumption in the future is less valuable than consumption now because of time preference). We will see in this lecture how repeated play of the same strategic game introduces new (desirable) equilibria by allowing players to condition their actions on the way their opponents played in the previous periods. 4 Game Theory: Lecture 15 Introduction Discounting We will model time preferences by assuming that future payoffs are discounted proportionately ("exponentially") at some rate [0, 1), called the discount rate. For example, in a two-period game with stage payoffs given by u 1 and u 2 , overall payoffs will be U = u 1 + u 2 . With the interest rate interpretation, we would have = where r is the interest rate. 1 , 1+r 5 Game Theory: Lecture 15 Introduction Mathematical Model More formally, imagine that I players playing a strategic form game G = I , (Ai )i I , (gi )i I for T periods. At each period, the outcomes of all past periods are observed by all players perfect monitoring Let us start with the case in which T is finite, but we will be particularly interested in the case in which T = . Here Ai denotes the set of actions at each stage, and gi : A R, where A = A1 AI . t That is, gi ait , a-i is the stage payoff to player i when action profile t = at , at a i -i is played. 6 Game Theory: Lecture 15 Introduction Mathematical Model (continued) We use the notation a = {at }t =0 to denote the sequence of action profiles. T We use the notation = {t }t =0 to be the profile of mixed strategies. The payoff to player i in the repeated game ui (a) = where [0, 1). We denote the T -period repeated game with discount factor by G T (). t t gi (ait , a-i ) T T t =0 7 Game Theory: Lecture 15 Introduction Finitely-Repeated Prisoners' Dilemma Recall Cooperate Defect Cooperate 1, 1 2, -1 Defect -1, 2 0, 0 What happens if this game was played T < times? We first need to decide what the equilibrium notion is. Natural choice, subgame perfect Nash equilibrium (SPE). Recall: SPE backward induction. Therefore, start in the last period, at time T . What will happen? 8 Game Theory: Lecture 15 Introduction Finitely-Repeated Prisoners' Dilemma (continued) In the last period,"defect" is a dominant strategy regardless of the history of the game. So the subgame starting at T has a dominant strategy equilibrium: (D, D ). Then move to stage T - 1. By backward induction, we know that at T , no matter what, the play will be (D, D ). Then given this, the subgame starting at T - 1 (again regardless of history) also has a dominant strategy equilibrium. With this argument, we have that there exists a unique SPE: (D, D ) at each date. In fact, this is a special case of a more general result. 9 Game Theory: Lecture 15 Introduction Equilibria of Finitely-Repeated Games Theorem Consider repeated game G T () for T < . Suppose that the stage game G has a unique pure strategy equilibrium a . Then G T has a unique SPE. In this unique SPE, at = a for each t = 0, 1, ..., T regardless of history. Proof: The proof has exactly the same logic as the prisoners' dilemma example. By backward induction, at date T , we will have that (regardless of history) aT = a . Given this, then we have aT -1 = a , and continuing inductively, at = a for each t = 0, 1, ..., T regardless of history. 10 Game Theory: Lecture 15 Infinitely-Repeated Games Infinitely-Repeated Games Now consider the infinitely-repeated game G , i.e., players play the game repeatedly at times t = 0, 1, . . .. The notation a = {at }t =0 now denotes the (infinite) sequence of action profiles. A period-t history is ht = {a0 , . . . , at -1 } (action profiles at all periods before t), and the set of all period-t histories is H t . A pure strategy for player i is si = {sit }, where sit : H t Ai The payoff to player i for the entire repeated game is then ui (a) = (1 - ) t t gi (ait , a-i ) t =0 where, again, [0, 1). Note: this summation is well defined because < 1. The term (1 - ) is introduced as a normalization, to measure stage and repeated game payoffs in the same units. The normalized payoff of having a utility of 1 per stage is 1. 11 Game Theory: Lecture 15 Infinitely-Repeated Games Trigger Strategies In infinitely-repeated games we can consider trigger strategies. A trigger strategy essentially threatens other players with a "worse," punishment, action if they deviate from an implicitly agreed action profile. A non-forgiving trigger strategy (or grim trigger strategy) s would involve this punishment forever after a single deviation. A non-forgiving trigger strategy (for player i) takes the following form: ait = ai ai if a = a for all < t if a = a for some < t Here a is the implicitly agreed action profile and ai is the punishment action. This strategy is non-forgiving since a single deviation from a induces player i to switch to ai forever. 12 Game Theory: Lecture 15 Infinitely-Repeated Games Cooperation with Trigger Strategies in the Repeated Prisoners' Dilemma Recall Cooperate Defect Cooperate 1, 1 2, -1 Defect -1, 2 0, 0 Suppose this game is played infinitely often. Is "Both defect in every period" still an SPE outcome? Suppose both players use the following non-forgiving trigger strategy s : Play C in every period unless someone has ever played D in the past Play D forever if someone has played D in the past. We next show that the preceding strategy is an SPE if 1/2 using one-stage deviation principle. 13 Game Theory: Lecture 15 Infinitely-Repeated Games Cooperation with Trigger Strategies in the Repeated Prisoners' Dilemma Step 1: cooperation is best response to cooperation. Suppose that there has so far been no D. Then given s being played by the other player, the payoffs to cooperation and defection are: 1 Payoff from C : (1 - )[1 + + 2 + ] = (1 - ) 1- = 1 Payoff from D : (1 - )[2 + 0 + 0 + ] = 2(1 - ) Cooperation better if 2(1 - ) 1. This shows that for 1/2, deviation to defection is not profitable. 14 Game Theory: Lecture 15 Infinitely-Repeated Games Cooperation with Trigger Strategies the in Repeated Prisoners' Dilemma (continued) Step 2: defection is best response to defection. Suppose that there has been some D in the past, then according to s , the other player will always play D. Against this, D is a best response. This argument is true in every subgame, so s is a subgame perfect equilibrium. Note: Cooperating in every period would be a best response for a player against s . But unless that player herself also plays s , her opponent would not cooperate. Thus SPE requires both players to use s . 15 Game Theory: Lecture 15 Infinitely-Repeated Games Remarks Cooperation is an equilibrium, but so are many other strategy profiles (depending on the size of the discount factor) Multiplicity of equilibria endemic in repeated games. If a is the NE of the stage game (i.e., it is a static equilibrium), then the strategies "each player, plays ai " form an SPE. Note that with these strategies, future play of the opponent is independent of how I play today, therefore, the optimal play is to maximize the current payoff, i.e., play a static best response.) Sets of equilibria for finite and infinite horizon versions of the "same game" can be quite different. Multiplicity of equilibria in prisoner's dilemma only occurs at T = . In particular, for any finite T (and thus by implication for T ), prisoners' dilemma has a unique SPE. Why? The set of Nash equilibria is an upper semicontinuous correspondence in parameters. It is not necessarily lower semicontinuous. 16 Game Theory: Lecture 15 Infinitely-Repeated Games Repetition Can Lead to Bad Outcomes The following example shows that repeated play can lead to worse outcomes than in the one shot game: A 2, 2 1, 2 0, 0 B 2, 1 1, 1 0, -1 C 0, 0 -1, 0 -1, -1 A B C For the game defined above, the action A strictly dominates B, C for both players, therefore the unique Nash equilibrium of the stage game is (A, A). If 1/2, this game has an SPE in which (B, B ) is played in every period. It is supported by a slightly more complicated strategy than grim trigger: I. Play B in every period unless someone deviates, then go to II. II. Play C . If no one deviates go to I. If someone deviates stay in II. 17 Game Theory: Lecture 15 Folk Theorems Folk Theorems In fact, it has long been a "folk theorem" that one can support cooperation in repeated prisoners' dilemma, and other "non-one-stage"equilibrium outcomes in infinitely-repeated games with sufficiently high discount factors. These results are referred to as "folk theorems" since they were believed to be true before they were formally proved. Here we will see a relatively strong version of these folk theorems. 18 Game Theory: Lecture 15 Folk Theorems Feasible Payoffs Consider stage game G = I , (Ai )i I , (gi )i I and infinitely-repeated game G (). Let us introduce the set of feasible payoffs: V = Conv{v RI | there exists a A such that g (a) = v }. That is, V is the convex hull of all I - dimensional vectors that can be obtained by some action profile. Convexity here is obtained by public randomization. Note: V is not equal to {v RI | there exists such that g () = v }, where is the set of mixed strategy profiles in the stage game. 19 Game Theory: Lecture 15 Folk Theorems Minmax Payoffs Minmax payoff of player i: the lowest payoff that player i's opponent can hold him to: vi = min -i max gi (i , -i ) . i The player can never receive less than this amount. Minmax strategy profile against i: i m-i = arg min -i max gi (i , -i ) i Finally, let mii denote the strategy of player i such that i gi (mii , m-i ) = v i . 20 Game Theory: Lecture 15 Folk Theorems Example Consider U M D L -2, 2 1, -2 0, 1 R 1, -2 -2, 2 0, 1 To compute v 1 , let q denote the probability that player 2 chooses action L. Then player 1's payoffs for playing different actions are given by: U 1 - 3q M -2 + 3q D0 21 Game Theory: Lecture 15 Folk Theorems Example Therefore, we have v 1 = min 1 2 1 and m2 [ 3 , 3 ]. 2 Similarly, one can show that: v 2 = 0, and m1 = (1/2, 1/2, 0) is the unique minimax profile. 0q 1 [max{1 - 3q, -2 + 3q, 0}] = 0, 22 Game Theory: Lecture 15 Folk Theorems Minmax Payoff Lower Bounds Theorem 1 Let be a (possibly mixed) Nash equilibrium of G and gi () be the payoff to player i in equilibrium . Then gi () v i . 2 Let be a (possibly mixed) Nash equilibrium of G () and ui ( ) be the payoff to player i in equilibrium . Then ui ( ) v i . Proof: Player i can always guarantee herself v i = mina-i [maxai ui (ai , a-i )] in the stage game and also in each stage of the repeated game, since v i = maxai [mina-i ui (ai , a-i )], meaning that she can always achieve at least this payoff against even the most adversarial strategies. 23 Game Theory: Lecture 15 Folk Theorems Folk Theorems Definition A payoff vector v RI is strictly individually rational if vi > v i for all i. Theorem (Nash Folk Theorem) If (v1 , . . . , vI ) is feasible and strictly individually rational, then there exists some < 1 such that for all > , there is a Nash equilibrium of G () with payoffs (v1 , , vI ). 24 Game Theory: Lecture 15 Folk Theorems Proof Suppose for simplicity that there exists an action profile a = (a1 , , aI ) s.t. gi (a) = vi [otherwise, we have to consider mixed strategies, which is a little more involved]. i Let m-i these the minimax strategy of opponents of i and mii be i's i best response to m-i . Now consider the following grim trigger strategy. For player i: Play (a1 , , aI ) as long as no one deviates. If some player j deviates, then play mij thereafter. We next check if player i can gain by deviating form this strategy profile. If i plays the strategy, his payoff is vi . 25 Game Theory: Lecture 15 Folk Theorems Proof (continued) If i deviates from the strategy in some period t, then denoting vi = maxa gi (a), the most that player i could get is given by: (1 - ) vi + vi + + t -1 vi + t v i + t +1 v i + t +2 v i + . Hence, following the suggested strategy will be optimal if vi 1 - t t +1 vi + t v i + v , 1- 1- 1- i thus if vi 1 - t vi + t (1 - ) v i + t +1 v i = vi - t [vi - (1 - )v i - v i + (vi - vi )]. The expression in the bracket is non-negative for any v i - vi max . i vi - vi This completes the proof. 26 Game Theory: Lecture 15 Folk Theorems Problems with Nash Folk Theorem The Nash folk theorem states that essentially any payoff can be obtained as a Nash Equilibrium when players are patient enough. However, the corresponding strategies involve this non-forgiving punishments, which may be very costly for the punisher to carry out (i.e., they represent non-credible threats). This implies that the strategies used may not be subgame perfect. The next example illustrates this fact. U D L (q) 6, 6 7, 1 R (1 - q) 0, -100 0, -100 The unique NE in this game is (D, L). It can also be seen that the minmax payoffs are given by v 1 = 0, v 2 = 1, 27 and the minmax strategy profile of player 2 is to play R. Game Theory: Lecture 15 Folk Theorems Problems with the Nash Folk Theorem (continued) Nash Folk Theorem says that (6,6) is possible as a Nash equilibrium payoff of the repeated game, but the strategies suggested in the proof require player 2 to play R in every period following a deviation. While this will hurt player 1, it will hurt player 2 a lot, it seems unreasonable to expect her to carry out the threat. Our next step is to get the payoff (6, 6) in the above example, or more generally, the set of feasible and strictly individually rational payoffs as subgame perfect equilibria payoffs of the repeated game. 28
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

MIT - CS - 6.254
6.254 : Game Theory with Engineering Applications Lecture 16: Repeated Games IIAsu Ozdaglar MITApril 13, 20101Game Theory: Lecture 16IntroductionOutlineRepeated Games perfect monitoring Folk Theorems Repeated Games imperfect monitoringPrice-trigge
MIT - CS - 6.254
6.254 : Game Theory with Engineering Applications Lecture 17: Games with Incomplete Information: Bayesian Nash EquilibriaAsu Ozdaglar MITApril 15, 20101Game Theory: Lecture 17IntroductionOutlineIncomplete information. Bayes rule and Bayesian infere
MIT - CS - 6.254
6.254 : Game Theory with Engineering Applications Lecture 18: Games with Incomplete Information: Bayesian Nash Equilibria and Perfect Bayesian EquilibriaAsu Ozdaglar MITApril 22, 20101Game Theory: Lecture 18IntroductionOutlineBayesian Nash Equilibr
MIT - CS - 6.254
6.254 : Game Theory with Engineering Applications Lecture 19: Mechanism Design IAsu Ozdaglar MITApril 29, 20101Game Theory: Lecture 19IntroductionOutlineMechanism design Revelation principleIncentive compatibility Individual rationality&quot;Optimal&quot;
MIT - CS - 6.254
6.254 : Game Theory with Engineering Applications Lecture 20: Mechanism Design IIAsu Ozdaglar MITMay 4, 20101Game Theory: Lecture 20IntroductionOutlineMechanism design from social choice point of view Implementation in dominant strategies Revelatio
MIT - CS - 6.254
6.254: Game TheoryFebruary 11, 2010Lecture 4: Correlated RationalizabilityLecturer: Asu Ozdaglar1Correlated RationalizabilityIn this note, we allow a player to believe that the other players' actions are correlated- in other words, the other players
MIT - CS - 6.254
6.254: Game Theory with Engineering Applications February 23, 2010Lecture 6: Continuous and Discontinuous GamesLecturer: Asu Ozdaglar1IntroductionIn this lecture, we will focus on: Existence of a mixed strategy Nash equilibrium for continuous games (
MIT - CS - 6.254
6.972 Game Theory and Equilibrium AnalysisMidterm Exam April 6, 2004; 1-2:30 pmProblem 1. (40 points) For each one of the statements below, state whether it is true or false. If the answer is true, explain why. If the answer is false, give a counterexam
MIT - CS - 6.254
6.254 Game Theory with Engineering ApplicationsMidterm April 11, 2006Problem 1 : (35 points) Consider a Bertrand competition between two firms, where each firm chooses a price pi [0, 1]. Assume that one unit of demand is to be split between the two firm
MIT - CS - 6.254
6.254 Game Theory with Engineering ApplicationsMidterm April 8, 2008Problem 1 : (35 points) Consider a game with two players, where the pure strategy of each player is given by xi [0, 1]. Assume that the payoff function ui of player i is given by ui (x1
MIT - CS - 6.254
6.254: Game Theory with Engr AppProject DescriptionAs part of the requirements of the course, you need to complete a project on a topic of your choice, related to the class material. We encourage you to work in groups of 2-3 people. Please email Ermin i
MIT - CS - 6.254
6.254 Game Theory with Engr AppMidtermThursday, April 8, 2010Problem 1 (35 points) For each one of the statements below, state whether it is true or false. If the answer is true, explain why. If the answer is false, give a counterexample. Explanations
MIT - CS - 6.254
6.254 Game Theory with Engr AppMidterm SolutionsThursday, April 8, 2010Problem 1 (35 points) For each one of the statements below, state whether it is true or false. If the answer is true, explain why. If the answer is false, give a counterexample. Exp
North Shore - COMPUTER - 268546
Every program is formed by combining as many sequence, selection, and repetiton staement as appropriate for the algorithm the program implementsa procedure for solving a problem in terms of actions to execute and the order in which these action execute i
North Shore - COMPUTER S - 126259
Linda Chhay Database Theory and ApplicationsProject Description:The objective of this project is to go through the entire process required in order to make a reliable and useful database. We get to extract business rules from an example model scenario i
As an aspiring college student that are both passionate and supportive of healthy food movement, I was more than pleased to have the opportunity to help my local farmers markets to increase both their profitability and the well being of their farmers by u
LSU - BIOL 1202 - 1202
Summa ry of Animal PhylaPorifera (sponges) Lack t rue t issues Have chanocytes o Collar cells unique f lagellated cells that ingest bacteria and tiny food particlesCnidar ia (hydras, jellies, sea anemones, corals) Unique stinging structures (cnidae) E
LSU - BIOL 1202 - 1202
Quiz 12 Question 1 The function of the corpus luteum is to _. a. nourish and protect the egg cell b. produce prolactin in the milk sacs of the mammary glands c. produce progesterone and estrogen d. produce estrogen and disintegrate following ovulation Cor
LSU - BIOL 1202 - 1202
Quiz 11 Top of Form Question 1 In the alveoli and lung capillaries, carbon dioxide and oxygen are exchanged by means of _. a. diffusion b. osmosis c. active transport d. endocytosis e. pinocytosis Correct Question 2 The function of pulmonary circulation i
LSU - BIOL 1202 - 1202
Quiz 3Question 1 The more the sequences of amino acids in homologous proteins vary, the more recently the two species have diverged. Answer: True False CorrectQuestion 2 A taxon such as the class Reptilia, which does not include its relatives, the birds
LSU - BIOL 1202 - 1202
Quiz #2The first living organisms were most likely aerobic prokaryotes. Answer: True False Correct Marks for this submission: 1/1. Question 2 Some species of Anopheles mosquito live in brackish water, some in running fresh water, and others in stagnant w
LSU - BIOL 1202 - 1202
Quiz 1Question 1 Marks: 1/1 In evolutionary terms, the more closely related two different organisms are, the Choose one answer. a. more similar their habitats are. b. less similar their DNA sequences are. c. more recently they shared a common ancestor. d
UC Davis - PSC 001 - PSC 001
3306_W_Weiten_Ch04 1/4/06 8:16 AM Page 118C H A P T E R4Psychophysics: Basic Concepts and IssuesThresholds: Looking for Limits Weighing the Differences: The JND Signal-Detection Theory Perception Without Awareness Sensory AdaptationSensation and Perc
UC Davis - PSC 001 - PSC 001
3/31/2010PSC1 Spring 2010, Dr. Liat SayfanDefining Psychology Psychology today Historical roots Emergence of modern perspectivesThe scientific study of the behavior of individuals and their mental processesConclusions are based on evidence Evidence is
UC Davis - PSC 001 - PSC 001
4/6/2010The body communication networks The nervous system The endocrine systemNeuronsPSC1 Spring 2010, Dr. Liat Sayfan structure Neurons in action Neural communicationNeurotransmitters and drugsCentral nervous system (CNS) brain spinal cordSOMAT
UC Davis - PSC 001 - PSC 001
4/4/2010PSC1 Spring 2010, Dr. Liat SayfanCommon sense vs. science The scientific method Research designs Ethical considerationsWhat is common sense? Having a `guts' feeling/intuition about a phenomenonDoes distance make the heart grow fonder? Do oppo
UC Davis - PSC 001 - PSC 001
Recap The Nervous System Neural CommunicationNeurotransmitters and drugs The BrainPSC1 Spring 2010, Dr. Liat Sayfan Structure Divisions of the cerebral cortex Hemispheres communication PlasticityExamples of neurotransmitters Acetylcholine Monoamine
UC Davis - PSC 001 - PSC 001
4/14/2010What is learning? Classical conditioning Operant conditioning Observational learningPSC1 Spring 2010, Dr. Liat Sayfanlearning relatively permanent change in behavior due to experience with the same stimuliNon-associative Learning Habituatio
UC Davis - PSC 001 - PSC 001
4/21/2010Defining sensation and perception Measuring the sensory experiencePSC1 Spring 2010, Dr. Liat SayfanFeeling pain HearingSensation detect information from the environmentPerception select, organize, and interpret sensationsTransductionTran
UC Davis - PSC 001 - PSC 001
4/26/2010Lecture 7: Sensation &amp; Perception IIMaking Sense of Our Visual WorldOutlineVision Attention processes Principles of perception Depth perception Bottom-up and Top-down processes Understanding perceptual illusionsPSC1 Spring 2010, Dr. Liat Say
UC Davis - PSC 001 - PSC 001
4/27/10What is memory?The persistence of learning over time through the storage and retrieval of information.MEMORY: ENCODING, STORAGE, AND RETRIEVALChapter 6What is memory?Ways of storing memoriesEncoding Storage RetrievalThe persistence of learn
UC Davis - PSC 001 - PSC 001
Today's Topic: IntelligenceIntroduction to Psychology PSC 1 Winter 2010Guest Lecturer: Christi BamfordWhat is intelligence? How do we measure intelligence? The extremes of intelligence Is intelligence inherited? The use &amp; abuse of intelligence testsWh
UC Davis - PSC 001 - PSC 001
5/5/2010Lecture 10: Motivation &amp; EmotionPSC1 Spring 2010, Dr. Liat SayfanLecture OutlineMotivationTheories: instinct, drive reduction, optimal arousal, incentive Maslow's hierarchy Hunger and eating behavior Achievement motivationEmotionWhat is Mot
UC Davis - PSC 001 - PSC 001
General Psychology PSC 1 Spring Quarter 2010 Course SyllabusInstructor: Dr. Liat Sayfan 268F Young Hall Office Hours: Mondays 12-2, or By Appointment lsayfan@ucdavis.edu TA1: Emily Newton 284A Young Hall Office Hours: Wednesdays 12-2 or By Appointment ek
UC Davis - PSC 001 - PSC 001
Introduction to PsychologyReview Session: Exam 2 TA-Michael BiehlEXAM REVIEW!BRING SCANTRON UCD 2000 (Blue) 50 questions Multiple Choice Check your answers before turning in exam Bubble in an option for every question You may write on your exams Write
UC Davis - PSC 001 - PSC 001
Exam 1 Review Sheet PSC 1 Spring 2010 Material from the textbook not covered in lecture is italicized. Lecture 1: What is Psychology? (Ch. 1) What is psychology? Subfields o Practice (clinical, counseling, industrial/organizational, educational/school) Di
UC Davis - PSC 001 - PSC 001
06/05/2010 01:25:00 space Somatosensory the somatosensory cortex in the brain's parietal lobe. Some Senses: vision, taste, smell, hearing, Vestibular responds to gravity and keeps you informed of your body's location in Stimulus (raw energy) light, sound
UC Davis - ARE 136 - ARE 136
Name:_Managerial Economics (ARE) 136 University of California, Davis, Spring 2009 Dr. John H. Constantine KEY-Quiz 1 (125 points), Wednesday April 8, 2009 Multiple Choice Questions-(60 points; 10 points each.) 1) Brand personality means that: a) brands a
UC Davis - ARE 136 - ARE 136
1Managerial Economics (ARE) 136 University of California, Davis, Spring 2010 Dr. John H. Constantine KEY-Quiz 2 (125 points), Wednesday April 15, 2010 Multiple Choice Questions-(60 points; 10 points each.) 1) Social classes are: a) frequently distinguish
UC Davis - ARE 136 - ARE 136
Name:_Managerial Economics (ARE) 136 University of California, Davis, Winter 2010 Dr. John H. Constantine KEY-Quiz 1 (125 points), Wednesday January 13, 2010 Multiple Choice Questions-(60 points; 10 points each.) 1) Integrated Brand Promotion a) is only
UC Davis - ARE 136 - ARE 136
Name:_Managerial Economics (ARE) 136 University of California, Davis, Winter 2010 Dr. John H. Constantine KEY-Quiz 2 (125 points), Wednesday January 20, 2010 Multiple Choice Questions-(60 points; 10 points each.) 1) Maslow's hierarchy of needs model has:
UC Davis - ARE 136 - ARE 136
Name:_Managerial Economics (ARE) 136 University of California, Davis, Winter 2010 Dr. John H. Constantine KEY-Quiz 3 (125 points), Wednesday January 27, 2010 Multiple Choice Questions-(60 points; 10 points each.) 1) A company that sells charcoal briquett
UC Davis - ARE 136 - ARE 136
Name:_Managerial Economics (ARE) 136 University of California, Davis, Winter 2010 Dr. John H. Constantine KEY-Quiz 4 (125 points), Wednesday February 3, 2010 Multiple Choice Questions-(60 points; 10 points each.) 1) Social stratification, or systematic i
UC Davis - ARE 136 - ARE 136
Name:_Managerial Economics (ARE) 136 University of California, Davis, Winter 2010 Dr. John H. Constantine KEY-Quiz 5 (125 points), Wednesday February 17, 2010 Multiple Choice Questions-(60 points; 10 points each.) 1) Gillette advertises its line of men's
UC Davis - ARE 136 - ARE 136
Name:_Managerial Economics (ARE) 136 University of California, Davis, Winter 2010 Dr. John H. Constantine KEY-Quiz 6 (125 points), Wednesday February 24, 2010 Multiple Choice Questions-(60 points; 10 points each.) 1) A manufacturing company wants to enco
UC Davis - ARE 136 - ARE 136
Name:_Managerial Economics (ARE) 136 University of California, Davis, Winter 2010 Dr. John H. Constantine KEY-Quiz 7 (125 points), Wednesday March 3, 2010 Multiple Choice Questions-(60 points; 10 points each.) 1) The _ phase of a situation analysis commo
UC Davis - ARE 136 - ARE 136
1 Name:_KEY_ Managerial Economics (ARE) 136 University of California, Davis, Winter 2010 Dr. John H. Constantine Quiz 8 (125 points), Wednesday March 10, 2010 Multiple Choice Questions-(60 points; 10 points each.) 1) An American company decides to conduct
UC Davis - ARE 136 - ARE 136
1University of California, Davis Department of Agricultural and Resource Economics Managerial Economics/ARE 136-Managerial Marketing (CRN-52511) Spring Quarter, 2010 Dr. John H. Constantine Lecture Meetings: 8:00 a.m. 10:00a.m. Where: Everson Hall, Room
University of Iowa - MATLAB - 006
Questions about MATLAB 1. Given the following matrix: M = [1 2 3 4; 2 3 4 5; 3 4 5 6]; Which Matlab statement sets the variable x equal to the first row of the matrix M defined above? A. x = M[1]; B. x = M(1); C. x = M(:,1); D. x = M(1,:); E. x = M[1,:];
Webster - ACCOUNTING - 343
Chapter 3Business CombinationsChapter 31Learning Objectives To define a business combination, and describe the two basic forms for achieving a business combination Purchase method Pooling method To describe the current acceptable method of accounting
Webster - ACCOUNTING - 343
Chapter 4Consolidated Statements on Date of AcquisitionChapter 41Learning Objectives To identify all factors that will determine if control exists To calculate &amp; allocate the purchase discrepancy To prepare a consolidated balance sheet on the date of
Webster - ACCOUNTING - 343
Chapter 8(A) Intercompany Profits in Depreciable Assets (part B is not covered in the course)Chapter 81Learning Objectives How to handle the elimination and subsequent realization of unrealized profits (and the associated depreciation) in intercompan
Webster - ACCOUNTING - 343
Chapter 2Investments in Equity Securities (Overview of the course)Chapter 21Outline Broad overview of accounting options when one company buys shares of another company Review of 5 different types of investments Held-for-trading Available-for-sale S
Webster - ACCOUNTING - 343
Chapter 12Translation and Consolidation of the Financial Statements of Foreign OperationsChapter 121Learning Objectives How do you consolidate statements of foreign operations which are produced in a foreign currency? Outline the differences between
Seneca - BUSINESS - AIT 707
CGA-CANADA FINANCIAL ACCOUNTING 4 EXAMINATION September 2005 Marks Time: 4 HoursNotes:1. 2. 3. 4. 5. 6. 7. All calculations must be shown in an orderly manner to obtain part marks. Round all calculations to the nearest dollar. Narratives for journal ent
Seneca - BUSINESS - AIT 707
CGA-CANADA FINANCIAL ACCOUNTING 4 EXAMINATION March 2005 Marks Time: 4 HoursNotes:1. 2. 3. 4. 5. 6. 7. All calculations must be shown in an orderly manner to obtain part marks. Round all calculations to the nearest dollar. Narratives for journal entries
Seneca - BUSINESS - AIT 707
CGA-CANADA FINANCIAL ACCOUNTING 4 EXAMINATION September 2006 Marks Time: 4 HoursNotes:1. 2. 3. 4. 5. 6. 7. All calculations must be shown in an orderly manner to obtain part marks. Round all calculations to the nearest dollar. Narratives for journal ent
Seneca - BUSINESS - AIT 707
CGA-CANADA FINANCIAL ACCOUNTING 4 EXAMINATION March 2004 Marks Time: 4 HoursNotes:1. 2. 3. 4. 5. 6. 7. All calculations must be shown in an orderly manner to obtain part marks. Round all calculations to the nearest dollar. Narratives for journal entries
Seneca - BUSINESS - AIT 707
CGA-CANADA FINANCIAL ACCOUNTING 4 EXAMINATION March 2005 Marks Time: 4 HoursNotes:1. 2. 3. 4. 5. 6. 7. All calculations must be shown in an orderly manner to obtain part marks. Round all calculations to the nearest dollar. Narratives for journal entries
Seneca - BUSINESS - AIT 707
CGA-CANADA FINANCIAL ACCOUNTING 4 EXAMINATION March 2006 Marks Time: 4 HoursNotes:1. 2. 3. 4. 5. 6. 7. All calculations must be shown in an orderly manner to obtain part marks. Round all calculations to the nearest dollar. Narratives for journal entries
Seneca - BUSINESS - AIT 707
CGA-CANADA FINANCIAL ACCOUNTING 4 EXAMINATION March 2007 Marks Time: 4 HoursNotes:1. 2. 3. 4. 5. 6. 7. All calculations must be shown in an orderly manner to obtain part marks. Round all calculations to the nearest dollar. Narratives for journal entries