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Econ398_HW2Solutions
School: University Of Michigan
Course: Strategy
Econ 398 Homework 2 Sketchy Solutions 1. There are four Nash Equilibria; each one involves one of the four writing down $3, while the other three each write down $10. Notice that in a strategy profile where two players, say Alice and Bertha, write do

Homework6
School: University Of Michigan
Course: Strategy
I; NotM.R.: 'uq () M I 0" 0 l, '1. ", 0 H '110.: C( S h. ~ 1'1"L '133~ C(<'1/ tcfw_ oN 3qg HoM wOf( K 0 q, It.t IJ ( ffo 0,0 1. I ( J, .2, ! tS )'/ I ,:ts 0,0 (j) v V\L \, "1 ( I I 1., ,15 ~+rvvJjJ 'T/ NA(L I CL1t ~ Jfro;1 ) I (. fV1L,.A ( It I ~ (

Strategy11Handout
School: University Of Michigan
Course: Strategy
10/9/2008 Mixed Strategies Matching Pennies In Matching Pennies, we found there was no Nash Equilibrium Guildenstern Heads Rosencrantz Heads Tails 1, 1 1, 1 Tails 1, 1 1,1 Why Mixed Strategies? If you were to play the same opponent repeatedly, you wou

Strategy12Handout
School: University Of Michigan
Course: Strategy
10/14/2008 Mixed Strategies Matching Pennies We denote the strategies on the game bimatrix Guildenstern q Heads Rosencrantz R t p 1p Heads H d Tails 1 , 1 1 1 , 1 1q Tails 1 , 1 1 1 , 1 Preferences Involving Gambles We revisit our description of pa

Strategy1Handout
School: University Of Michigan
Course: Strategy
9/10/2008 Personnel for Econ 398: Strategy Econ 398: Strategy A Study of Strategic Interaction in Games Chris Proulx Lorch Hall M107 rabbit@umich.edu Office Hours: Tu, Th 10:3011:30 Instructor: Chris Proulx, rabbit@umich.edu Office Hours: TuTh 10:3011:3

Strategy2Handout
School: University Of Michigan
Course: Strategy
9/10/2008 Analyzing Games We need three things to specify a game Players Possible strategies for each player Payoffs for eac p aye o e ou co es ayo s o each player over outcomes Analyzing Games Players have welldefined and wellbehaved preferences over o

Strategy15Handout
School: University Of Michigan
Course: Strategy
10/29/2008 Expert Advice We often rely on professionals to diagnose problems and recommend and carry out fixes Doctors Auto Mechanics and Repair Technicians p Lawyers Financial Advisors and Real Estate Agents Teachers and Researchers Expert Advice A custo

Strategy13Handout
School: University Of Michigan
Course: Strategy
10/16/2008 Mixed Strategies Matching Pennies We denote the strategies on the game bimatrix Guildenstern q Heads Rosencrantz R t p 1p Heads H d Tails 1 , 1 1 1 , 1 1q Tails 1 , 1 1 1 , 1 Mixed Strategies Matching Pennies Rosencrantz's & Guildenstern

Strategy14Handout
School: University Of Michigan
Course: Strategy
10/23/2008 Your Choice of Gambles A1= A2= .2 .8 .8 .2 $4000 $0 $4000 $0 Your Choice of Gambles $3000 $0 $3000 $0 B1= B2= .25 .75 1 0 A1= A2= .2 .8 .8 .2 $4000 $0 $4000 $0 B1= B2= $0 .25 .75 1 0 $3000 $0 $3000 $0 .75 It turns out that if you preferred A1 t

Strategy16Handout
School: University Of Michigan
Course: Strategy
10/30/2008 Midterm 2: Next Tuesday Exam focuses on new material Chapter 5 to beginning of Chapter 9 Lectures 816, HW 46 Signaling with Strategic Uncertainty Otto Stag Ludwig Stag Hare 2,2 1,0 Hare 0,1 1,1 Come early and bring a UMID No cellphones or ip

Strategy17Handout
School: University Of Michigan
Course: Strategy
11/10/2008 Spence: Education as a Screen Education does not affect productivity Two types of people Able types worth $150,000 Challenged types worth $100,000 $100 000 Types are indistinguishable, can't be tested Spence: Education as a Screen SelfSelectin

Strategy10Handout
School: University Of Michigan
Course: Strategy
10/2/2008 Midterm 1: Next Tuesday Covers up through Chpt. 5 & HW 3 Come early and bring a UMID No cellphones or ipods allowed Calculators must be simple nongraphing simple, nongraphing, noncomplex, noncomputerlike calculators with one memory registe

Strategy9Handout
School: University Of Michigan
Course: Strategy
10/1/2008 Simultaneous/Sequential Mix Up We might wish to model situations involving both sequential and simultaneous moves We can combine the concepts of Nash Equilibrium with Rollback to analyze such q y games Consider a somewhat complex relationship be

Strategy8Handout
School: University Of Michigan
Course: Strategy
9/24/2008 Upheaval in Financial Markets A panel of distinguished alumni from the Department of Economics will discuss the ongoing crisis in financial markets. Speakers include: David Berson MPP `79; PhD `82 econ D id B Peter Borish, P t B i h AB `81; MPP

HW3
School: University Of Michigan
Course: Strategy
Econ 398 Homework 3 Due Sept. 26, 2008 1) Dixit & Skeath, Chapter 4, problems 2b, 2c. 2) Dixit & Skeath, Chapter 4, problems 3b, 3c. 3) Dixit & Skeath, Chapter 4, problem 10. 4) Dixit & Skeath, Chapter 5, problem 3. 5) Alice and Bob are each considering c

HW6Sol
School: University Of Michigan
Course: Strategy
Econ 398 Homework 6 Suggested Solutions 1) Use the characterization from class to check for mixedstrategy Nash Equilibria. First note that there are four pure strategy equilibria, each where one person drives Straight, and the other person either swerves

Roywchen_12608_1534Econ_398_Practice_Exam_3
School: University Of Michigan
Course: Strategy
Practice Exam 3 (1 3) Mckouwski & Miller, a consulting firm wants to hire some workers for its vacant positions. There are 2 types of jobs: challenging and mundane and two types of workers: highly productive and less productive. In a challenging job, the

Roywchen_103108_17308Eco...ummary_of_topics_Midterm_2
School: University Of Michigan
Course: Strategy
Econ 398: Summary of topics relevant to Midterm 2 Simultaneous and sequential games Changing the rules/order of play Portraying games in different forms o Sequential games strategic/normal form o Simultaneous games extensive form Subgames Subgameperfect

Strategy3Handout
School: University Of Michigan
Course: Strategy
9/10/2008 Homework Due Friday 4PM Hand homework into your GSI during discussion section OR Turn in homework to the specially marked box outside Lorch Hall 109 by 4PM Extensive Form Games  Strategies A strategy is a complete plan of action Tells a player

Strategy4Handout
School: University Of Michigan
Course: Strategy
9/11/2008 Simultaneous Move Games Extensive form games capture the timing structure of sequential move games Often games are simultaneous, or the sequential nature doesn't matter q Tennis serve Production planning Bidding for a contract Voting Example Was

Strategy5Handout
School: University Of Michigan
Course: Strategy
9/15/2008 Finding Nash Equilibria We'd like a method for finding NE Player 2 1 A Player 1 B C D 5,7 2,6 3,9 0,0 2 6,4 15 , 3 2,6 0,1 3 11 , 12 1,0 19 , 9 9 , 17 4 8 , 22 7,2 6,5 17 , 12 Example Attributed to A.W. Tucker Two Prisoner's brought in for inter

Strategy6Handout
School: University Of Michigan
Course: Strategy
9/18/2008 MAXIMIN MINIMAX 9 soldiers, three are 5 feet tall, three are 6 feet tall, three are 7 feet tall 5 7 6 6 5 7 7 6 5 Min = 5 Min = 5 Min = 5 A Note About Equilibria Some games Get feel for what an equilibrium might be Show that if everyone does it

Strategy7Handout
School: University Of Michigan
Course: Strategy
9/23/2008 Imperfect Competition We consider competition in a market with a linear demand curve: Q = D( P) = 302 P Inverse demand: P = 302 Q First think of a monopolist with cost C (Q) = 2Q Monopolist seeks to maximize profit: Imperfect Competition: Courno

Strategy18Handout
School: University Of Michigan
Course: Strategy
11/11/2008 Bayes Rule Bayes Rule A B A B Universe of Possibility P[A&B] = P[BA]P[A] = P[AB]P[B] P[BA] = P[AB]P[B] / P[A] Bayes' Rule Bayes' Rule P[BA] = P[AB]P[B] / P[A] = P[AB]P[B] / (P[AB]P[B] + P[AB]P[B] ) Bayes Rule Consider testing for a pa

Strategy19Handout
School: University Of Michigan
Course: Strategy
11/13/2008 Strategic Moves Change the rules of the game to benefit yourself Usually involves making a pregame move 1st Actions must be Observable Irreversible Strategic Moves Strategic moves are to deter or compel Unconditional commitments Try to change

Ch18_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 18 Exercises SOLVED EXERCISES S1. The father and daughter were implicitly negotiating about how much freedom from parental control she would have. The fathers BATNA was low: breakdown of negotiation would lead to a tantrum or a scene

Ch19_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 19 Exercises SOLVED EXERCISES S1. (a) The existence of buyer B2 means that buyer B1 will not be able to buy at any price below 200. If B1 tried to strike a deal at (for example) 190, B2 could offer to pay 191; if B2 bought at that pri

Ch02_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 2 Exercises SOLVED EXERCISES S1. (a) Assuming a sufficient supply of yogurt is available for all shoppers, each shopper is simply making a decision. If some flavors of yogurt were in short supply, then it would be a game, because shop

Ch03_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 3 Exercises SOLVED EXERCISES S1. (a) There is one initial node (I) for Hansel making the first move; three decision nodes (D) including the initial node, which represent the points where either Hansel or Gretel make a decision; and si

Ch04_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 4 Exercises SOLVED EXERCISES S1. False. A dominant strategy yields you the highest payoff available to you against each of your opponents strategies. Playing a dominant strategy does not guarantee that you end up with the highest of a

Ch05_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 5 Exercises SOLVED EXERCISES S1. (a) Rs bestresponse rule is given by y = 10x x. L spends $16 million, so x = 16. Then Rs best response is y = 1016 16 = 10(4) 16 = 40 16 = 24, or $24 million. (b) simultaneously: x = 10(10x x)1/2 10x

Ch06_solutions_S11 Correx
School: University Of Michigan
Solutions to Chapter 6 Exercises SOLVED EXERCISES S1. Secondmover advantage. In a sequential game of tennis, the second mover will be able to respond best to the first movers chosen action. Put another way, the second mover will be able to exploit the in

Ch07_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 7 Exercises SOLVED EXERCISES S1. False. A players equilibrium mixture is devised in order to keep her opponent indifferent among all of her (the opponents) possible mixed strategies; thus, a players equilibrium mixture yields the oppo

Ch08_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 8 Exercises SOLVED EXERCISES S1. False. A players equilibrium mixture is devised in order to keep her opponent indifferent among all of her (the opponents) possible mixed strategies; thus, a players equilibrium mixture yields the oppo

Ch09_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 9 Exercises SOLVED EXERCISES S1. (a) Your neighbor has a sure income of $100,000. In addition, under the insurance contract, he will receive x when you have a good year and pay you $60,000 when you have a bad year. The lowest value of

Ch17_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 17 Exercises SOLVED EXERCISES S1. The painter can compare her estimated cost to a jobs true cost only when she does the job. But the painter does a job only when she agrees (through the bidding process) to do it for less than anybody

Ch16_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 16 Exercises SOLVED EXERCISES S1. Under truthful voting, A should match Geology and Sociology in the first vote, with the winner (Geology) to face Philosophy in the second round. Under strategic voting, A should match Philosophy and S

Strategy20Handout
School: University Of Michigan
Course: Strategy
11/20/2008 The Entry Game (200,100) Fight Burning Money I E Challenger F A (200, 100) (100, 100) INCUMBENT SO Don t Don't Invest Acquiesce (0, (0 300) (100,100) Incumbent I Invest E A Challenger (100, 0) F (200, 10) CHALLENGER Enter Stay Out (0,300)

Strategy21Handout
School: University Of Michigan
Course: Strategy
11/20/2008 The Prisoner's Dilemma It's so famous, the payoffs have names! T>R>P>S Clyde Barrow Cooperate Bonnie Parker Cooperate Defect R,R T,S Defect S,T P, P Finitely Repeated Prisoner's Dilemma Clyde Barrow Cooperate Bonnie Parker Cooperate Defect 3,3

Strategy22Handout
School: University Of Michigan
Course: Strategy
12/2/2008 Collective Action Problems Often, the welfare of society is best served if individuals take a particular "socially responsible" action. On the other hand, individuals may not find it in their interest to take the "socially socially responsible"

Strategy23Handout
School: University Of Michigan
Course: Strategy
12/2/2008 Collective Action Games N = population n = # of participants who take an action Nn = # of shirkers who do not take the action Participant g p gets: p( ) p(n) Shirker gets: s(n) Collective Action Games Suppose there are n participants and Nn1

Strategy24Handout
School: University Of Michigan
Course: Strategy
12/4/2008 Evolutionary Game Theory Darwin's Origin of Species explained evolution of organisms Certain members of a species are better adapted to their environment (more fit) The traits that make those members more fit are embedded in genes More fit membe

Ch11_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 11 Exercises SOLVED EXERCISES S1. False. The players are not assured that they will reach the cooperative outcome. Rollback reasoning shows that the subgameperfect equilibrium of a finitely played repeated prisoners dilemma will enta

Ch12_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 12 Exercises SOLVED EXERCISES S1. (a) (b) The number choosing X should decrease to move the population division between X and Because the line for action X is above the line for action Y when 100 people choose X, Y away from the unsta

Ch13_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 13 Exercises SOLVED EXERCISES S1. (a) The payoff table for the two types of travelers is: High High Low 100, 100 70, 30 Low 30, 70 50, 50 (b) The graph is: (c) There are three possible equilibria: a stable monomorphic equilibrium of a

Ch14_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 14 Exercises SOLVED EXERCISES S1. Some examples of incentive schemes that help induce more care on the part of policy holders: 1. The insurer can provide a multiyear contract or otherwise establishes an ongoing relationship in which f

Ch15_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 15 Exercises SOLVED EXERCISES S1. (a) In the purethreat case, the unions expected payoff is 50(1 p) 100p = 50 150p. The unions expected payoff goes to zero for p = 1/3 and is negative for p > 1/3. Thus the pure threat is too big from

Ch10_solutions_solved Edit
School: University Of Michigan
Solutions to Chapter 10 Exercises SOLVED EXERCISES S1. The statement is true because promises, when successfully used as strategic moves, require that you follow through on the promised action; you will not promise an arbitrarily large reward. You may thr

Econpexam
School: University Of Michigan
Course: Strategy
Practice Exam 2 1. Take the following gambles: A1 = A2 = 0.3 0.7 0.6 0.4 $10 $0 $10 $0 B1 = B2 = 0.1 0.9 x y $5 $0 $5 $0 Assume that you prefer A1 to B1, and that you prefer B2 to A2. Your preferences can be summarized by some vonNeumann/Morgenstern util

Answers To Midterm 1 Practice Problems Fall 06
School: University Of Michigan
Answers to Midterm 1 Practice Problems 1) b 2) d (When x>2 (L,H) is the unique NE. When x<2 (H,H) is the unique NE. When x=2, both (H,H) and (L,H) are pure strategy equilibria.) 3) d (Martin maximizes (100PM+2/3 PE)( PM10) with respect to PM. The b

Midterm 1 Practice1
School: University Of Michigan
ECON 398 Fall 2006 Midterm 1 Practice Exam 1 Professor Ozdenoren INSTRUCTIONS You have 80 minutes to complete the exam. There are 16 questions. 1. Consider the following simultaneous game, which has a variable x for two of the payoffs. High High Lo

Midterm 1 Practice2
School: University Of Michigan
ECON 398 Fall 2006 Midterm 1 Practice Exam 2 Professor Ozdenoren INSTRUCTIONS You have 80 minutes to complete the exam. There are 16 questions. 1. Notice that there is a variable x in the payoffs of the following game: Carrie R U 3,4 D 1,3 Rhonda

Midterm 1 Practice3
School: University Of Michigan
ECON 398 Fall 2006 Midterm 1 Practice Exam 3 Professor Ozdenoren INSTRUCTIONS You have 80 minutes to complete the exam. There are 16 questions. Wonder Cloak Inc. (C) and Scary Mask Inc. (M) are two shops situated on the opposite side of State Stree

Midterm 1 Practice4
School: University Of Michigan
ECON 398 Fall 2006 Midterm 1 Practice Exam 4 Professor Ozdenoren INSTRUCTIONS You have 80 minutes to complete the exam. There are 16 questions. Elbonia and Sylvonia are two neighboring countries where Elbonia is much larger in size and it is more i

Econ398_HW1Solutions
School: University Of Michigan
Course: Strategy
Econ 398 Homework 1 Sketch of Solutions 1. For Olaf and Phil, it is handy to number the nodes like this: Then Olafs strategies specify what he does at node 1 and what he does at node 5. His strategy set is {(U,T), (M,T), (D,T), (U,B), (M,B), (D,B)}.

Econ398_HW3
School: University Of Michigan
Course: Strategy
Econ 398 Homework 3 Due Feb 6, 2009 1. Alice and Bob are each considering contributing to a public park which will be enjoyed by all. Alice has $24, of which shell contribute $a. Bob has $15 of which hell contribute $b. Alices payoff depends on the t

Econ398_HW3Solutions
School: University Of Michigan
Course: Strategy
Econ 398 Homework 3 Sketchy Solutions 1. You can calculate the best response functions and then solve the two functions simultaneously to get a*=11, b*=2. Show that if each person adds one dollar to their own contribution, each persons utility level

Econ398_HW4
School: University Of Michigan
Course: Strategy
Econ 398 Homework 4 Due Friday, February 20, 2009 1) Dixit & Skeath, Chapter 6, problem 1 2) This is a variant on the War of Attrition discussed in class. In this example, each player places no value on the time spent waiting for the other player to

Econ398_HW5
School: University Of Michigan
Course: Strategy
Econ 398 Homework 5 Due Friday, March 6, 2009 1) Dixit & Skeath, Chapter 6, problem 4 2) Dixit & Skeath, Chapter 6, problem 5 3) In the game depicted above, suppose that firm 2 operates both in Kalamazoo and in Toledo. Firm 1 is a potential entrant

Econ398win08hw5sol
School: University Of Michigan
Course: Strategy
ECON 398 SOLUTIONS FOR HOMEWORK 5 Professor Ozdenoren a) Firm 1 has 8 strategies, examples are: (Player 1 plays West Coast, plays A if East Coast, plays A if West Coast) or (Player 1 plays West Coast, plays F if East Coast, plays A if West Coast) et

Econ398win08hw4sol
School: University Of Michigan
Course: Strategy
ECON 398 HOMEWORK 4 SOLUTIONS Professor Ozdenoren 1. For each of the following sequential games, write the equivalent strategic form and solve for all pure strategy Nash equilibria. Indicate which one is the subgame perfect Nash equilibrium (i.e. th

Econ398win08hw3sol
School: University Of Michigan
Course: Strategy
ECON 398 HOMEWORK 3 Professor Ozdenoren 1. In a small town called Ham Harbour there are two shops. Wingerman's has great cheese and Trader Moe's has good wine. Demand for Wingerman's cheese is given by QW = 32  2PW  PM and demand for Trader Moe's

Midterm 2 Practice Problems Fall06
School: University Of Michigan
Midterm 2 Practice Problems The new generation of ipod has just been introduced and every student at the U of M is deciding whether to buy it or not. The net benefit of buying the new ipod depends on what percentage of U of M students also buy it a

Homework 1
School: University Of Michigan
Course: Strategy
ECON 398 HOMEWORK 1 Professor Ozdenoren 1) For the following games. List the strategies available to all players. What is the equilibrium outcome? What are the equilibrium strategies? a) 0,4 Out 1 In Accomodate 2,2 2 Price War 1,1 b) 1,4 5,2 1

Homework 1 Answers
School: University Of Michigan
Course: Strategy
SOLUTIONS FOR ECON 398 HOMEWORK 1 Professor Ozdenoren 1) a) For player 1 available strategies are {Out, In}. For player 2 available strategies are {Accommodate, Price War}. Equilibrium outcome is (2,2) and equilibrium strategies are In for player 1

Homework 2
School: University Of Michigan
Course: Strategy
ECON 398 HOMEWORK 2 Professor Ozdenoren 1. In the following game between Donna's and Pierce's find the equilibrium using iterated elimination of dominated strategies. PIERCE'S High High DONNA'S Medium 36,20 50,30 35,30 Low 36,35 30,25 25,55 60,6

Homework 2 Answers
School: University Of Michigan
Course: Strategy
ECON 398 HOMEWORK 2 SOLUTIONS Professor Ozdenoren 1. In the following game between Donna's and Pierce's find the equilibrium using iterated elimination of dominated strategies. PIERCE'S High High DONNA'S Medium 36,20 50,30 35,30 Low 36,35 30,25 2

Homework 3
School: University Of Michigan
Course: Strategy
ECON 398 HOMEWORK 3 Professor Ozdenoren 1. In a small town called Ham Harbour there are two shops. Wingerman's has great cheese and Trader Moe's has good wine. Demand for Wingerman's cheese is given by QW = 32  2PW  PM and demand for Trader Moe's

Econ 398 Syllabus Winter 2008
School: University Of Michigan
Course: Strategy
Economics 398: Strategy Class Syllabus and Policies Winter 2008 Professor: Class Time: Emre Ozdenoren Tuesday and Thursday 2:30 4 pm Class Location: 1120 Weill Office: Phone: Email: Office Hours: Course Page: Course GSI's: 341 Lorch Hall 647560

Econ398win08hw1sol
School: University Of Michigan
Course: Strategy
SOLUTIONS FOR ECON 398 HOMEWORK 1 Professor Ozdenoren 1) a) For player 1 available strategies are {Out, In}. For player 2 available strategies are {Accommodate, Price War}. Equilibrium outcome is (2,2) and equilibrium strategies are In for player 1

Econ398win08hw2sol
School: University Of Michigan
Course: Strategy
ECON 398 HOMEWORK 2 SOLUTIONS Professor Ozdenoren 1. In the following game between Donna's and Pierce's find the equilibrium using iterated elimination of dominated strategies. PIERCE'S High High DONNA'S Medium 36,20 50,30 35,30 Low 36,35 30,25 2

Econ398_HW6
School: University Of Michigan
Course: Strategy
Econ 398 Homework 6 Due Friday, March 13, 2009 1) Dixit & Skeath, Chapter 8, problem 4 2) Dixit & Skeath, Chapter 8, problem 6 3) Recall the game discussed in lecture called Glorified Chicken: Daisy Duke Billy Jo Bob Left Left Straight Right 1,1 2

Econ398_PracticeQuestionsExam1
School: University Of Michigan
Course: Strategy
Practice Questions for Exam 1 1. The following game has exactly one Nash equilibrium if COLUMN Down Right 4,5 9,y x,6 10,2 ROW a. b. c. d. e. x = 4, y = 2 x = 5, y = 2 x = 3, y = 6 x = 2, y = 7 None of the above Up Left 2. Suppose there are 10 peo

Econ398_PracticeQuestionsExam2
School: University Of Michigan
Course: Strategy
Practice Exam 2 1. Take the following gambles: A1 = 0.3 0.7 0.6 0.4 $10 $0 $10 $0 B1 = 0.1 0.9 x y $5 $0 $5 $0 A2 = B2 = Assume that you prefer A1 to B1, and that you prefer B2 to A2. Your preferences can be summarized by some vonNeumann/Morgenst

Lecture12
School: University Of Michigan
Course: Strategy
3/3/2009 Mixed Strategies Matching Pennies We denote the strategies on the game bimatrix Guildenstern q Heads Rosencrantz R t p 1p Heads Hd Tails 1 , 1 1 1 , 1 1q Tails 1 , 1 1 1 , 1 Preferences Involving Gambles We revisit our description

Lecture13
School: University Of Michigan
Course: Strategy
3/3/2009 Mixed Strategies Matching Pennies We denote the strategies on the game bimatrix Guildenstern q Heads Rosencrantz R t p 1p Heads Hd Tails 1 , 1 1 1 , 1 1q Tails 1 , 1 1 1 , 1 Mixed Strategies Matching Pennies Rosencrantzs & Guilden

Lecture14
School: University Of Michigan
Course: Strategy
3/5/2009 Your Choice of Gambles A1= A2= .2 .8 .8 .2 $4000 $0 $4000 $0 Your Choice of Gambles $3000 $0 $3000 $0 B1= B2= .25 .75 1 0 A1= A2= .2 .8 .8 .2 $4000 $0 $4000 $0 B1= B2= .25 .75 1 0 $3000 $0 $3000 $0 Suppose you prefer A1 to B1, but

Lecture15
School: University Of Michigan
Course: Strategy
3/10/2009 Expert Advice We often rely on professionals to diagnose problems and recommend and carry out fixes Doctors Auto Mechanics and Repair Technicians p Lawyers Financial Advisors and Real Estate Agents Teachers and Researchers Expert Advice A

Lecture 1
School: University Of Michigan
Course: Strategy
1/13/2009 Strategic Situations Econ 398: Strategy A Study of Strategic Interaction in Games Chris Proulx Lorch Hall M107 rabbit@umich.edu Office Hours: Tu, Th 4:155:15 Many (2) people Each has many possible actions Different actions yield differe

Lecture 5
School: University Of Michigan
Course: Strategy
1/22/2009 Homework Due Friday 4:15PM Hand homework in to your GSI during discussion section OR Turn in homework to the specially marked box outside Lorch Hall 109 by 4:15PM Today: Chapter 4, Next Week: Chapter 5 Homework Due Friday 4:15PM Dixit & S

Test1
School: University Of Michigan
Course: Strategy
MultipleChoice Questions: Select the best answer. Each correct answer is worth 5 points. Each wrong answer is worth zero points. Answers left blank are worth 1 point. Use the following to answer questions 12: Michigan and OSU are playing a footbal

Lecture11
School: University Of Michigan
Course: Strategy
2/17/2009 Mixed Strategies Matching Pennies In Matching Pennies, we found there was no Nash Equilibrium Guildenstern Heads Rosencrantz Heads Tails 1, 1 1, 1 Tails 1, 1 1,1 Why Mixed Strategies? If you were to play the same opponent repeatedly,

Lecture10
School: University Of Michigan
Course: Strategy
2/17/2009 Grading Policy You have two weeks after homework is handed back to seek a grading correction Please check the CTools gradebook to make C Tools sure we have no recording errors Simultaneous/Sequential Mix Up We might wish to model situati

Lecture9
School: University Of Michigan
Course: Strategy
2/5/2009 Midterm 1: Next Tuesday Covers up through Chpt. 5 & HW 3 Bring a UMID for checkin No cellphones or ipods allowed Calculators must be simple nongraphing simple, nongraphing, noncomplex, noncomputerlike calculators with one memory regi

Econ398_Test2
School: University Of Michigan
Course: Strategy
TrueFalse Questions: Answer A for "True" and B for "False". Each correct answer is worth 2 points. Each wrong answer is worth zero points. Answers left blank are worth 1 point. MultipleChoice Questions: Select the best answer. Each correct answer

HW1
School: University Of Michigan
Course: Strategy
Econ 398 Homework 1 Due Jan 23, 2009 1. For the following game involving Olaf and Phil, list each players available strategies. Find the rollback equilibria. 2. Michigan and OSU are playing a football game, and it is early in the first half. Michiga

HW2
School: University Of Michigan
Course: Strategy
Econ 398 Homework 2 Due Jan 30, 2009 1. Four players, Alice, Bertha, Cora, and Delores are put into separate rooms so they cannot communicate with one another. They have to write either $3 or $10 on a piece of paper, and then the papers are collected

Lecture2
School: University Of Michigan
Course: Strategy
1/13/2009 Analyzing Games We need three things to specify a game Players Possible strategies for each player Payoffs for eac p aye o e ou co es ayo s o each player over outcomes Analyzing Games Players have welldefined and wellbehaved preferences

Lecture3
School: University Of Michigan
Course: Strategy
1/15/2009 Example George and Hiromi (2,0) R Example The Smoking Decision Carmen wants to try smoking, and then quit GEORGE 1 S T HIROMI 2 U (3,1) 3 GEORGE V (0,0) W (1,2) Example The Smoking Decision Addiction creates a Future Carmen w

Lecture4
School: University Of Michigan
Course: Strategy
1/20/2009 Homework Due Friday 4PM Hand homework in to your GSI during discussion section OR Turn in homework to the specially marked box outside Lorch Hall 109 by 4:15 PM This week: Dixit and Skeath, Chapter 4 Simultaneous Move Games Extensive form

Lecture6
School: University Of Michigan
Course: Strategy
1/27/2009 Homework Due Friday 4:15PM Hand homework in to your GSI during discussion section OR Turn in homework to the specially marked box outside Lorch Hall 109 by 4:15PM Be Reading Chapter 5 A Note About Equilibria Some games Get feel for what

Lecture7
School: University Of Michigan
Course: Strategy
1/29/2009 Imperfect Competition We consider competition in a market with a linear demand curve: Q = D( P) = 302 P Inverse demand: P = 302 Q First think of a monopolist with cost C (Q) = 2Q Monopolist seeks to maximize profit: Imperfect Competitio

Lecture8
School: University Of Michigan
Course: Strategy
2/5/2009 A Note About Equilibria Some games Get feel for what an equilibrium might be Show that if everyone does it, nobody has an incentive to change Show everything else isnt equilibrium: for each other possible strategy profile, somebody has an