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Course: ECON 4349, Fall 2008School: U. Houston
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4349 Econ Homework #2 For each simultaneous-move game below, let Player 1s strategy be (p,1-p) and Player 2s strategy be (q,1-q), and find, if possible, a. a condition on q such that A is Player 1s best response, b. a condition on q such that B is Player 1s best response, c. a condition on q such that Player 1 is willing to choose a mixed strategy, d. a condition on p such that X is Player 2s best response, e. a...
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4349 Econ Homework #2
For each simultaneous-move game below, let Player 1s strategy be (p,1-p) and Player 2s strategy be (q,1-q), and find, if possible, a. a condition on q such that A is Player 1s best response, b. a condition on q such that B is Player 1s best response, c. a condition on q such that Player 1 is willing to choose a mixed strategy, d. a condition on p such that X is Player 2s best response, e. a condition p on such that Y is Player 2s best response, f. a condition on p such that Player 2 is willing to choose a mixed strategy, g. the Nash equilibrium/equilibria of the game. 1. Player 1 A B X 5,2 2,5 Player 2 Y 1,6 4,3
2. Player 1 A B X 2,5 0,0
P...
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NMSU - MATH - 683
Sheaf CohomologyIn this note we give the background needed to dene sheaf cohomology. In particular, we prove the following two facts. First, the category Ab(X) of sheaves on a topological space X has enough injectives. Second, if is the global fun
U. Houston - ECON - 4349
Econ 4349 Homework #2 solutionsFor all problems, Player 1s strategy is (p,1-p) and Player 2s strategy is (q,1-q). Also, best-response diagrams are given for each problem; Player 1s best-response correspondence is shown as thick lines, and Player 2s
U. Houston - ECON - 4349
Econ 4349 Homework #3For each simultaneous-move game below, let the players mixed strategies be (p,1-p) (for Player 1), (q,1-q) (for Player 2), and (r,1-r) (for Player 3), and find a. all three players expected payoffs to both of their available str
U. Houston - ECON - 4349
Econ 4349 Homework #3 solutionsFor all problems, Player 1s strategy is (p,1-p), Player 2s is (q,1-q), and Player 3s is (r,1-r). Note that all three games are symmetric, so for a given game, all three players expected payoff calculations and best res
U. Houston - ECON - 4349
Econ 4349 Homework #41. For each simultaneous-move game below, find i. Player 1s pure-strategy best-response function, ii. Player 2s pure-strategy best-response function, iii. the pure-strategy Nash equilibrium of each game. In each game, x1 denotes
NMSU - MATH - 683
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GWU - ECE - 001
A Biomed CurriculumInterschool Working Group Summer 2001 Approved by the BOT February 2002Educational Objectives The BME Program is designed to ensure that eachstudent develops a strong educational foundation in the basic sciences, as well as i
U. Houston - ECON - 4349
Econ 4349 Homework #4 solutions1. a. Player 1s payoff is 1 = (60x1x2)x1 and Player 2s payoff is 2 = (60x1x2)x2. Player 1s payoff can be written as (60x2)x1x12, which fits the form A+Bx1+Cx12 (where A = 0, B = 60x2, and C= 1). So, the value of x1 tha
NMSU - MATH - 683
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U. Houston - ECON - 4349
Name:ID#:Econ 4349 Midterm #1Answer all questions as completely as possible. Partial credit may be given for progress toward a solution. True but irrelevant information receives no credit. Unless stated otherwise, assume that a player's payoff i
Allan Hancock College - COMP - 5348
Scenario! DHL Pracel Germany: automatic parcel machines (PackStation) service! ! ! ! ! Generalizes the P.O. Box principle to parcels Both ways: Parcels can be left and collected to avoid courier costs in most German cities and public places (e.g. U
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Midterm #2Answer all questions as completely as possible. Partial credit may be given for progress toward a solution. True but irrelevant information receives no credit. Unless stated otherwise, assume that a player's payoff i
NMSU - MATH - 683
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U. Houston - ECON - 4349
Econ 4349 Midterm #2 solutions1. (16 points) Player 1 A B C D 4,0 2,6 3,2 Player 2 E 4,2 5,7 6,5 F 7,1 3,1 6,2a. (4 points) Player 1 has no dominant strategy. If Player 2 chooses D or F, Player 1's unique best response is A; if Player 2 chooses E,
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Midterm #3Answer all questions as completely as possible. Partial credit may be given for progress toward a solution. True but irrelevant information receives no credit. You may write on the backs of these pages, as long as I
U. Houston - ECON - 4349
Econ 4349 Midterm #3 solutions1. (30 points) a. (10 points)b. (10 points)c. (10 points)2. (30 points) In the strategic form below, boldface payoffs correspond to pure-strategy best responses. Player 2 Player 1 A B A B 1,1,1 0,9,0 9,0,0 1,1,1 P
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Midterm #4Answer all questions as completely as possible. Partial credit may be given for progress toward a solution. True but irrelevant information receives no credit. You may write on the backs of these pages, as long as I
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Quiz #1Consider a game with this payoff matrix. Player 2 W 4,6 2,9 6,8Player 1A B CV 7,1 5,5 9,3X 3,2 8,7 1,4a. If Player 1 chooses A and Player 2 chooses X, what will Player 1s payoff be?b. If Player 1 chooses B a
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Quiz #10Due at beginning of class Nov. 29Consider the following two-player card game. First, Player 1 and Player 2 are each dealt one card, which can be either an A or a K. There is a chance that both are dealt As, a chance
NMSU - MATH - 683
Spectral SequencesIn this document we gather together facts and calculations about spectral sequences.1Motivation of Spectral Sequences by Double Complexes0 Let T be a rst quadrant double complex. We write Epq for the (p, q) term in T . We ha
U. Houston - ECON - 4349
Econ 4349 Quiz #10 Solutionsa. One acceptable game tree is shown below.b. This game has no proper subgames, so every Nash equilibrium is also a subgame perfect equilibrium. To find the Nash equilibria, we represent the game with a strategic form.
U. Houston - ECON - 4349
Econ 4349 Quiz #1 SolutionsPlayer 1 A B C V 7,1 5,5 9,3 Player 2 W 4,6 2,9 6,8 X 3,2 8,7 1,4a. If Player 1 chooses A and Player 2 chooses X, Player 1s payoff will be 3. b. If Player 1 chooses B and Player 2 chooses V, Player 2s payoff will be 5. c
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Quiz #2Consider a game with this payoff matrix. Player 2 Y 1,2 8,7 2,1Player 1A B CX 7,1 5,8 9,3Z 4,3 2,9 6,4a. Does Player 1 have a dominant strategy in this game? If so, which one(s)?b. Does Player 1 have a domin
U. Houston - ECON - 4349
Econ 4349 Quiz #2 SolutionsPlayer 1 A B C X 7,1 5,8 9,3 Player 2 Y 1,2 8,7 2,1 Z 4,3 2,9 6,4a. Player 1 has no dominant strategy. b. Player 1 has a dominated strategy, A (which is dominated by C). c. Player 2 has a dominant strategy, Z. d. Player
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Quiz #3Consider a game with this payoff matrix. Player 2 Player 1 A B W 6,1 4,4 X 1,0 2,3 Y 7,5 0,4 Z 2,6 2,5a. Write Player 1s best-response correspondence in the space below.b. Write Player 2s best-response correspondenc
U. Houston - ECON - 4349
Econ 4349 Quiz #3 SolutionsPlayer 2 Player 1 A B W 6,1 4,4 X 1,0 2,3 Y 7,5 0,4 Z 2,6 2,5a. Player 1s best-response correspondence is BR(W)=A BR(X)=B BR(Y)=A BR(Z)={A,B} b. Player 2s best-response correspondence is BR(A)=Z BR(B)=Z c. Nash equilibri
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Quiz #4Due at beginning of class Sept. 201. Consider the game below. Player 2 H J 1,3,7 7,1,11 4,5,2 10,6,1 5,12,6 8,2,9 Player 3: X Player 2 H J 9,4,8 12,7,5 11,10,4 3,8,10 2,9,12 6,11,3 Player 3: YPlayer 1A B CPlayer
U. Houston - ECON - 4349
Econ 4349 Quiz #4 Solutions1. Player 1 A B C Player 2 H J 1,3,7 7,1,11 4,5,2 10,6,1 5,12,6 8,2,9 Player 3: X Player 1 A B C Player 2 H J 9,4,8 12,7,5 11,10,4 3,8,10 2,9,12 6,11,3 Player 3: Ya. If Player 1 chooses C, Player 2 chooses J, and Player
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Quiz #5Due at beginning of class Oct. 13Consider the game below. Player 2 W X Player A 6,1 2,5 1 B 3,4 4,3 a. Find any pure-strategy Nash equilibria of this game. b. Let (p,1-p) denote Player 1s (mixed) strategy, and (q,1-q)
U. Houston - ECON - 4349
Econ 4349 Quiz #5 SolutionsPlayer 2 Player 1 A B W 6,1 3,4 X 2,5 4,3a. This game has no pure-strategy Nash equilibria. b. Given the players mixed strategies, Player 1s expected payoff to A is 2+4q and her expected payoff to B is 4-q. So, A is her
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Quiz #6Consider the game tree below.a. In the space below, list the strategies available to Player 1.b. In the space below, list the strategies available to Player 2.
U. Houston - ECON - 4349
Econ 4349 Quiz #6 Solutionsa. Player 1 has only one decision node, and two choices at that node: A and B. So, her only available strategies are A and B. b. Player 2 has two decision nodes, the left one (after Player 1 has chosen A) and the right on
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Quiz #71. Represent the following game tree as a game matrix. (You do not need to solve it!)2. Represent the following game matrix as a game tree. (You do not need to solve it!) Player 2 D 3,2 2,3Player 1A BC 5,0 1,4
U. Houston - ECON - 4349
Econ 4349 Quiz #7 Solutions1. Note that Player 1 has three strategies: A, B, and C. Player 2 has four strategies: WY, WZ, XY, and XZ. Player 2 Player 1 A B C WY 6,2 5,0 7,1 WZ 6,2 5,0 2,3 XY 4,4 5,0 7,1 XZ 4,4 5,0 2,32. Other game trees are accept
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Quiz #8Due at beginning of class Nov. 8Consider the two simultaneous-move games below. Player 2 Y Z Player A 7,-7 6,-6 Player 1 1 B 8,-8 9,-9 Game 1 Player 2 W X 2,-1 0,1 -1,2 1,0 Game 2C DNow, consider the following game
U. Houston - ECON - 4349
Econ 4349 Quiz #8 Solutionsa. One acceptable game tree is shown below; others are possible.b. To solve this game using the modified version of backward induction discussed in class, we first find the subgames. Besides the entire game (which is a s
U. Houston - ECON - 4349
Name:ID#:Econ 4349 Quiz #9Consider the following game. First, a fair coin is tossed (so that Heads and Tails are equally likely). Player 1 is told the result of the coin toss; Player 2 is not. Then, the two players themselves simultaneously choo
U. Houston - ECON - 4349
Econ 4349 Quiz #9 Solutionsa. One acceptable game tree is shown below.b. Player 1 has two information sets, each with only one node. At either information set, she can choose either H or T. So, her available pure strategies are HH, HT, TH, and TT.
U. Houston - ECON - 4349
Syllabus: Introduction to Game Theory (Econ 4349)The goal of this course is to teach you how to analyze simple strategic situations with the use of gametheoretic techniques. Times of class: Instructor: TTh 1-2:30 pm Nick Feltovich Phone: Fax: Office
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Allan Hancock College - COMP - 5348
Copyright warningCOMMONWEALTH OF AUSTRALIA Copyright Regulations 1969 WARNING This material has been reproduced and communicated to you by or on behalf of the University of Sydney pursuant to Part VB of the Copyright Act 1968 (the Act). The material
U. Houston - ECON - 7342
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U. Houston - ECON - 7342
Econ 7342 Midterm Exam #3 Solutions3 3 (1) We have Ui = 6ea eb ei , for i = a, b. 1 1 3 3 (a) The sum of Anns and Bills utilities is Ua + Ub = 12ea eb ea eb . This is maximized by setting partial derivatives (with respect to ea and eb ) to zero:
U. Houston - ECON - 7342
Syllabus: Microeconomic Theory II (Econ 7342-04420)Times of Class: Instructor: Office: Office Hours: MW 9-10:30 am Location of Class: McElhinney 104 Nick Feltovich McElhinney 202-C Phone: 743-3815 Email: nfelt@mail.uh.edu Fax: 743-3798 WWW: www.uh.e
NMSU - MATH - 683
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Allan Hancock College - COMP - 5348
CopyrightwarningCOMMONWEALTH OF AUSTRALIA Copyright Regulations 1969 WARNING This material has been reproduced and communicated to you by or on behalf of the University of Sydney pursuant to Part VB of the Copyright Act 1968 (the Act). The material
NMSU - MATH - 683
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NMSU - MATH - 683
Exercises From Section 5.1In this note we ll in some of the details from Chapter 5.1 of Weibel. Let E be a double complex of modules. The rst result we do is part 1 of Exercise 5.1.2, which gives a 2 description of Epq .2 Problem 1 (5.1.2). The mo
Allan Hancock College - COMP - 5348
CopyrightwarningCOMMONWEALTH OF AUSTRALIA Copyright Regulations 1969 WARNING This material has been reproduced and communicated to you by or on behalf of the University of Sydney pursuant to Part VB of the Copyright Act 1968 (the Act). The material
NMSU - MATH - 683
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NMSU - MATH - 683
Mathematics 683 Assignment 2Fall 2006Work three of the following problems. These are due on 8 December. 1. Let n be a positive integer. If n : A ! A is the multiplication by n map on a G-module A, show, by means of using the bar resolution, that th
NMSU - MATH - 683
Handouts for Mathematics 683 Topics in Group TheoryPatrick J. Morandi Fall 20022Contents1 Group Actions 2 Simplicity of An 3 Automorphism Groups of Sn and of An 4 Free Groups 4.1 Construction of Free Groups . . . . . . . . . . . . . . . . . . .
NMSU - MATH - 683
Free GroupsIn this note we give an alternative construction of free groups by working with semigroups. We also give some basic properties of free groups. A semigroup is a nonempty set with an associative binary operation. If S is a semigroup, we de
U. Houston - ECON - 4349
Econ 4349 Homework #11. Consider a sequential-move game with this game tree. (Notice that if Player 1 chooses D, the game ends without Player 2 making a move.)a. List all strategies available to Player 1.b. List all strategies available to Playe
U. Houston - ECON - 4349
Econ 4349 Homework #21. Three people simultaneously decide whether to contribute to a public project. Contributing costs $20. If at least one person contributes, the project is successful and all three people get a benefit: Player 1 gets $50, Player
NMSU - MATH - 683
Some Groups of Order 27Let G = x, y | x9 = y 9 = 1, xy 4 = y 7 x, yx4 = x7 y . In this note we determine the structure of G. For our rst observation, we note that, by the symmetry of the relations, there is an automorphism of G with (x) = y and (y
U. Houston - ECON - 4349
Econ 4349 Homework #2 solutions1. We abbreviate the strategies as C=contribute and N=not contribute. a. One possible payoff table is shown here; others are possible. Player 2 C N 30,10,-10 30,30,-10 50,10,-10 50,30,-10 Player 3: C Player 2 C N 30,10
U. Houston - ECON - 4349
Econ 4349 Homework #3 solutions1. Players are abbreviated: P1=Player 1, P2=Player 2, P3=Player 3. Strategies are abbreviated: 0=dont contribute, 1=contribute one unit, and 2=contribute two units. a. One possible payoff table is shown here; others ar
NMSU - MATH - 683
Changing GeneratorsIf a group G = X | R is given by generators and relations, and if Y is another generating set, can one use the given presentation to present G with the new generating set? There is a natural guess of how to do this, which we desc
U. Houston - ECON - 4349
Econ 4349 Homework #5For each game below, find all Nash equilibria (pure- and mixed-strategy). 1. Player 2 Player 1 2. Player 2 Player 1 3. Player 2 Player 1 4. Player 2 Player 1 C D C 0,0 2,6 D 9,3 0,0 S R S 70,70 60,10 R 10,60 60,60 H T H 4,0 0,2
NMSU - MATH - 683
Extensions of Groups1IntroductionTo better understand groups it is often useful to see how a group can be built from smaller groups. For example, given two groups G and H, we can form the direct product G H. This new group can be studied in te