Exam (elaborations) TEST BANK FOR Strategy An Introduction to Game Theory 3rd Edition By Joel Watson (solution manual)

Exam (elaborations) TEST BANK FOR Strategy An Introduction to Game Theory 3rd Edition By Joel Watson (solution manual) Contents I General Materials 7 II Chapter-Specic Materials 12 1 Introduction 13 2 The Extensive Form 15 3 Strategies and the Normal Form 18 4 Beliefs, Mixed Strategies, and Expected Payos 21 5 General Assumptions and Methodology 23 6 Dominance and Best Response 24 7 Rationalizability and Iterated Dominance 27 8 Location, Partnership, and Social Unrest 29 9 Nash Equilibrium 32 10 Oligopoly, Taris, Crime, and Voting 34 11 Mixed-Strategy Nash Equilibrium 35 12 Strictly Competitive Games and Security Strategies 37 13 Contract, Law, and Enforcement in Static Settings 38 14 Details of the Extensive Form 41 15 Sequential Rationality and Subgame Perfection 43 16 Topics in Industrial Organization 45 17 Parlor Games 46 3 Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. CONTENTS 4 18 Bargaining Problems 48 19 Analysis of Simple Bargaining Games 50 20 Games with Joint Decisions; Negotiation Equilibrium 52 21 Unveriable Investment, hold up, Options, and Ownership 54 22 Repeated Games and Reputation 56 23 Collusion, Trade Agreements, and Goodwill 58 24 Random Events and Incomplete Information 60 25 Risk and Incentives in Contracting 63 26 Bayesian Nash Equilibrium and Rationalizability 65 27 Lemons, Auctions, and Information Aggregation 66 28 Perfect Bayesian Equilibrium 68 29 Job-Market Signaling and Reputation 70 30 Appendices 71 III Solutions to the Exercises 72 2 The Extensive Form 73 3 Strategies and the Normal Form 76 4 Beliefs, Mixed Strategies, and Expected Payos 79 6 Dominance and best response 80 7 Rationalizability and Iterated Dominance 81 Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. CONTENTS 5 8 Location, Partnership, and Social Unrest 83 9 Nash Equilibrium 86 10 Oligopoly, Taris, Crime, and Voting 89 11 Mixed-Strategy Nash Equilibrium 95 12 Strictly Competitive Games and Security Strategies 102 13 Contract, Law, and Enforcement in Static Settings 103 14 Details of the Extensive Form 108 15 Sequential Rationality and Subgame Perfection 110 16 Topics in Industrial Organization 114 17 Parlor Games 117 18 Bargaining Problems 119 19 Analysis of Simple Bargaining Games 121 20 Games with Joint Decisions; Negotiation Equilibrium 123 21 Unveriable Investment, Hold Up, Options, and Ownership 127 22 Repeated Games and Reputation 131 23 Collusion, Trade Agreements, and Goodwill 135 24 Random Events and Incomplete Information 138 25 Risk and Incentives in Contracting 140 26 Bayesian Nash Equilibrium and Rationalizability 142 Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. CONTENTS 6 27 Lemons, Auctions, and Information Aggregation 145 28 Perfect Bayesian Equilibrium 148 29 Job-Market Signaling and Reputation 151 30 Appendix B 155 IV Sample Questions 156 Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. 7 Part I General Materials This part contains some notes on outlining and preparing a game theory course for those adopting Strategy: An Introduction to Game Theory. Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. 8 Sample Syllabi Most of the book can be covered in a semester-length (13-15 week) course. Here is a sample thirteen-week course outline: Weeks Topics Chapters A. Representing Games 1 Introduction, extensive form, strategies, 1{3 and normal form 1{2 Beliefs and mixed strategies 4{5 B. Analysis of Static Settings 2{3 Best response, rationalizability, applications 6{8 3{4 Equilibrium, applications 9{10 5 Other equilibrium topics 11{12 5 Contract, law, and enforcement 13 C. Analysis of Dynamic Settings 6 Extensive form, backward induction, 14{15 and subgame perfection 7 Examples and applications 16{17 8 Bargaining 18{19 9 Negotiation equilibrium and problems of 20{21 contracting and investment 10 Repeated games, applications 22{23 D. Information 11 Random events and incomplete information 24 11 Risk and contracting 25 12 Bayesian equilibrium, applications 26{27 13 Perfect Bayesian equilibrium and applications 28{29 In a ten-week (quarter system) course, most, but not all, of the book can be covered. For this length of course, you can easily leave out (or simply not cover in class) some of the chapters. For example, any of the chapters devoted to applications (Chapters 8, 10, 16, 21, 23, 25, 27, and 29) can be covered selectively or skipped Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. 9 without disrupting the ow of ideas and concepts. Chapters 12 and 17 contain ma- terial that may be regarded as more esoteric than essential; one can easily have the students learn the material in these chapters on their own. Instructors who prefer not to cover contract can skip Chapters 13, 20, 21, and 25. Below is a sample ten-week course outline that is formed by trimming some of the applications from the thirteen-week outline. This is the outline that I use for my quarter-length game theory course. I usually cover only one application from each of Chapters 8, 10, 16, 23, 27, and 29. I avoid some end-of-chapter advanced topics, such as the innite-horizon alternating-oer bargaining game, I skip Chapter 25, and, depending on the pace of the course, I selectively cover Chapters 18, 20, 27, 28, and 29. Weeks Topics Chapters A. Representing Games 1 Introduction, extensive form, strategies, 1-3 and normal form 1-2 Beliefs and mixed strategies 4-5 B. Analysis of Static Settings 2-3 Best response, rationalizability, applications 6-8 3-4 Equilibrium, applications 9-10 5 Other equilibrium topics 11-12 5 Contract, law, and enforcement 13 C. Analysis of Dynamic Settings 6 Backward induction, subgame perfection, 14-17 and an application 7 Bargaining 18-19 7-8 Negotiation equilibrium and problems of 20-21 contracting and investment 8-9 Repeated games, applications 22-23 D. Information 9 Random events and incomplete information 24 10 Bayesian equilibrium, application 26-27 10 Perfect Bayesian equilibrium and an application 28-29 Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. 10 Experiments and a Course Competition In addition to assigning regular problem sets, it can be fun and instructive to run a course-long competition between the students. The competition is mainly for sharpening the students' skills and intuition, and thus the students' performance in the course competition should not count toward the course grades. The competi- tion consists of a series of challenges, classroom experiments, and bonus questions. Students receive points for participating and performing near the top of the class. Bonus questions can be sent by e-mail; some experiments can be done by e-mail as well. Prizes can be awarded to the winning students at the end of the term. Some suggestions for classroom games and bonus questions appear in various places in this manual. Level of Mathematics and Use of Calculus Game theory is a technical subject, so the students should come into the course with the proper mathematics background. For example, students should be very comfortable with set notation, algebraic manipulation, and basic probability theory. Appendix A in the textbook provides a review of mathematics at the level used in the book. Some sections of the textbook benet from the use of calculus. In particular, a few examples and applications can be analyzed most easily by calculating derivatives. In each case, the expressions requiring dierentiation are simple polynomials (usually quadratics). Thus, only the most basic knowledge of dierentiation suces to follow the textbook derivations. You have two choices regarding the use of calculus. First, you can make sure all of the students can dierentiate simple polynomials; this can be accomplished by either (a) specifying calculus as a prerequisite or (b) asking the students to read Appendix A at the beginning of the course and then perhaps reinforcing this by holding an extra session in the early part of the term to review how to dierentiate a simple polynomial. Second, you can avoid calculus altogether by either providing the students with non-calculus methods to calculate maxima or by skipping the textbook examples that use calculus. Here is a list of the examples that are analyzed with calculus in the textbook:  the partnership example in Chapters 8 and 9,  the Cournot application in Chapter 10 (and the tari and crime applications in this chapter, but the analysis of these applications is not done in the text),  the Stackelberg example in Chapter 15,  the advertising and limit capacity applications in Chapter 16 (they are based on the Cournot model), Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. 11  the dynamic oligopoly model in Chapter 23 (Cournot-based),  the discussion of risk-aversion in Chapter 25 (in terms of the shape of a utility function),  the Cournot example in Chapter 26, and  the analysis of auctions in Chapter 27. Each of these examples can be easily avoided, if you so choose. There are also some related exercises that you might avoid if you prefer that your students not deal with examples having continuous strategy spaces. My feeling is that using a little bit of calculus is a good idea, even if calculus is not a prerequisite for the game theory course. It takes only an hour or so to explain slope and the derivative and to give students the simple rule of thumb for calculating partial derivatives of simple polynomials. Then one can easily cover some of the most interesting and historically important game theory applications, such as the Cournot model and auctions. Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. 12 Part II Chapter-Specic Materials This part contains instructional materials that are organized according to the chapters in the textbook. For each textbook chapter, the following is provided:  a brief overview of the material covered in the chapter;  lecture notes (including an outline); and  suggestions for classroom examples and/or experiments. The lecture notes are merely suggestions for how to organize lectures of the textbook material. The notes do not represent any claim about the right" way to lecture. Some instructors may nd the guidelines herein to be in tune with their own teach- ing methods; these instructors may decide to use the lecture outlines without much modication. Others may have a very dierent style or intent for their courses; these instructors will probably nd the lecture outlines of limited use, if at all. We hope this material will be of some use to you. Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. 1 Introduction This chapter introduces the concept of a game and encourages the reader to begin thinking about the formal analysis of strategic situations. The chapter contains a short history of game theory, followed by a description of noncooperative theory" (which the book emphasizes), a discussion of the notion of contract and the related use of cooperative theory," and comments on the science and art of applied theoretical work. The chapter explains that the word game" should be associated with any well-dened strategic situation, not just adversarial contests. Finally, the format and style of the book are described. Lecture Notes The non-administrative segment of a rst lecture in game theory may run as follows.  Denition of a strategic situation.  Examples (have students suggest some): chess, poker, and other parlor games; tennis, football, and other sports; rm competition, international trade, inter- national relations, rm{employee relations, and other standard economic exam- ples; biological competition; elections; and so on.  Competition and cooperation are both strategic topics. Game theory is a general methodology for studying strategic settings (which may have elements of both competition and cooperation).  The elements of a formal game representation.  A few simple examples of the extensive-form representation (point out the basic components). Examples and Experiments 1. Clap game. Ask the students to stand, and then, if they comply, ask them to clap. (This is a silly game.) Show them how to diagram the strategic situation as an extensive-form tree. The game starts with your decision about whether to ask them to stand. If you ask them to stand, then they (modeled as one player) have to choose between standing and staying in their seats. If they stand, then you decide between saying nothing and asking them to clap. If you ask them to clap, then they have to decide whether to clap. Write the outcomes at terminal nodes in descriptive terms such as professor happy, students confused." Then show how these outcomes can be converted into payo numbers. 13 Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. 1 INTRODUCTION 14 2. Auction the textbook. Many students will probably not have purchased the textbook by the rst class meeting. These students may be interested in pur- chasing the book from you, especially if they can get a good deal. However, quite a few students will not know the price of the book. Without announcing the bookstore's price, hold a sealed-bid, rst-price auction (using real money). This is a common-value auction with incomplete information. The winning bid may exceed the bookstore's price, giving you an opportunity to talk about the winner's curse" and to establish a fund to pay students in future classroom experiments. Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. 2 The Extensive Form This chapter introduces the basic components of the extensive form in a nontechnical way. Students who learn about the extensive form at the beginning of a course are much better able to grasp the concept of a strategy than are students who are taught the normal form rst. Since strategy is perhaps the most important concept in game theory, a good understanding of this concept makes a dramatic dierence in each student's ability to progress. The chapter avoids the technical details of the extensive-form representation in favor of emphasizing the basic components of games. The technical details are covered in Chapter 14. Lecture Notes The following may serve as an outline for a lecture.  Basic components of the extensive form: nodes, branches. Nodes are where things happen. Branches are individual actions taken by the players.  Example of a game tree.  Types of nodes: initial, terminal, decision.  Build trees by expanding, never converging back on themselves. At any place in a tree, you should always know exactly how you got there. Thus, the tree summarizes the strategic possibilities.  Player and action labels. Try not to use the same label for dierent places where decisions are made.  Information sets. Start by describing the tree as a diagram that an external observer creates to map out the possible sequences of decisions. Assume the external observer sees all of the players' actions. Then describe what it means for a player to not know what another player did. This is captured by dashed lines indicating that a player cannot distinguish between two or more nodes.  We assume that the players know the game tree, but that a given player may not know where he is in the game when he must make any particular decision.  An information set is a place where a decision is made.  How to describe simultaneous moves.  Outcomes and how payo numbers represent preferences. 15 Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. 2 THE EXTENSIVE FORM 16 Examples and Experiments Several examples should be used to explain the components of an extensive form. In addition to some standard economic examples (such as rm entry into an industry and entrant/incumbent competition), here are a few we routinely use: 1. Three-card poker. In this game, there is a dealer (player 1) and two potential betters (players 2 and 3). There are three cards in the deck: a high card, a middle card, and a low card. At the beginning of the game, the dealer looks at the cards and gives one to each of the other players. Note that the dealer can decide which of the cards goes to player 2 and which of the cards goes to player 3. (There is no move by Nature in this game. The book does not deal with moves of Nature until Part IV. You can discuss moves of Nature at this point, but it is not necessary.) Player 2 does not observe the card dealt to player 3, nor does player 3 observe the card dealt to player 2. After the dealer's move, player 2 observes his card and then decides whether to bet or to fold. After player 2's decision, player 3 observes his own card and also whether player 2 folded or bet. Then player 3 must decide whether to fold or bet. After player 3's move, the game ends. Payos indicate that each player prefers winning to folding and folding to losing. Assume the dealer is indierent between all of the outcomes (or specify some other preference ordering). 2. Let's Make a Deal game. This is the three-door guessing game that was made famous by Monty Hall and the television game show Let's Make a Deal. The game is played by Monty (player 1) and a contestant (player 2), and it runs as follows. First, Monty secretly places a prize (say, $1000) behind one of three doors. Call the doors a, b, and c. (You might write Monty's actions as a0, b0, and c0, to dierentiate them from those of the contestant.) Then, without observing Monty's choice, the contestant selects one of the doors (by saying a," b," or c"). After this, Monty must open one of the doors, but he is not allowed to open the door that is in front of the prize, nor is he allowed to open the door that the contestant selected. Note that Monty does not have a choice if the contestant chooses a dierent door than Monty chose for the prize. The contestant observes which door Monty opens. Note that she will see no prize behind this door. The contestant then has the option of switching to the other unopened door (S for switch") or staying with the door she originally selected (D for don't switch"). Finally, the remaining doors are opened, and the contestant wins the prize if it is behind the door she chose. The contestant obtains a Instructor's Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008, 2010, 2013 by Joel Watson. For instructors only; do not distribute. 2 THE EXTENSIVE FORM 17 payo 1 if she wins, zero otherwise. Monty is indierent between all of the outcomes. For a bonus question, you can challenge the students to draw the extensive- form representation of the Let's Make a Deal game or the three-card poker game. Students who submit a correct extensive form can be given points for the class competition. The Let's Make a Deal extensive form is pictured in the illustration that