Games of Strategy 4th Edition

PART ONEIntroduction and General Principles CHAPTER 1: Basic Ideas and Examples and CHAPTER 2: How to Think about Strategic Games Teaching Suggestions These chapters try to arouse the students interest and prepare the groundwork for the analysis to come. Chapter 1 uses several stories or examples to illustrate different kinds of strategic games, and Chapter 2

GAME 4The Tire Story (The Pure Coordination Game) Another game that we have successfully played in the first lecture is based on the We cant take the exam; we had a flat tire story from Section 2 of Chapter 1. Even if the students have read ahead, the discussion in the text

CHAPTER 10 The Prisoners Dilemma and Repeated Games Teaching Suggestions The idea that tacit cooperation can be sustained in an ongoing relationship is very simple and students easily accept it. The formal analysis in a repeated game is much harder if your students do not have an economics or business background and are not familiar

Game Playing in Class GAME 1Paired Prisoners Dilemma Students can be paired off and instructed to play several versions of a particular game with a prisoners dilemma structure. Provide each pair with a sheet describing the payoff table for the game and with space available to indicate the choices made by each player

Solutions to Chapter 10 Exercises SOLVED EXERCISES S1. False. The players are not assured that they will reach the cooperative outcome. Rollback reasoning shows that the subgame-perfect equilibrium of a finitely played repeated prisoners dilemma will entail constant cheating. reasoning shows that the subgame-perfect equilibrium of a finitely played repeated prisoners dilemma will

Solutions to Chapter 10 Exercises UNSOLVED EXERCISES U1. See the following payoff table: Baker 10 100 Cutler50:50 5, 5 50, 5090:10 9, 1 90, 10 Cutler50:50 5, 5 50, 5090:10 9, 1 90, 10 Cutler 50:50 5, 5 50, 50 90:10 9, 1 90, 10 Both players have dominant strategies, 90:10 for Cutler and 100 for Baker. Therefore, the equilibrium

CHAPTER 11 Collective-Action Games Teaching Suggestions A good way to introduce the topic of coordination games is to have the students play one. There are two suggestions below. One can be used to lead into a general discussion of the issues surrounding games of this type; the other can be used as a numerical example

Game Playing in Class GAME 1Check Marks Prepare a handout or cards and ask students to place either a blank line or a check mark on the paper. Tell them that if fewer than half of the students in the class answer with a check mark, 5 points (if you count experiment points

Solutions to Chapter 11 Exercises SOLVED EXERCISES S1. (a) The number choosing X should decrease to move the population division between X and Y away from the unstable center equilibrium. S1. (a) The number choosing X should decrease to move the population division between X and Y away from the unstable center

CHAPTER 12 Evolutionary Games Teaching Suggestions How much time you want to spend on this material will depend on the focus of your course. For many social science courses, a general exposure to the ideas, based on a quick run through the special examples of the Prisoners Dilemma and Chicken games will suffice. If your class

Solutions to Chapter 12 Exercises SOLVED EXERCISES S1. (a) The payoff table for the two types of travelers follows: High Low High 100, 100 30, 70Low 70, 30 50, 50 High 100, 100 30, 70Low 70, 30 50, 50 High 100, 100 30, 70 Low 70, 30 50, 50 (b) The graph is shown below: (c) There are three

Solutions to Chapter 12 Exercises UNSOLVED EXERCISES U1. (a) Payoff table is shown below. When two fighters meet, each has a 50% probability of getting 200 calories and expends 50 calories in fighting, so each fighters expected net calorie intake is0.5 200 50 = 50. A fighter gets all the food when he

U7. (a) When t = 0.5, the fitness of tortoises is FT = 0.5c + 0.5(2) = 0.5c 1, and the fitness of hares is FH = 0.5(1) + 0.5(0) = 0.5. Tortoises are more fit than hares when 0.5c 1 > 0.5, that is, when c > 3. The

CHAPTER 13 Mechanism Design Teaching Suggestions A good way to get students to understand the key issues and concepts of this chapter may be to remind or tell them about Karl Marxs claims about the communist society he envisioned (in his 1875 Critique of the Gotha Program [Rockville, Md.: Wildside Press, 2008]): From each according

Solutions to Chapter 13 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 future insurance premiums depend on current outcomes. The premium would decrease after,

S7. (a) As in Exercise S3, part (a), we can conclude that there are only three sensible prices to consider for popcorn: $1.50, $3.50, or $4.00. These three prices yield the following quantities sold, given individuals values for popcorn: P = $1.50: Q = 3,000, so profit = ($1.50)(3,000) =

Solutions to Chapter 13 Exercises S12. (a) If Oceania only offers a contract designed for the low-cost type of firm, then we have no incentive-compatibility constraint to worry about. We only need to worry about the participation constraint, which is to make sure that the firm earns at least zero profit.

U4. (a) If the team owners can identify the type of each fan, they will sell blue-collar fans an ordinary seat for $14 and white-collar fans a luxury seat for $22. Under this scheme they earn a profit of * = 600($12 $4) + 400($22 $8) = $10,400. ordinary seat

U10. (a) L = M 0.1Q H = M 0.16Q (b) IC1: M1 0.1Q1 M2 0.1Q2 IC2: M2 0.16Q2 M1 0.16Q1 (c) PC1: M1 0.1Q1 0 PC2: M2 0.16Q2 0 (b) IC1: M1 0.1Q1 M2 0.1Q2 IC2: M2 0.16Q2 M1 0.16Q1 (c) PC1: M1 0.1Q1 0 PC2: M2 0.16Q2 0 (b)

PART FOURApplication to Specific Strategic Situations CHAPTER 14 Brinkmanship: The Cuban Missile Crisis Teaching Suggestions If you are going to use the Cuban missile crisis case presented in the text as your teaching vehicle for brinkmanship, we urge you to prepare students by screening the movie Thirteen Days in the previous class, or at least by

Solutions to Chapter 14 Exercises SOLVED EXERCISES S1. (a) In the pure-threat 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 bigfrom the unions perspective.

Solutions to Chapter 14 Exercises UNSOLVED EXERCISES U1. (a) The diagram is shown below: Games of Strategy, Fourth Edition Copyright 2015 W. W. Norton & Company (b) The effectiveness condition specifies the minimum value of q for the United States that will deter the soft-type Soviets. Here, the soft-type Soviets will withdraw if 4

U5. (a) ANTI-BALLISTIC MISSLE SITE IN POLAND In August 2008, after 18 months of negotiations, the United States signed an agreement with Poland to base anti-ballistic-missile missilesor interceptorson Polish soil.1 A related radar site is planned for the Czech Republic. The United States maintains that the interceptors, currently deployed in

CHAPTER 15 Strategy and Voting Teaching Suggestions Most students will be familiar with at least a few of the vari ous aggregation methods used to determine winners in elections. You may want to poll the class and come up with a list of different methods that they know about or have used. Even a simple

Solutions to Chapter 15 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 andSociology in the first round. In order to prevent a Geology outcome, B

CHAPTER 16 Bidding Strategy and Auction Design Teaching Suggestions Most students nowadays will have used some Internet auction sites, certainly as buyers, and several as sellers. You can start a discussion related to their own experiences and bring in the appropriate terminology as appropriate. In this way, you should be able to address the differences between

Solutions to Chapter 16 Exercises SOLVED EXERCISES S1. The painter can compare her estimated cost with 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 else would charge. The fact

CHAPTER 17 Bargaining Teaching Suggestions Newspapers often print articles of advice on bargaining for buyers of houses, autos, and so on. We found a particularly good one that we mention in the text: Andre Brooks, Honing Haggling Skills (New York Times, December 5, 1993). It mentions (not in technical language) several points that relate to

Solutions to Chapter 17 Exercises SOLVED EXERCISES S1. The businessmans BATNA is probably quite low; holding onto the domain name may be worth very little to him. Owning the domain name, which makes it easier for people to find the Alta Vista site, is important to Compaq, so its BATNA is also, apparently,

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 shoppers could, for example, make sure to arrive at

PART TWOConcepts and Techniques CHAPTER 3 Games with Sequential Moves Teaching Suggestions Most students find the idea of rollback very simple and natural, even without drawing or understanding trees. Of course, they start by being able to do only one or two steps. A very simple way to get them to think about carrying the process

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 six terminal nodes (T): including the initial node, which represent the

Solutions to Chapter 3 Exercises S10. (a) The game tree is shown below: Games of Strategy, Fourth Edition Copyright 2015 W. W. Norton & Company Games of Strategy, Fourth Edition Copyright 2015 W. W. Norton & Company (b) The Proposer has one node with 11 actions; thus the Proposer has 11 complete

CHAPTER 4 Simultaneous-Move Games: Discrete Strategies Teaching Suggestions This chapter develops a succession of examples to illustrate the concept of Nash equilibrium when each player chooses from a finite number of discrete pure strategies. It also addresses the various issues that arise when looking for equilibria in such games, including dominance solvability, multiple equilibria, and nonexistence

Solutions to Chapter 4 Exercises SOLVED EXERCISES S1. (a) For Rowena, Up strictly dominates Down, so Down may be eliminated. For Colin, Right strictly dominates Left, so Left may be eliminated. These actions leave the pure-strategy Nash equilibrium(Up, Right).(b) Down is dominant for Rowena and Left is dominant for Colin. Equilibrium: (Down,

Solutions to Chapter 4 Exercises UNSOLVED EXERCISES U1. (a) For Colin, Right dominates Left, so Left is eliminated. Then for Rowena Up dominates Down, so Down is eliminated, giving the pure-strategy Nash equilibrium (Up, Right). Down, so Down is eliminated, giving the pure-strategy Nash equilibrium (Up, Right). Down, so Down is eliminated, giving the

CHAPTER 5 Simultaneous-Move Games: Continuous Strategies, Discussion, and Evidence Teaching Suggestions The basic concepts of simultaneous moves, best responses, and Nash equilibrium were motivated in Chapter 4 in the context of discrete strategies. The new issues arising when strategies are continuous variables are of a slightly more technical kind and include drawing best-response curves, finding best-response

Solutions to Chapter 5 Exercises SOLVED EXERCISES S1. (a) Rs best-response 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. Rs best response is y =

Solutions to Chapter 5 Exercisess UNSOLVED EXERCISES U1. (a) DTCs profit is YDTC = PQDTC 12QDTC = (120 QDTC)QDTC 12QDTC = QDTC2 + 108QDTC. The profit-maximizing quantity for DTC is QDTC = 54. At this profit-maximizing quantity, the wholesale price is given by P = 120 QDTC = 120 54 = 66,

CHAPTER 6 Combining Sequential and Simultaneous Moves Teaching Suggestions This chapter introduces three new concepts and associated techniques: (1) multistage games where a simultaneous-move game occurs at one or more of the stages; (2) the effects of changing the rules concerning the order of moves in a gamethe source and nature of first- and second-mover advantages;

Solutions to Chapter 6 Exercises SOLVED EXERCISES S1. Second-mover advantage. In a sequential game of tennis, the second mover can best respond to the first movers chosen action. Put another way, the second mover can exploit the information she learns from the first movers action. However, since there is no Nash equilibrium

Solutions to Chapter 6 Exercises S10. (a) The game tree is shown below: Friedas has two actions at one node, so it has two strategies. Big Giant has two actions at each of three nodes, so it has 2 2 = 4 strategies.Titan has two actions at each of four nodes, so it

U4. (a) The strategic form of the game follows: Severus = x Severus = y Pure-strategy Nash equilibria are indicated by double borders. The unique subgame-perfect Nash equilibrium is (SS, aa, y), with payoffs of (2, 1, 1). (b) The equilibria (SN, aa, x), (SN, ab, x), and (SN, aa, y) cannot be

U10. (a) The game table for the first-stage game follows: Nancy Yes No Monica Yes 2.667, 2.667 5.5, 7.25No 6.653, 6.143 2.667, 2.667 Yes 2.667, 2.667 5.5, 7.25No 6.653, 6.143 2.667, 2.667 Yes 2.667, 2.667 5.5, 7.25 No 6.653, 6.143 2.667, 2.667 (b) The two pure-strategy Nash equilibria are indicated by double borders in the preceding table: (Y,

CHAPTER 7 Simultaneous-Move Games: Mixed Strategies Teaching Suggestions This chapter introduces mixed strategies and the methods used to solve for mixed-strategy equilibria in zero-sum and non-zero-sum games. For zero-sum games, students are likely to accept the idea of randomization more readily if they think of it themselves. One way to lead them to the idea

Classical Game Theory You can give a more rigorous treatment of bimatrix games, building on some of the material in the online appendix to this chapter. The best reference for this is still Luce and Raiffas Games and Decisions (New York: Wiley, 1957). Rationalizability You can take the concept of domination by a mixed strategy,

U11. (a) Yes. The pure-strategy Nash equilibrium is (Land, Sea). (b) Let p1 be the probability that Patton plays Air and p2 be the probability that Patton plays Sea, so that 1 p1 p2 is the probability that he plays Land. Similarly, let q1, q2 , and 1 q1 q2

Solutions to Chapter 7 Exercises SOLVED EXERCISES S1. (a) The game most resembles an assurance game because the two Nash equiibria occur when the players use symmetric moves. (Here they both use the same moves to arrive at the Nash equilibria; in other games, they might use exactly opposite moves to arrive at

Solutions to Chapter 7 Exercises S12. (a) The kickers expected payoffs playing against the goalies mixed strategy of L 42.2%, R 42.2%, and C 15.6% are as follows: HL 42.2(0.50) + 15.6(0.85) + 42.2(0.85) = 70.23 LL 42.2(0.40) + 15.6(0.95) + 42.2(0.95) = 71.79HC 42.2(0.85) + 15.6(0) + 42.2(0.85) = 71.74LC 42.2(0.70) +

PART THREESome Broad Classes of Games and Strategies CHAPTER 8 Uncertainty and Information Teaching Suggestions Section 1 The crucial idea to convey is that reducing risk by sharing or pooling depends on the risks not being too positively correlated. A good example is the 2008 financial and economic crisis. Too many of the risks associated with

Solutions to Chapter 8 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 x such that your neighbor

Oscars play after Felixs payoff when card draws are Felixs expected payoff Hi Lo Hi Lo HiHi HiLo LoHi LoLo P P F F 0 8 8 0 0 P P S S 0 8 8 0 0 P P S F 0 8 8 0 0 P P F S 0 8 8 0 0R R F

U8. (a) The extensive form of this game is shown below: (b) eBay has an incentive to bluff, which in this case would consist of proposing a stingy settlement (S) when it is guilty. If eBay proposes a stingy settlement, AT&T doesnt know if it is because eBay is innocent or

Solutions to Chapter 8 Exercises UNSOLVED EXERCISES U1. (a) Jacks expected utility is 0.5 250,000 + 0.5 90,000 = 400. (b) Since Jacks utility is the square root of his income, to achieve a utility of 400 Jack wouldneed a certain income of 4002 = $160,000.(c) The four possible luck outcome pairs for

CHAPTER 9 Strategic Moves Teaching Suggestions The ideas in this chapter can be brought to life and the students can better appreciate the subtleties of various strategic moves and their credibility if you hold classroom discussions based on situations where such strategies are of the essence. Depending on your preference, you can either have the discussion

DEADLINES If the location is one where the authorities control the food and water supply, and the terrorists have limited numbers, time is on the governments side. Then the authorities may simply seal the place, prevent media coverage, and wait it out. They will certainly try to draw out negotiations, for example, invoke

Solutions to Chapter 9 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 threaten an arbitrarily large punishment, however, if you can be certain your threat