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1 1 Lesson overview BA 592 Lesson I.4 Sequential Move Applications Chapter 3 Games with Sequential Moves Lesson I.3 Sequential Move Theory Lesson I.4 Sequential Move Applications Each Example Game introduces applications or techniques Example 1: AdvertisingExample 1: Advertising Example 2: Entry DeterrenceExample 2: Entry Deterrence Example 3: Car LoanExample 3: Car Loan Example 4: RenegotiationExample 4: Renegotiation Example 5: Compatible Web BrowsersExample 5: Compatible Web Browsers Example 6: Evicting TenantsExample 6: Evicting Tenants Example 7: Strategic VotingExample 7: Strategic Voting Example 8: Nuisance SuitsExample 8: Nuisance Suits Review ProblemsReview Problems

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2 2 BA 592 Lesson I.4 Sequential Move Applications Each example game in this Sequential Move Applications lesson, or in any of the other Applications lessons in the course, is presented in the same way as questions on an exam: I describe a game verbally and ask questions about its solution. You must formulate the game (identifying players, strategies, payoffs, …) then answer those questions by solving the game. Example 1: Advertising

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3 3 BA 592 Lesson I.4 Sequential Move Applications Question: Incumbant Senator Gray will run for reelection. The challenger is Congresswoman Green. Senator Gray first decides whether or not to run advertisements early on. The challenger Green must then decide whether or not to enter the race. Issues to think about in modeling the game: n Players are Gray and Green. Gray moves first. n Strategies for Gray are Ads, No Ads; for Green: In or Out. n Ads are costly, so Gray would prefer not to run ads. n Green will find it possible to win if Gray does not run ads, but impossible if Gray does run ads. Define a game tree for this Advertising Game, choosing payoff numbers consistent with the issues above. Then, find the rollback solution. Example 1: Advertising

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4 4 BA 592 Lesson I.4 Sequential Move Applications Answer: Game tree Example 1: Advertising

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5 5 BA 592 Lesson I.4 Sequential Move Applications Answer: Rollback solution. Grey plays Ads and gets payoff 3. Green plays {In if No Ads, Out if Ads} and gets payoff 3. Example 1: Advertising

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6 6 Supplementary Question: Is there a first mover advantage in the Advertising Game? BA 592 Lesson I.4 Sequential Move Applications Example 1: Advertising

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7 7 Instructors Note: To see if the order matters in any game, rearrange the sequence of moves.To see if the order matters in any game, rearrange the sequence of moves. Examples in which order may matter:Examples in which order may matter: n Adoption of new technology. Better to be first or last? n Class presentation of a project. Better to be first or last? Sometimes order does not matter, such as the Prisoners dilemma with Confess the dominate strategy for both players.Sometimes order does not matter, such as the Prisoners dilemma with Confess the dominate strategy for both players. Is there such a thing as a second-mover advantage? Sometimes, for example:Is there such a thing as a second-mover advantage? Sometimes, for example: n Sequential biding by two contractors. n Cake-cutting: One person cuts, the other gets to decide how the two pieces are allocated. n Poker. BA 592 Lesson I.4 Sequential Move Applications Example 1: Advertising

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8 8 BA 592 Lesson I.4 Sequential Move Applications Answer to Supplementary Question: Suppose the sequence of play in the Advertising Game is changed so that Green gets to first commit to enter the race before Grey commits to Ads. The payoffs for the possible outcomes are exactly the same as before, except now, Greens payoff is listed first. Example 1: Advertising

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9 9 BA 592 Lesson I.4 Sequential Move Applications Rollback Solution: Green plays In and gets payoff 4. Grey plays {No Ads if Out, No Ads if In} and gets payoff 2. There is a first-mover advantage. Example 1: Advertising

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10 BA 592 Lesson I.4 Sequential Move Applications Example 2: Entry Deterrence Question: A monopolist faces the prospect of loosing part of its $10M profit by a potential competitor entering the industry. If the competitor elects not to enter, it earns profits of $0 and the monopolist maintains its profit of $10M. If the competitor enters, the monopolist must either accommodate the entry or fight. If the monopolist accommodates, both firms earn $4M. If the monopolist fights, both firms lose $4M. Should the competitor enter?

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11 BA 592 Lesson I.4 Sequential Move Applications Answer: Game tree and its rollback solution. Entrant plays In and gets payoff 4. Monopolist plays Accommodate if In and gets payoff 4. Example 2: Entry Deterrence

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12 Supplementary Question: Is there a first mover advantage in the Advertising Game? BA 592 Lesson I.4 Sequential Move Applications Example 2: Entry Deterrence

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13 BA 592 Lesson I.4 Sequential Move Applications Answer to Supplementary Question: Suppose the sequence of play is changed so that Monopolist gets to first commit to Accommodate or Fight before Entrant commits to Entry. The payoffs for the four possible outcomes are exactly the same as before, except now, Monopolists payoff is listed first. Example 2: Entry Deterrence

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14 BA 592 Lesson I.4 Sequential Move Applications Rollback Solution: Monopolist plays Fight and gets payoff 10. Entrant plays {In if Accom., Out if Fight} and gets payoff 0. There is a first-mover advantage. Example 2: Entry Deterrence

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15 BA 592 Lesson I.4 Sequential Move Applications Example 3: Car Loan Question: A bank must decide whether to offer Joe an auto loan or not. The loan would be for $11,000, and the bank must decide on a total amount L of principal and interest that he must repay at the end of the year. If Joe accepts the loan, he can buy a car worth $12,000 to him. He then decides whether to work hard, earning $15,000, or loaf, earning $8,000. Joe would pay up to $5,000 to be able to loaf. Joe has no other assets. If he decides not to repay the loan, he loses the car and gets value $500 for using the car for a year, and the bank collects $7,000 by reselling the car. If Joe keeps the car, it retains its value of $12,000 to him even if it is a year old. Consider an interest rate of 0%. Should the bank offer a loan? If so, what should be the principal and interest?

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16 BA 592 Lesson I.4 Sequential Move Applications Example 3: Car Loan Answer: The Bank first decides whether to offer a loan, and at what principal and interest L. Since L can be any real number, we cannot draw a full game graph because it would have a continuum of branches coming off it. So first fix L, then graph the subgame. The Bank looses money if L 11. The decision nodes in the subgame are in this order. Bank: Offer loan or or don't offer one. Joe: Accept or reject the offer. Joe: Work or loaf. (If he loafs, he does not have the money to pay back the loan.) Joe: Repay or lose the car to the bank.

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17 BA 592 Lesson I.4 Sequential Move Applications Example 3: Car Loan Subgame graph given L: If the Bank does not offer a loan, or if Joe turns down the loan, its payoff is 0 and Joes is 15 if he works or 13 (8+5) if he loafs. If Joe works and repays, the Bank gets L-11 and Joe gets 15+12 -L; if he does not repay, the Bank gets 7-11 and Joe gets 15. If Joe loafs and so does not repay, the Bank gets 7-11 and Joe gets 8+5.

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18 BA 592 Lesson I.4 Sequential Move Applications Example 3: Car Loan Some of Joes Choices are independent of L.

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19 BA 592 Lesson I.4 Sequential Move Applications Example 3: Car Loan When L > 11.5: The equilibrium path is the Bank does not offer the loan, and Joe works. That path ends in payoff 0 for the bank.

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20 BA 592 Lesson I.4 Sequential Move Applications Example 3: Car Loan When L = 11.5: There are multiple rollback solutions because if the Bank Offers Loan, and Joe Accepts Loan, and Joe Works, then Joe is indifferent between Not Paying Back the Loan, and Paying Back the Loan. Let us avoid this case.

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21 BA 592 Lesson I.4 Sequential Move Applications Example 3: Car Loan When 11 < L < 11.5: The Banks strategy is offer the loan, and it gets payoff L-11.

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22 BA 592 Lesson I.4 Sequential Move Applications Example 3: Car Loan The Banks rollback equilibrium payoffs thus depend on L: If L > 11.5, payoff = 0.If L > 11.5, payoff = 0. If L = 11.5, there are multiple rollback equilibria.If L = 11.5, there are multiple rollback equilibria. If 11 < L < 11.5, payoff = L 11.If 11 < L < 11.5, payoff = L 11. Should the bank offer a loan? If so, what should be the principal and interest? Yes, offer the loan at principal and interest L = 11.5-, and so earn payoff.5. Joe earns payoff 15.5+, which is.5+ more than if he did not get the loan.

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23 BA 592 Lesson I.4 Sequential Move Applications Example 4: Renegotiation Supplementary Question: Now suppose Joe has another option: if Joe loafs and so cannot repay the full amount of the loan, he can offer the bank some smaller amount S not to foreclose on the loan and repossess the car. What would that amount S be? How does the outcome change if both Joe and the bank know that this kind of renegotiation is possible?

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24 BA 592 Lesson I.4 Sequential Move Applications Example 4: Renegotiation The bank collects $7,000 by reselling the car, so if Joe loafs and offers any S > $7,000, then the Bank would accept. So offer S = $7,000+e. Hence, the game tree changes:

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25 BA 592 Lesson I.4 Sequential Move Applications When L > 11.5: The equilibrium path is the Bank does not offer the loan, and Joe works. That path ends in payoff 0 for the bank. Example 4: Renegotiation

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26 BA 592 Lesson I.4 Sequential Move Applications When 11 < L < 11.5: The Banks strategy is offer the loan, and it gets payoff L-11. Example 4: Renegotiation

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27 BA 592 Lesson I.4 Sequential Move Applications Example 4: Renegotiation Summary: When Joe has the option to loaf and offer the bank some smaller amount S not to foreclose on the loan and repossess the car, he would offer S = $7,000+e. But when both Joe and the Bank know that this kind of renegotiation is possible, the Bank no longer offers the loan, which eliminates the previous gains of payoff.5-e to the Bank and.5+e to Joe.

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28 BA 592 Lesson I.4 Sequential Move Applications Example 5: Compatible Web Browsers Question: Microsoft and Google are planning to introduce a new type of Web browser. They must choose between two platforms, ActiveX and Java. If they introduce different platforms, their profits are zero. If they introduce the same platform, their profits are 1, plus Microsoft gets 1 more if the platform is ActiveX and Google gets 1 more if the platform is Java. Which platform should Microsoft choose if it can choose first? Which platform should Google choose if it can choose first? Is there a first mover advantage? Now suppose Microsoft can choose first unless Google rushes development of their browser. Rushing development cost Google 0.5, and it allows Google to choose their platform first. Should Google rush their development?

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29 BA 592 Lesson I.4 Sequential Move Applications Answer: Which platform should Microsoft choose if it can choose first? ActiveX, giving Microsoft 2 and Google 1. Which platform should Google choose if it can choose first? Java, giving Microsoft 1 and Google 2. Is there a first mover advantage? Yes, either firm earns 1 more moving first rather than second. Should Google rush? Yes, they earn 1 more at a cost of 0.5 Example 5: Compatible Web Browsers

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30 BA 592 Lesson I.4 Sequential Move Applications Example 6: Evicting Tenants Question: A landlord has three tenants, Alfred, Betty, and Charlie, in a rent-controlled apartment building in New York City. A new law says that the landlord has the right to evict one tenant per building. The landlord calculates that the value of a vacant apartment is $15,000, both to the tenant and to her. She sends the following letter to each of her tenants: Tomorrow I will be visiting your building. I will offer A $1,000 if he agrees to vacate his apartment voluntarily; otherwise, I will evict him. If A agrees to vacate voluntarily, I will then offer B $1,000 if she agrees to vacate his apartment voluntarily; otherwise, I will evict her. If B agrees to vacate voluntarily, I will evict C. How many vacant apartments will the landlord have? What profit will the landlord have?

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31 BA 592 Lesson I.4 Sequential Move Applications Answer: This is a game between tenants A and B. (The Landlord has committed to the letter, and C has no choices.) A and B both vacate, and C gets evicted. The landlord thus gains 3 vacant apartments and pays $2,000. So the landlord gains $45,000 = $43,000 $2,000. Example 6: Evicting Tenants

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32 BA 592 Lesson I.4 Sequential Move Applications Example 7: Strategic Voting Question: Three legislators, Alfred, Betty, and Charlie, are voting on whether to give themselves a pay raise. The raise is worth b, but each legislator who votes for the raise incurs a cost of voter resentment equal to a < b. The outcome is decided by majority rule. A votes first, then B sees As choice and votes, then C sees As and Bs choice and votes. How should A vote?

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33 BA 592 Lesson I.4 Sequential Move Applications Answer: A should vote Against, believing that B and C will then vote For the raise. Example 7: Strategic Voting

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34 BA 592 Lesson I.4 Sequential Move Applications Example 8: Nuisance Suits Question: Alfred contemplates suing Betty over the purported damage done to Alfreds son sustained while using the bike jump in Bettys yard. Suppose As court cost for initiating a suit is a, his legal costs of going to trial are b, and Bettys cost of defending herself is c. Suppose both sides know these costs and also share the knowledge that the probability that A will win the suit is p and the expected amount of the settlement is x. Assume px < b. Finally, suppose that before the case goes to trial (but after the suit is initiated), the parties can settle out of court for the amount s. Should A file suit?

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35 BA 592 Lesson I.4 Sequential Move Applications Answer: There are two rollback solutions, depending on whether A choose Offer to Settle or No Offer to Settle. But in either rollback solution, A does not file suit. Example 8: Nuisance Suits

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36 BA 592 Lesson I.4 Sequential Move Applications Review Problems Mall Location Game Page 83, Question S8. Answer

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37 BA 592 Lesson I.4 Sequential Move Applications Review Problems Political Game Page 85, Question U4. Answer

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38 End of Lesson I.4 BA 592 Game Theory BA 592 Lesson I.4 Sequential Move Applications

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