# 1 1 Deep Thought BA 445 Lesson B.6 Prisoner Dilemmas If I ever went to war, instead of throwing a grenade, I’d throw one of those small pumpkins. Then.

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1 1 Deep Thought BA 445 Lesson B.6 Prisoner Dilemmas If I ever went to war, instead of throwing a grenade, I’d throw one of those small pumpkins. Then maybe my enemy would pick up the pumpkin and think about the futility of war. And that would give me the time I need to hit him with a real grenade. ~ Jack Handey. (Translation: Today’s lesson demonstrates why people might not cooperate or collude even if it is in their best interests to do so.)

2 2 BA 445 Lesson B.6 Prisoner Dilemmas ReadingsReadings Baye “Oligopoly” (see the index) Dixit Chapter 4

3 3 BA 445 Lesson B.6 Prisoner Dilemmas OverviewOverview

4 4Overview The Prisoners’ Dilemma shows why people might not cooperate even if it is profitable. Cournot duopoly is a prisoners’ dilemma. Lower output by all is profitable but lower output by you is unprofitable. Duopoly with Substitutes is a prisoners’ dilemma with firms simultaneously choosing prices and producing gross substitutes. Profitable cooperation raises prices. Duopoly with Complements is a prisoners’ dilemma with firms simultaneously choosing prices and producing gross substitutes. Profitable cooperation lowers prices. Advertising is a prisoners’ dilemma when advertising mostly transfers customers between firms rather than generating new customers. Profitable cooperation reduces advertising. Cleaning and Other Public Goods are prisoner dilemmas when public good purchases by all is profitable but purchases by you are unprofitable. Profitable cooperation increases good purchases. Noise and Other Externalities can be prisoner dilemmas. Profitable cooperation decreases the negative externalities (like noise) and increases the positive externalities (like entertainment).

5 5 BA 445 Lesson B.6 Prisoner Dilemmas Example 1: The Prisoners’ Dilemma

6 6 BA 445 Lesson B.6 Prisoner Dilemmas Example 1: The Prisoners’ Dilemma Overview The Prisoners’ Dilemma shows why people might not cooperate even if it is profitable. Cournot duopoly is a prisoners’ dilemma. Lower output by all is profitable but lower output by you is unprofitable.

7 7 BA 445 Lesson B.6 Prisoner Dilemmas Example 1: The Prisoners’ Dilemma Comment: A Prisoners’ Dilemma demonstrates why people might not cooperate or collude even if it is in their best interests to do so. The strongest form of the prisoners’ dilemma is when non-cooperation is a dominate strategy for each person. The first game called a “Prisoners’ Dilemma” described prisoners, and has been used in law enforcement. The solution to that game also solves a variety of business applications.

8 8 BA 445 Lesson B.6 Prisoner Dilemmas Example 1: The Prisoners’ Dilemma In the original dilemma, two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one confesses for the prosecution against the other and the other remains silent, the confessor goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both are sentenced to only six months in jail for a minor charge. If each confesses against the other, each receives a five-year sentence. Each prisoner must choose to confess or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should each prisoner act? Are there mutual gains from cooperation? If so, can each trust the other to cooperate?

9 9 BA 445 Lesson B.6 Prisoner Dilemmas Example 1: The Prisoners’ Dilemma One way to write the normal form of the game is for payoffs to be the negative of the number of years of imprisonment. Each prisoner should confess since it is the dominate strategy. Prisoners would both increase their payoff, from -5 to -.5 (gaining 4.5), if they each cooperated and remained silent. Neither prisoner can trust the other to cooperate and remain silent since Confess is the best response to the other prisoner remaining Silent.

10 BA 445 Lesson B.6 Prisoner Dilemmas Question: Verizon and AT&T control a large share of the U.S. telecommunications market. They simultaneously decide on the size of manufacturing plants for the next generation of smart phones. Suppose the firms’ goods are perfect substitutes, and market demand defines a linear inverse demand curve P = 20 – (Q V + Q A ), where output quantities Q V and Q A are the thousands of phones produced weekly by Verizon and AT&T. Suppose unit costs of production are c V = 2 and c A = 2 for both Verizon and AT&T. Suppose Verizon and AT&T consider any quantities Q V = 4.5 or 6, and Q A = 4.5 or 6. What quantity should Verizon choose in this Cournot Duopoly? Are there mutual gains from cooperation? Can Verizon trust AT&T to cooperate? Can AT&T trust Verizon to cooperate? Example 1: The Prisoners’ Dilemma

11 BA 445 Lesson B.6 Prisoner Dilemmas Answer: To begin, fill out the normal form for this game of simultaneous moves. For example, at Verizon quantity 4.5 and AT&T quantity 6.0, price = 20-10.5 = 9.5, so Verizon profits = (9.5-2)4.5 = 33.75 and AT&T profits = (9.5-2)6 = 45. Example 1: The Prisoners’ Dilemma

12 BA 445 Lesson B.6 Prisoner Dilemmas Example 1: The Prisoners’ Dilemma Each player should choose 6 since it is the dominate strategy for each player: 6 gives better payoffs for that player compared with 4.5, no matter whether the other player chooses 4.5 or 6. There are mutual gains if both Verizon and AT&T cooperate and produce 4.5. But Verizon cannot trust AT&T to cooperate because AT&T cooperating and choosing 4.5 is not a best response to Verizon cooperating and choosing 4.5. Likewise, AT&T cannot trust Verizon to cooperate because Verizon cooperating and choosing 4.5 is not a best response to AT&T cooperating and choosing 4.5.

13 BA 445 Lesson B.6 Prisoner Dilemmas Example 2: Duopoly with Substitutes

14 BA 445 Lesson B.6 Prisoner Dilemmas Overview Duopoly with Substitutes is a prisoners’ dilemma with firms simultaneously choosing prices and producing gross substitutes. Profitable cooperation raises prices. Example 2: Duopoly with Substitutes

15 BA 445 Lesson B.6 Prisoner Dilemmas Question: MillerCoors and Anheuser-Busch control a large share of the U.S. Domestic beer market. The unit cost of a keg to both retailers is \$75. The retailers compete on price but consumers do not find the goods to be perfect substitutes. Suppose MillerCoors and Anheuser- Busch consider prices \$85 and \$95. If both choose price \$85, each has demand 50; if both \$95, each has 40; and if one chooses \$85 and the other \$95, the lower price has demand 85 and the higher price 5. Are the two goods gross substitutes or gross complements? What price should MillerCoors choose in this Price Competition Game? Are there mutual gains from cooperation? Can MillerCoors trust Anheuser-Busch to cooperate? Can Anheuser-Busch trust MillerCoors to cooperate? Example 2: Duopoly with Substitutes

16 BA 445 Lesson B.6 Prisoner Dilemmas Answer: To begin, fill out the normal form for this game of simultaneous moves. For example, at Miller price \$95 and Busch price \$85, Miller’s demand is 5 and Busch’s is 85, so Miller profits \$(95-75)x5 = \$100 and Busch profits \$(85-75)x85 = \$850. Goods are gross substitutes because a higher price for one means higher demand for the other. Example 2: Duopoly with Substitutes

17 BA 445 Lesson B.6 Prisoner Dilemmas Each player should choose \$85 since it is the dominate strategy for each player: \$85 it gives better payoffs for that player compared with \$95, no matter whether the other player chooses \$85 or \$95. There are mutual gains if both MillerCoors and Anheuser-Busch cooperate and charge \$95. But MillerCoors cannot trust Anheuser- Busch to cooperate because Anheuser-Busch cooperating and choosing \$95 is not a best response to MillerCoors cooperating and choosing \$95. Likewise, Anheuser-Busch cannot trust MillerCoors to cooperate because MillerCoors cooperating and choosing \$95 is not a best response to Anheuser-Busch cooperating and choosing \$95. Example 2: Duopoly with Substitutes

18 BA 445 Lesson B.6 Prisoner Dilemmas Example 3: Duopoly with Complements

19 BA 445 Lesson B.6 Prisoner Dilemmas Overview Duopoly with Complements is a prisoners’ dilemma with firms simultaneously choosing prices and producing gross substitutes. Profitable cooperation lowers prices. Example 3: Duopoly with Complements

20 BA 445 Lesson B.6 Prisoner Dilemmas Question: Wii video game consoles are made by Nintendo, and some games are produced by third parties, including Sega. The unit cost of a console to Nintendo is \$50, and of a game to Sega is \$10. Suppose Nintendo considers prices \$250 and \$350 for consoles, and Sega considers \$40 and \$50 for games. If they choose prices \$250 and \$40 for consoles and games, then demands are 1 and 2 (in millions); if \$250 and \$50, then.8 and 1.6 (in millions); if \$350 and \$40, then.7 and 1.4 (in millions); and if \$350 and \$50, then.6 and 1.2 (in millions). Are the two goods gross substitutes or gross complements? What price should Nintendo choose if both companies choose simultaneously? Are there mutual gains from cooperation? Can Nintendo trust Sega to cooperate? Can Sega trust Nintendo to cooperate? Example 3: Duopoly with Complements

21 BA 445 Lesson B.6 Prisoner Dilemmas Answer: To begin, fill out the normal form for this game of simultaneous moves. For example, at Nintendo price \$350 and Sega price \$40, Nintendo’s demand is.7 and Sega’s is 1.4, so Nintendo profits \$(350- 50)x.7 = \$210 and Sega profits \$(40-10)x1.4 = \$42. Goods gross complements because a higher price for one means lower demand for the other. Example 3: Duopoly with Complements

22 BA 445 Lesson B.6 Prisoner Dilemmas Nintendo should choose \$350 since it is the dominate strategy, and Sega should choose \$50 since it is the dominate strategy. There are mutual gains if both Nintendo and Sega cooperate and charge their lower price. But Nintendo cannot trust Sega to cooperate because Sega cooperating and choosing \$40 is not a best response to Nintendo cooperating and choosing \$250. Likewise, Sega cannot trust Nintendo to cooperate because Nintendo cooperating and choosing \$250 is not a best response to Sega cooperating and choosing \$40. Example 3: Duopoly with Complements

23 BA 445 Lesson B.6 Prisoner Dilemmas Comment: The dilemma with Sam’s and Costco producing gross substitutes is the dominate strategy for each prices goods too low. The dilemma with Nintendo and Sega producing gross complements is the dominate strategy for each prices goods too high. Example 3: Duopoly with Complements

24 BA 445 Lesson B.6 Prisoner Dilemmas Example 4: Advertising

25 BA 445 Lesson B.6 Prisoner Dilemmas Overview Advertising is a prisoners’ dilemma when advertising mostly transfers customers between firms rather than generating new customers. Profitable cooperation reduces advertising. Example 4: Advertising

27 BA 445 Lesson B.6 Prisoner Dilemmas Question: R.J. Reynolds Tobacco Corp. and Philip Morris Corp. must decide how much money to spend on advertising. They consider spending either \$10,000 or zero. If one advertises and the other does not, the advertiser pays \$10,000, then takes \$100,000 profit from the other. If each advertises, each pays \$10,000 but the advertisements cancel out and neither player takes profit from the other. Should R.J. Reynolds spend \$10,000 or zero on advertising if both companies choose simultaneously? Are there mutual gains from cooperation? Can R.J. Reynolds trust Philip Morris to cooperate? Can Philip Morris trust R.J. Reynolds to cooperate? Example 4: Advertising

28 BA 445 Lesson B.6 Prisoner Dilemmas Answer: To begin, fill out the normal form for this game of simultaneous moves, with payoffs in thousands of dollars. For example, if Reynolds advertises and Philip does not, Reynolds pays \$10,000, then takes \$100,000 profit from Philip. Hence, Reynolds makes \$90,000 and Philip looses \$100,000. Write payoffs in thousands of dollars. Example 4: Advertising

30 BA 445 Lesson B.6 Prisoner Dilemmas Example 5: Cleaning and Other Public Goods

31 BA 445 Lesson B.6 Prisoner Dilemmas Overview Cleaning and Other Public Goods are prisoner dilemmas when public good purchases by all is profitable but purchases by you are unprofitable. Profitable cooperation increases good purchases. Example 5: Cleaning and Other Public Goods

33 BA 445 Lesson B.6 Prisoner Dilemmas Answer: No one should clean since Not Cleaning is a dominate strategy. For any strategies by each of the other 24 stores, the extra payoff to Store X from cleaning is a \$10 increase minus a \$100 cost, which makes the payoff \$90 less than for Not Cleaning. When each of the 25 stores follows its dominate strategy, no one cleans, and the payoff to each store is 0. But if each of the 25 stores cleans, each receives a \$10x25 increase minus a \$100 cost, which makes the payoff \$150 more than in the dominance solution. But no business can trust the others to cooperate because Store X cooperating and choosing Cleaning is not a best response to all the other stores cooperating and choosing Cleaning. Example 5: Cleaning and Other Public Goods

34 BA 445 Lesson B.6 Prisoner Dilemmas Example 6: Noise and Other Externalities

35 BA 445 Lesson B.6 Prisoner Dilemmas Overview Noise and Other Externalities can be prisoner dilemmas. Profitable cooperation decreases the negative externalities (like noise) and increases the positive externalities (like entertainment). Example 6: Noise and Other Externalities

36 BA 445 Lesson B.6 Prisoner Dilemmas Comment: October 23, 2008 marked the date that many downtown Fullerton regulars cried a tear. The Rockin' Taco Cantina was shut down after being served an eviction notice. No more dueling pianos, no more drunk dance floors, no more disorderly conduct outside in the alley. Was government action needed to control disorderly conduct? Example 6: Noise and Other Externalities

37 BA 445 Lesson B.6 Prisoner Dilemmas Question: Consider a downtown Fullerton street on which 12 bars are run, and which suffers from a serious drunkenness problem that detracts customers because of the violence and smell. It costs \$200 daily in foregone profit for each bar to enforce moderation stop serving customers before they become drunk. If a bar owner decides to enforce moderation, all bars on the street will have improved sales and profits. Suppose every bar on the street will have a \$20 increase in daily profit for each bar that decides to enforce moderation. If more than ten bars enforce moderation, then all of the bars will make more money, including the bars that enforce moderation. If some businesses enforce moderation but fewer than ten do so, then the bars that enforce moderation will lose money, while the bars that do not will gain money. Should anyone enforce moderation if all bars choose simultaneously? Are there mutual gains from cooperation? Can any bar trust other bars to cooperate? Example 6: Noise and Other Externalities

38 BA 445 Lesson B.6 Prisoner Dilemmas Answer: No one should enforce moderation since Not Enforce Moderation is a dominate strategy. For any strategies by each of the other 11 bars, the extra payoff to Bar X from enforcing moderation is a \$20 increase minus a \$200 cost, which makes the payoff \$180 less than for Not Enforce Moderation. When each of the 12 bars follows its dominate strategy, no one enforces moderation, and the payoff to each store is 0. But if each of the 12 bars enforce moderation, each receives a \$20x12 increase minus a \$200 cost, which makes the payoff \$40 more than in the dominance solution. So mutual gains are possible. But no bar can trust the others to cooperate because Bar X cooperating and choosing Enforce Moderation is not a best response to the other bars choosing Enforce Moderation. Example 6: Noise and Other Externalities

39 Review Questions BA 445 Lesson B.6 Prisoner Dilemmas Review Questions  You should try to answer some of the review questions (see the online syllabus) before the next class.  You will not turn in your answers, but students may request to discuss their answers to begin the next class.  Your upcoming Exam 2 and cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exams.

40 End of Lesson B.6 BA 445 Managerial Economics BA 445 Lesson B.6 Prisoner Dilemmas

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