1 1 Deep Thought BA 210 Lesson II.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 210 Lesson II.6 Prisoner DilemmasOverviewOverview

3 3 Lesson Overview BA 210 Lesson II.6 Prisoner Dilemmas Lesson II.6 Prisoner Dilemmas Example 1: The Prisoners’ Dilemma Example 2: Bertrand Duopoly Example 3: Duopoly with Substitutes Example 4: Duopoly with Complements Example 5: Cournot Duopoly Example 6: Advertising Summary Review Questions Lesson II.7 Repeated Dilemmas

4 4 BA 210 Lesson II.6 Prisoner Dilemmas Example 1: The Prisoners’ Dilemma

5 5 BA 210 Lesson II.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.

6 6 BA 210 Lesson II.6 Prisoner Dilemmas Example 1: The Prisoners’ Dilemma Question: 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?

7 7 BA 210 Lesson II.6 Prisoner Dilemmas Example 1: The Prisoners’ Dilemma Answer: 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.

8 8 BA 210 Lesson II.6 Prisoner Dilemmas Example 2: Bertrand Duopoly

9 9 BA 210 Lesson II.6 Prisoner Dilemmas Question: Sam’s Club and Costco both sell emergency food supplies in a weather-proof bucket that provides 275 delicious easy-to-prepare meals, including potato soup and corn chowder. The unit cost to both retailers is $75. The retailers compete on price: the low-price retailer gets all the market and they split the market if they have equal prices. Suppose they consider prices $85 and $95, and suppose market demands at those prices are 100 and 80. What price should Costco choose in this Price Competition Game, also called a Bertrand Duopoly (named after French mathematician Joseph Louis François Bertrand ( )). Are there mutual gains from cooperation? Can Costco trust Sam’s to cooperate? Can Sam’s trust Costco to cooperate? Example 2: Bertrand Duopoly

10 BA 210 Lesson II.6 Prisoner Dilemmas Answer: To begin, fill out the normal form for this game of simultaneous moves. For example, at Sam's Club price $95 and Costco price $85, Costco gets the entire market demand of 100. Hence, Sam's makes $0 and Costco makes $(85-75)x100 = $1,000. Example 2: Bertrand Duopoly

11 BA 210 Lesson II.6 Prisoner Dilemmas Example 2: Bertrand Duopoly 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 Sam’s and Costco cooperate and charge $95. But Costco cannot trust Sam’s to cooperate because Sam’s cooperating and choosing $95 is not a best response to Costco cooperating and choosing $95. Likewise, Sam’s cannot trust Costco to cooperate because Costco cooperating and choosing $95 is not a best response to Sam’s cooperating and choosing $95.

12 BA 210 Lesson II.6 Prisoner Dilemmas Example 3: Duopoly with Substitutes

13 BA 210 Lesson II.6 Prisoner Dilemmas Question: Sam’s Club and Costco both sell emergency food supplies in a weather-proof bucket that provides 275 delicious easy-to-prepare meals, including potato soup and corn chowder. The unit cost to both retailers is $75. The retailers compete on price but consumers do not find the goods to be perfect substitutes. Suppose Sam’s Costco 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 Costco choose in this Price Competition Game? Are there mutual gains from cooperation? Can Costco trust Sam’s to cooperate? Can Sam’s trust Costco to cooperate? Example 3: Duopoly with Substitutes

14 BA 210 Lesson II.6 Prisoner Dilemmas Answer: To begin, fill out the normal form for this game of simultaneous moves. For example, at Sam’s Club price $95 and Costco price $85, Sam’s demand is 5 and Costco’s is 85, so Sam’s profits $(95-75) x 5 = $100 and Costco profits $(85-75) x 85 = $850. Goods gross substitutes because a higher price for one means higher demand for the other. Example 2: Bertrand Duopoly

15 BA 210 Lesson II.6 Prisoner Dilemmas Example 2: Bertrand Duopoly 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 Sam’s and Costco cooperate and charge $95. But Costco cannot trust Sam’s to cooperate because Sam’s cooperating and choosing $95 is not a best response to Costco cooperating and choosing $95. Likewise, Sam’s cannot trust Costco to cooperate because Costco cooperating and choosing $95 is not a best response to Sam’s cooperating and choosing $95.

16 BA 210 Lesson II.6 Prisoner Dilemmas Example 4: Duopoly with Complements

17 BA 210 Lesson II.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? Are there mutual gains from cooperation? Can Nintendo trust Sega to cooperate? Can Sega trust Nintendo to cooperate? Example 4: Duopoly with Complements

18 BA 210 Lesson II.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) x 1.4 = $42. Goods gross complements because a higher price for one means lower demand for the other. Example 4: Duopoly with Complements

19 BA 210 Lesson II.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 4: Duopoly with Complements

20 BA 210 Lesson II.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 4: Duopoly with Complements

21 BA 210 Lesson II.6 Prisoner Dilemmas Example 5: Cournot Duopoly

22 BA 210 Lesson II.6 Prisoner Dilemmas Question: Intel and AMD simultaneously decide on the size of manufacturing plants for the next generation of microprocessors for consumer desktop computers. Suppose the firms’ goods are perfect substitutes, and market demand defines a linear inverse demand curve P = 20 – (Q I + Q A ), where output quantities Q I and Q A are the thousands of processors produced weekly by Intel and AMD. Suppose unit costs of production are c I = 2 and c A = 2 for both Intel and AMD. Suppose Intel and AMD consider any quantities Q I = 4.5 or 6, and Q A = 4.5 or 6. What quantity should Intel choose in this Cournot Duopoly? Are there mutual gains from cooperation? Can Intel trust AMD to cooperate? Can AMD trust Intel to cooperate? Example 5: Cournot Duopoly

23 BA 210 Lesson II.6 Prisoner Dilemmas Answer: To begin, fill out the normal form for this game of simultaneous moves. For example, at Intel quantity 4.5 and AMD quantity 6.0, price = = 9.5, so Intel profits = (9.5- 2)4.5 = and AMD profits = (9.5-2)6 = 45. Example 5: Cournot Duopoly

24 BA 210 Lesson II.6 Prisoner Dilemmas Each player should choose 6 since it is the dominate strategy for each player: 6 it 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 Intel and AMD cooperate and produce 4.5. But Intel cannot trust AMD to cooperate because AMD cooperating and choosing 4.5 is not a best response to Intel cooperating and choosing 4.5. Likewise, AMD cannot trust Intel to cooperate because Intel cooperating and choosing 4.5 is not a best response to AMD cooperating and choosing 4.5. Example 5: Cournot Duopoly

25 BA 210 Lesson II.6 Prisoner Dilemmas Example 6: Advertising

26 BA 210 Lesson II.6 Prisoner Dilemmas Comment: Advertising is a real life example of the prisoner’s dilemma. When cigarette advertising on television was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A’s advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period the advertising cancels out, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A would benefit by advertising and Firm B would lose. As in any prisoner’s dilemma, each player cannot trust the other to cooperate. In the case of cigarette advertising, that lack of trust made cigarette manufacturers endorse the creation in the U.S. of the Public Health Cigarette Smoking Act banning cigarette advertising on television, understanding that this would reduce costs and increase profits across the industry. Example 6: Advertising

27 BA 210 Lesson II.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? 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 6: Advertising

28 BA 210 Lesson II.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 6: Advertising

29 BA 210 Lesson II.6 Prisoner Dilemmas Each player should choose to advertise since it is the dominate strategy for each player: Ad gives better payoffs for that player compared with No Ad, no matter whether the other player chooses Ad or No Ad. There are mutual gains if both Reynolds and Philip cooperate and choose No Ad. But Reynolds cannot trust Philip to cooperate because Philip cooperating and choosing No Ad is not a best response to Reynolds cooperating and choosing No Ad. Likewise, Philip cannot trust Reynolds to cooperate because Reynolds cooperating and choosing No Ad is not a best response to Philip cooperating and choosing No Ad. Example 6: Advertising

30 Review Questions BA 210 Lesson II.6 Prisoner Dilemmas Review Questions  You should try to answer some of the questions above 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.

31 End of Lesson II.6 BA 210 Lesson II.6 Prisoner Dilemmas BA 210 Introduction to Microeconomics