1 1 Deep Thought BA 210 Lesson II.6 Prisoner Dilemmas If I ever went to war, instead of throwing a...

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Deep ThoughtDeep Thought

BA 210 Lesson II.6 Prisoner DilemmasBA 210 Lesson II.6 Prisoner Dilemmas

If I ever went to war, If I ever went to war, instead of instead of throwing a grenade, I’d throw one of throwing a grenade, I’d throw one of those small pumpkins. Then maybe those small pumpkins. Then maybe my enemy would pick up the pumpkin my enemy would pick up the pumpkin and think about the futility of war. And and think about the futility of war. And that would give me the time I need to that would give me the time I need to hit him with a real grenade. ~ Jack hit him with a real grenade. ~ Jack HandeyHandey..

(Translation: Today’s lesson (Translation: Today’s lesson demonstrates why people might not demonstrates why people might not cooperate or collude even if it is in their best interests to do so.cooperate or collude even if it is in their best interests to do so.))

2 2BA 210 Lesson II.6 Prisoner DilemmasBA 210 Lesson II.6 Prisoner Dilemmas

OverviewOverview

OverviewOverview

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Lesson OverviewLesson Overview

BA 210 Lesson II.6 Prisoner Dilemmas

Lesson II.6 Prisoner DilemmasLesson II.6 Prisoner DilemmasExample 1: The Prisoners’ DilemmaExample 1: The Prisoners’ DilemmaExample 2: Bertrand DuopolyExample 2: Bertrand DuopolyExample 3: Example 3: Duopoly with Duopoly with SubstitutesSubstitutesExample 4: Example 4: Duopoly with Duopoly with ComplementsComplementsExample 5: Cournot DuopolyExample 5: Cournot DuopolyExample 6: AdvertisingExample 6: AdvertisingSummarySummaryReview QuestionsReview QuestionsLesson II.7 Repeated DilemmasLesson II.7 Repeated Dilemmas


Example 1: The Prisoners’ DilemmaExample 1: The Prisoners’ Dilemma


5 5BA 210 Lesson II.6 Prisoner Dilemmas


Comment: A Prisoners’ Dilemma Comment: A Prisoners’ Dilemma demonstrates why people demonstrates why people might not cooperate or collude even if it is in their best interests 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 to do so. The strongest form of the prisoners’ dilemma is when non-cooperation is a dominate strategy for each person. non-cooperation is a dominate strategy for each person.

The first game called a “Prisoners’ Dilemma” described The first game called a “Prisoners’ Dilemma” described prisoners, and has been used in law enforcement. The solution to prisoners, and has been used in law enforcement. The solution to that game also solves a variety of business applications. that game also solves a variety of business applications.



Question: Two suspects are arrested Question: Two suspects are arrested by the police. The police by the police. The police have insufficient evidence for a conviction, and, having separated have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one both prisoners, visit each of them to offer the same deal. If one confesses for the prosecution against the other and the other confesses for the prosecution against the other and the other remains silent, the confessor goes free and the silent accomplice remains silent, the confessor goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both are 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 sentenced to only six months in jail for a minor charge. If each confesses against the other, each receives a five-year sentence. confesses against the other, each receives a five-year sentence. Each prisoner must choose to confess or to remain silent. Each Each prisoner must choose to confess or to remain silent. Each one is assured that the other would not know about the betrayal one is assured that the other would not know about the betrayal before the end of the investigation. before the end of the investigation.

How should each prisoner act? Are there mutual gains from How should each prisoner act? Are there mutual gains from cooperation? If so, can each trust the other to cooperate?cooperation? If so, can each trust the other to cooperate?



Answer: One way to write Answer: One way to write the the normal form of the game is fornormal form of the game is forpayoffs to be the negative of payoffs to be the negative of the number of years of the number of years of imprisonment. imprisonment.

Each prisoner should confess since it is the dominate strategy.Each prisoner should confess since it is the dominate strategy.

Prisoners would both increase their payoff, from -5 to -.5 Prisoners would both increase their payoff, from -5 to -.5 (gaining 4.5), if they each cooperated and remained silent.(gaining 4.5), if they each cooperated and remained silent.

Neither prisoner can trust the other to cooperate and remain silent Neither prisoner can trust the other to cooperate and remain silent since Confess is the best response to the other prisoner remaining since Confess is the best response to the other prisoner remaining Silent.Silent.

Confess Silent

Confess -5,-5 0,-10

Silent -10,-10 -.5,-.5

Prisoner B

Prisoner A


Example 2: Bertrand DuopolyExample 2: Bertrand Duopoly



Question: Sam’s Club and Costco Question: Sam’s Club and Costco both sell emergency food both sell emergency food supplies in a weather-proof bucket that provides 275 delicious supplies in a weather-proof bucket that provides 275 delicious easy-to-prepare meals, including potato soup and corn chowder. easy-to-prepare meals, including potato soup and corn chowder. The unit cost to both retailers is $75. The retailers compete on 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 price: the low-price retailer gets all the market and they split the market if they have equal prices. Suppose they consider prices market if they have equal prices. Suppose they consider prices $85 and $95, and suppose market demands at those prices are $85 and $95, and suppose market demands at those prices are 100 and 80.100 and 80.

What price should Costco choose in this What price should Costco choose in this Price Competition Price Competition Game, Game, also called a also called a Bertrand Duopoly Bertrand Duopoly (named after (named after French French mathematicianmathematician Joseph Louis François Bertrand (1822-1900))Joseph Louis François Bertrand (1822-1900))..

Are there mutual gains from cooperation? Can Costco trust Are there mutual gains from cooperation? Can Costco trust Sam’s to cooperate? Can Sam’s trust Costco to cooperate? Sam’s to cooperate? Can Sam’s trust Costco to cooperate?


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$85 $95$85 500,500 1000,0$95 0,1000 800,800

Costco

Sam's


Answer: Answer: To begin, fill out the normal form for this game of To begin, fill out the normal form for this game of simultaneous moves. For example, at Sam's Club price $95 and simultaneous moves. For example, at Sam's Club price $95 and Costco price $85, Costco gets the entire market demand of 100. Costco price $85, Costco gets the entire market demand of 100. Hence, Sam's makes $0 and Costco makes $(85-75)Hence, Sam's makes $0 and Costco makes $(85-75)xx100 = 100 = $1,000.$1,000.



$85 $95$85 500,500 1000,0$95 0,1000 800,800

Costco

Sam's


Each player should choose $85 Each player should choose $85 since it is the dominate strategy since it is the dominate strategy for each player: $85 it gives for each player: $85 it gives better payoffs for that player better payoffs for that player compared with $95, no matter whether the other player chooses compared with $95, no matter whether the other player chooses $85 or $95. $85 or $95.

There are mutual gains if both Sam’s and Costco cooperate and There are mutual gains if both Sam’s and Costco cooperate and charge $95. But Costco cannot trust Sam’s to cooperate becausecharge $95. But Costco cannot trust Sam’s to cooperate becauseSam’s cooperating and choosing $95 is not a best response to Sam’s cooperating and choosing $95 is not a best response to Costco cooperating and choosing $95. Likewise, Sam’s cannotCostco cooperating and choosing $95. Likewise, Sam’s cannottrust Costco to cooperate because Costco cooperating and trust Costco to cooperate because Costco cooperating and choosing $95 is not a best response to Sam’s cooperating and choosing $95 is not a best response to Sam’s cooperating and choosing $95. choosing $95.


Example 3: Duopoly with SubstitutesExample 3: Duopoly with Substitutes



Question: Sam’s Club and Costco Question: Sam’s Club and Costco both sell emergency food both sell emergency food supplies in a weather-proof bucket that provides 275 delicious supplies in a weather-proof bucket that provides 275 delicious easy-to-prepare meals, including potato soup and corn chowder. easy-to-prepare meals, including potato soup and corn chowder. The unit cost to both retailers is $75. The retailers compete on The unit cost to both retailers is $75. The retailers compete on price but consumers do not find the goods to be perfect price but consumers do not find the goods to be perfect substitutes. Suppose Sam’s Costco consider prices $85 and $95. substitutes. Suppose Sam’s Costco consider prices $85 and $95. If both choose price $85, each has demand 50; if both $95, each 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 40; and if one chooses $85 and the other $95, the lower price has demand 85 and the higher price 5.has demand 85 and the higher price 5.

Are the two goods gross substitutes or gross complements? What Are the two goods gross substitutes or gross complements? What price should Costco choose in this Price Competition Game?price should Costco choose in this Price Competition Game?

Are there mutual gains from cooperation? Can Costco trust Are there mutual gains from cooperation? Can Costco trust Sam’s to cooperate? Can Sam’s trust Costco to cooperate? Sam’s to cooperate? Can Sam’s trust Costco to cooperate?


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$85 $95$85 500,500 850,100$95 100,850 800,800

Costco

Sam's


Answer: Answer: To begin, fill out the normal form for this game of To begin, fill out the normal form for this game of simultaneous moves. For example, at Sam’s Club price $95 and 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 Costco price $85, Sam’s demand is 5 and Costco’s is 85, so Sam’s profits $(95-75)Sam’s profits $(95-75)xx5 = $100 and Costco profits $(85-75)5 = $100 and Costco profits $(85-75)xx85 85 = $850. = $850.

Goods gross substitutes because a higher price for one means Goods gross substitutes because a higher price for one means higher demand for the other. higher demand for the other.



$85 $95$85 500,500 850,100$95 100,850 800,800

Costco

Sam's


Each player should choose $85 Each player should choose $85 since it is the dominate strategy since it is the dominate strategy for each player: $85 it gives for each player: $85 it gives better payoffs for that player better payoffs for that player compared with $95, no matter whether the other player chooses compared with $95, no matter whether the other player chooses $85 or $95. $85 or $95.

There are mutual gains if both Sam’s and Costco cooperate and There are mutual gains if both Sam’s and Costco cooperate and charge $95. But Costco cannot trust Sam’s to cooperate becausecharge $95. But Costco cannot trust Sam’s to cooperate becauseSam’s cooperating and choosing $95 is not a best response to Sam’s cooperating and choosing $95 is not a best response to Costco cooperating and choosing $95. Likewise, Sam’s cannotCostco cooperating and choosing $95. Likewise, Sam’s cannottrust Costco to cooperate because Costco cooperating and trust Costco to cooperate because Costco cooperating and choosing $95 is not a best response to Sam’s cooperating and choosing $95 is not a best response to Sam’s cooperating and choosing $95. choosing $95.


Example 4: Duopoly with Example 4: Duopoly with ComplementsComplements

Example 4: Duopoly with ComplementsExample 4: Duopoly with Complements


Question: Wii video game Question: Wii video game consoles are made by Nintendo, and consoles are made by Nintendo, and some games are produced by third parties, including Sega. The 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 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 is $10. Suppose Nintendo considers prices $250 and $350 for consoles, and Sega considers $40 and $50 for games. If they consoles, and Sega considers $40 and $50 for games. If they choose prices $250 and $40 for consoles and games, then choose prices $250 and $40 for consoles and games, then demands are 1 and 2 (in millions); if $250 and $50, then .8 and 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); 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). and if $350 and $50, then .6 and 1.2 (in millions).

Are the two goods gross substitutes or gross complements? What Are the two goods gross substitutes or gross complements? What price should Nintendo choose?price should Nintendo choose?

Are there mutual gains from cooperation? Can Nintendo trust Are there mutual gains from cooperation? Can Nintendo trust Sega to cooperate? Can Sega trust Nintendo to cooperate? Sega to cooperate? Can Sega trust Nintendo to cooperate?


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$40 $50$250 200,60 160,64$350 210,42 180,48

Sega

Nintendo


Answer: Answer: To begin, fill out the normal form for this game of To begin, fill out the normal form for this game of simultaneous moves. For example, at Nintendo price $350 and simultaneous moves. For example, at Nintendo price $350 and Sega price $40, Nintendo’s demand is .7 and Sega’s is 1.4, so Sega price $40, Nintendo’s demand is .7 and Sega’s is 1.4, so Nintendo profits $(350-50)Nintendo profits $(350-50)xx.7 = $210 and Sega profits $(40-.7 = $210 and Sega profits $(40-10)10)xx1.4 = $42. 1.4 = $42.

Goods gross complements because a higher price for one means Goods gross complements because a higher price for one means lower demand for the other. lower demand for the other.



Nintendo should choose $350 Nintendo should choose $350 since it is the dominate strategy,since it is the dominate strategy,And Sega should choose $50And Sega should choose $50since it is the dominate strategy. since it is the dominate strategy.

There are mutual gains if both Nintendo and Sega cooperate and There are mutual gains if both Nintendo and Sega cooperate and charge their lower price. But Nintendo cannot trust Sega to charge their lower price. But Nintendo cannot trust Sega to cooperate because Sega cooperating and choosing $40 is not a cooperate because Sega cooperating and choosing $40 is not a best response to Nintendo cooperating and choosing $250. best response to Nintendo cooperating and choosing $250. Likewise, Sega cannot trust Nintendo to cooperate because Likewise, Sega cannot trust Nintendo to cooperate because Nintendo cooperating and choosing $250 is not a best response to Nintendo cooperating and choosing $250 is not a best response to Sega cooperating and choosing $40. Sega cooperating and choosing $40.


$40 $50$250 200,60 160,64$350 210,42 180,48

Sega

Nintendo


Comment: Comment: The dilemma with The dilemma with Sam’s and Costco producing Sam’s and Costco producing gross substitutes gross substitutes is the is the dominate strategy for each dominate strategy for each prices goods too prices goods too lowlow. .

The dilemma with Nintendo The dilemma with Nintendo and Sega producing and Sega producing gross gross complementscomplements is the dominate is the dominate strategy for each prices goods strategy for each prices goods too too highhigh. .


$40 $50$250 200,60 160,64$350 210,42 180,48

Sega

Nintendo

$85 $95$85 500,500 850,100$95 100,850 800,800

Costco

Sam's


Example 5: Cournot DuopolyExample 5: Cournot Duopoly



Question: Question: Intel and AMD simultaneously decide on the size of Intel and AMD simultaneously decide on the size of manufacturing plants for the next generation of manufacturing plants for the next generation of microprocessors microprocessors for consumer desktop computers. Suppose the for consumer desktop computers. Suppose the firms’ goods are firms’ goods are perfect substitutes, and market demand defines a linear inverse perfect substitutes, and market demand defines a linear inverse demand curve P = 20 – (Qdemand curve P = 20 – (QI I + Q+ QAA), where output quantities Q), where output quantities QI I and and QQA A are the thousands of processors produced weekly by Intel and are the thousands of processors produced weekly by Intel and AMD. Suppose unit costs of production are cAMD. Suppose unit costs of production are cI I = 2 and c= 2 and cA A = 2 for = 2 for both Intel and AMD. Suppose Intel and AMD consider any both Intel and AMD. Suppose Intel and AMD consider any quantities Qquantities QI I = 4.5 or 6, and Q= 4.5 or 6, and QA A = 4.5 or 6.= 4.5 or 6.

What quantity What quantity should Intel choose in this should Intel choose in this Cournot Duopoly? Cournot Duopoly?

Are there mutual gains from cooperation? Can Are there mutual gains from cooperation? Can IntelIntel trust AMD trust AMD to cooperate? Can AMD trust to cooperate? Can AMD trust IntelIntel to cooperate? to cooperate?



Answer: Answer: To begin, fill out the normal form for this game of To begin, fill out the normal form for this game of simultaneous moves. For example, at Intel quantity 4.5 and simultaneous moves. For example, at Intel quantity 4.5 and AMD quantity 6.0, price = 20-10.5 = 9.5, so Intel profits = (9.5-AMD quantity 6.0, price = 20-10.5 = 9.5, so Intel profits = (9.5-2)4.5 = 33.75 and AMD profits = (9.5-2)6 = 45.2)4.5 = 33.75 and AMD profits = (9.5-2)6 = 45.

4.5 6.04.5 40.5,40.5 33.75,456.0 45,33.75 36,36

AMD

Intel



Each player should choose 6Each player should choose 6since it is the dominate strategy since it is the dominate strategy for each player: 6 it gives for each player: 6 it gives better payoffs for that player better payoffs for that player compared with 4.5, no matter whether the other player chooses compared with 4.5, no matter whether the other player chooses 4.5 or 6. 4.5 or 6.

There are mutual gains if both Intel and AMD cooperate and There are mutual gains if both Intel and AMD cooperate and produce 4.5. But Intel cannot trust AMD to cooperate becauseproduce 4.5. But Intel cannot trust AMD to cooperate becauseAMD cooperating and choosing 4.5 is not a best response to Intel AMD cooperating and choosing 4.5 is not a best response to Intel cooperating and choosing 4.5. Likewise, AMD cannotcooperating and choosing 4.5. Likewise, AMD cannottrust Intel to cooperate because Intel cooperating and choosing trust Intel to cooperate because Intel cooperating and choosing 4.5 is not a best response to AMD cooperating and choosing 4.5. 4.5 is not a best response to AMD cooperating and choosing 4.5.

4.5 6.04.5 40.5,40.5 33.75,456.0 45,33.75 36,36

AMD

Intel



Example 6: AdvertisingExample 6: Advertising



Comment:Comment: Advertising is a real life example of the prisoner’s dilemma. When Advertising is a real life example of the prisoner’s dilemma. When cigarette advertising on television was legal in the United States, competing cigarette advertising on television was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A’s advertising was partially advertising. The effectiveness of Firm A’s advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted 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 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 period the advertising cancels out, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, reduction in advertising. However, should Firm B choose not to advertise, Firm A would benefit by advertising and Firm B would lose. 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. 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 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 manufacturers endorse the creation in the U.S. of the Public Health Cigarette Smoking Act banning cigarette advertising on television, understanding that Smoking Act banning cigarette advertising on television, understanding that this would reduce costs and increase profits across the industry.this would reduce costs and increase profits across the industry.



Question: R.J. Reynolds Tobacco Corp. and Philip Morris Corp. Question: R.J. Reynolds Tobacco Corp. and Philip Morris Corp. must decide how much money to spend on advertising. They must decide how much money to spend on advertising. They consider spending either $10,000 or zero. If one advertises and consider spending either $10,000 or zero. If one advertises and the other does not, the advertiser pays $10,000, then takes the other does not, the advertiser pays $10,000, then takes $100,000 profit from the other. If each advertises, each pays $100,000 profit from the other. If each advertises, each pays $10,000 but the advertisements cancel out and neither player $10,000 but the advertisements cancel out and neither player takes profit from the other. takes profit from the other.

Should R.J. Reynolds spend $10,000 or zero on advertising?Should R.J. Reynolds spend $10,000 or zero on advertising?

Are there mutual gains from cooperation? Can R.J. Reynolds Are there mutual gains from cooperation? Can R.J. Reynolds trust Philip Morris to cooperate? Can Philip Morris trust R.J. trust Philip Morris to cooperate? Can Philip Morris trust R.J. Reynolds to cooperate? Reynolds to cooperate?


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Ad No AdAd -10,-10 90,-100

No Ad -100,90 0,0

Philip

Reynolds


Answer: Answer: To begin, fill out the normal form for this game of To begin, fill out the normal form for this game of simultaneous moves, with payoffs in thousands of dollars. For simultaneous moves, with payoffs in thousands of dollars. For example, if Reynolds advertises and Philip does not, Reynolds example, if Reynolds advertises and Philip does not, Reynolds pays $10,000, then takes $100,000 profit from Philip. Hence, pays $10,000, then takes $100,000 profit from Philip. Hence, Reynolds makes $90,000 and Philip looses $100,000. Write Reynolds makes $90,000 and Philip looses $100,000. Write payoffs in thousands of dollars.payoffs in thousands of dollars.



Each player should choose toEach player should choose toadvertise advertise since it is the dominatesince it is the dominatestrategy for each player: Ad strategy for each player: Ad gives gives better payoffs for that better payoffs for that player compared with No Ad, no matter whether the other player player compared with No Ad, no matter whether the other player chooses Ad or No Ad. chooses Ad or No Ad.

There are mutual gains if both Reynolds and Philip cooperate and There are mutual gains if both Reynolds and Philip cooperate and choose No Ad. But Reynolds cannot trust Philip to cooperate choose No Ad. But Reynolds cannot trust Philip to cooperate because Philip cooperating and choosing No Ad is not a best because Philip cooperating and choosing No Ad is not a best response to Reynolds cooperating and choosing No Ad. response to Reynolds cooperating and choosing No Ad. Likewise, Philip cannot trust Reynolds to cooperate because Likewise, Philip cannot trust Reynolds to cooperate because Reynolds cooperating and choosing No Ad is not a best response Reynolds cooperating and choosing No Ad is not a best response to Philip cooperating and choosing No Ad. to Philip cooperating and choosing No Ad.

Ad No AdAd -10,-10 90,-100

No Ad -100,90 0,0

Philip

Reynolds


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Review QuestionsReview Questions


Review QuestionsReview Questions You should try to answer some of the questions above You should try to answer some of the questions above before the next class.before the next class. You will not turn in your answers, but students may request You will not turn in your answers, but students may request to discuss their answers to begin the next class. to discuss their answers to begin the next class. Your upcoming Exam 2 and cumulative Final Exam will Your upcoming Exam 2 and cumulative Final Exam will contain some similar questions, so you should eventually contain some similar questions, so you should eventually consider every review question before taking your exams.consider every review question before taking your exams.

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End of Lesson II.6End of Lesson II.6


BA 210 Introduction to BA 210 Introduction to MicroeconomicsMicroeconomics

1 1 Deep Thought BA 210 Lesson II.6 Prisoner Dilemmas If I ever went to war, instead of throwing a...

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