Deep Thought
.
(Translation: Today’s lesson considers whether people can cooperate or collude when they can communicate but not punish.)
BA 210 Lesson II.7 Repeated Dilemmas 1

Overview
BA 210 Lesson II.7 Repeated Dilemmas 2

Lesson Overview
Lesson II.6 Prisoner Dilemmas
Lesson II.7 Repeated Dilemmas
Example 1: Bonuses and Tipping
Example 2: Stackelberg Duopoly
Example 3: Buying Online
Example 4: Solving a Dilemma with Pre-Commitment
Example 5: Solving a Dilemma with Immediate Punishment
Summary
Review Questions
BA 210 Lesson II.7 Repeated Dilemmas 3

Example 1: Bonuses and Tipping
BA 210 Lesson II.7 Repeated Dilemmas 4

Example 1: Bonuses and Tipping
Question: Consider ways for Professor Burke To Insure
Promptness (TIP) when out to lunch at Islands Fine Burgers and
Drinks. Suppose Maria, his usual server, chooses whether to offer
Prompt service or Slow Service, and after being served Prof. B chooses whether to tip $2 or 0. If Maria chooses Prompt, she looses $1 worth of energy because of the extra effort but Prof. B gains $3 worth of time.
Should Maria be Prompt? Should Prof. B Tip? Are there mutual gains from cooperation? Can Prof. B trust Maria to cooperate?
Can Maria trust Prof. B to cooperate?
BA 210 Lesson II.7 Repeated Dilemmas 5

Example 1: Bonuses and Tipping
Answer: To begin, fill out the normal form for this game of sequential moves. On the one hand, if Prof. B chooses to Tip $2
(first row), then Prof. B and Maria gain 1=3-2 and 1=2-1 if Maria chooses Prompt; and gain -2=0-2 and 2=2-0 if Maria chooses
Slow.
On the other hand, if Prof. B chooses to No Tip (second row), then Prof. B and Maria gain
3=3-0 and -1=0-1 if Maria
chooses Prompt; and gain 0=0-0 and 0=0-0 if chooses Slow.
Prompt Slow
Tip $2
No Tip
1,1
3,-1
BA 210 Lesson II.7 Repeated Dilemmas
-2,2
0,0
6

Example 1: Bonuses and Tipping
Prof. B should choose No Tip since he moves second and
No Tip is the dominate strategy.
Maria should then choose Slow
Profes s or
Tip $2
No Tip
Prompt Slow
1,1
3,-1
Maria
-2,2
0,0 as the best response to Prof. B choosing No Tip. {No Tip, Slow} is thus the rollback solution .
There are mutual gains if both Prof. B and Maria cooperate with
Prof. B choosing Tip $2 and Maria X choosing Prompt. But
Maria cannot trust Prof. B to cooperate because Prof. B cooperating and choosing Tip $2 is not a best response to Maria cooperating and choosing Prompt.
The question of whether Prof. B can trust Maria to cooperate is irrelevant because Maria chooses before Prof. B.
BA 210 Lesson II.7 Repeated Dilemmas 7

Example 1: Bonuses and Tipping
Profes s or
Tip $2
No Tip
Maria
Prompt Slow
1,1
3,-1
-2,2
0,0
Comment: Since No Tip is the dominate strategy for Prof. B and
Slow is the dominate strategy for Maria, the solution to the game remains {No Tip, Slow} regardless of whether Maria continues to serve first, or whether Prof. B tips first (like he does at the
Bellagio Gourmet Buffet in Vegas), or whether they (somehow) serve and tip simultaneously.
BA 210 Lesson II.7 Repeated Dilemmas 8

Example 2: Stackelberg Duopoly
BA 210 Lesson II.7 Repeated Dilemmas 9

Example 2: Stackelberg Duopoly
Comment: A Prisoners’ Dilemma demonstrates why people might not cooperate or collude even if it is in their best interests to do so. While the strongest form of a prisoners’ dilemma is when non-cooperation is a dominate strategy for each person (as in Example 1), there are weaker forms, like when noncooperation is the unique dominance solution, or when noncooperation is the unique rollback solution.
BA 210 Lesson II.7 Repeated Dilemmas 10

Example 2: Stackelberg Duopoly
Question: You are a manager of Marvel Comics and you compete directly with DC Comics selling comic books. Consumers find the two products to be indistinguishable. The inverse market demand for comic books is P = 5-Q (in dollars). Your marginal costs of production are $1, and the marginal costs of DC Comics are $1. Suppose you choose your output of comic books before
DC Comics, and DC Comics knows your output before they decide their own output. Suppose Marvel Comics and DC
Comics each consider producing quantities 1.0 or 1.1 or 1.8 or
2.0 (in thousands).
How many comic books should you produce? Are there mutual gains from cooperation? Can Marvel Comics trust DC Comics to cooperate? Can DC Comics trust Marvel Comics to cooperate?
BA 210 Lesson II.7 Repeated Dilemmas 11

Example 2: Stackelberg Duopoly
Answer: To begin, fill out the normal form for this game of sequential moves. For example, at Marvel quantity 1.8 and DC quantity 2.0, price = 5.0-3.8 = 1.2, so Marvel profits = (1.2-
1.0)1.8 = 0.36 and DC profits = (1.2-1.0)2.0 = 0.4
1.0
1.1
1.8
2.0
1.0
2,2 1.9,2.09
1.2,2.16
1,2
1.1
2.09,1.9 1.98,1.98 1.21,1.98 0.99,1.8
1.8
2.16,1.2 1.98,1.21 0.72,0.72 0.36,0.4
2.0
2,1 1.8,0.99
0.4,0.36
0,0
BA 210 Lesson II.7 Repeated Dilemmas 12

Example 2: Stackelberg Duopoly
DC
Marvel is the leader in a
1.0
1.1
1.8
2.0
Stackelberg Duopoly Game.
Start from the end of the game: Marvel
1.0
2,2 1.9,2.09
1.2,2.16
1,2
1.1
2.09,1.9 1.98,1.98 1.21,1.98 0.99,1.8
1.8
2.16,1.2 1.98,1.21 0.72,0.72 0.36,0.4
Given Marvel’s choice 1.0, 2.0
2,1 1.8,0.99
0.4,0.36
0,0
DC’s best response is 1.8; given Marvel’s choice 1.1, DC’s best response is either 1.1 or 1.8; given Marvel’s choice 1.8, DC’s best response is 1.1; and given Marvel’s choice 2.0, DC’s best response is 1.0. Of those four choices, the best payoffs for
Marvel are for choosing 2.0 and generating payoff 2.
BA 210 Lesson II.7 Repeated Dilemmas 13

Example 2: Stackelberg Duopoly
Marvel
DC
1.0
1.1
1.8
2.0
1.0
2,2 1.9,2.09
1.2,2.16
1,2
1.1
2.09,1.9 1.98,1.98 1.21,1.98 0.99,1.8
1.8
2.16,1.2 1.98,1.21 0.72,0.72 0.36,0.4
2.0
2,1 1.8,0.99
0.4,0.36
0,0
There are mutual gains if both Marvel and DC cooperate and
Marvel produces either 1.1 or 1.8 and DC produces 1.0.
But Marvel cannot trust DC to cooperate because DC cooperating and choosing 1.0 is not a best response to Marvel cooperating and choosing either 1.1 or 1.8.
The question of whether DC can trust Marvel to cooperate is irrelevant because Marvel chooses before DC.
BA 210 Lesson II.7 Repeated Dilemmas 14

Example 3: Buying Online
BA 210 Lesson II.7 Repeated Dilemmas 15

Example 3: Buying Online
Comment: Buyers and Sellers trading over the internet face a prisoners’ dilemma because they risk sending money or goods and not getting what was agreed upon. One attempted solution that reduces their exposure to risk is to trade a little at a time.
Does trading a little at a time solve that prisoners’ dilemma?
BA 210 Lesson II.7 Repeated Dilemmas 16

Example 3: Buying Online
Question: Suppose Charlie values 4 disposable DVDs (Gladiator, …) at $3 each, suppose it costs Blockbuster $1 to provide each DVD, and suppose
Blockbuster sells DVDs for $2 each. Should Blockbuster send the first DVD to Charlie?
• If the first DVD is sent, Charlie (C) faces a decision: steal the DVD and terminate the relationship; or, send $2 for the first DVD.
• If the first $2 is sent, Blockbuster (B) faces a decision: take the $2 and terminate the relationship; or, send the second DVD to C.
• If the second DVD is sent, C faces a decision: steal the DVD and terminate the relationship; or, send $2 for the second DVD.
• If the second $2 is sent, B faces a decision: take the $2 and terminate the relationship; or, send the third DVD to C.
• And so on.
• If the fourth DVD is sent, C faces a decision: steal the DVD and terminate the relationship; or, send $2 for the fourth DVD.
Are there mutual gains from cooperation? Can each player trust the other to cooperate?
BA 210 Lesson II.7 Repeated Dilemmas 17

Example 3: Buying Online
B
Answer: Here is a Game Tree where payoffs list the gains from trade, with payoffs to the first player to act (Blockbuster) listed first. (This game is sometimes called the Centipede
Game since the game tree looks like a Centipede.)
Do Not Send 1
0,0
Send 1
Do Not Pay 1
-1,3
C
Pay 1
Do Not Send 2
1,1
B
0,4
Send 2
Do Not Pay 2
C
Do Not Send 2
Pay 2
B
Send 3
2,2 C
Do Not Pay 3
1,5
Do Not Send 4
3,3
Pay 3
B
Send 4
C
Do Not Pay 4
2,6
Pay 4
4,4
BA 210 Lesson II.7 Repeated Dilemmas 18

Example 3: Buying Online
B
Starting at the end of the game,
Blockbuster predicts rational responses to alternative strategies. Charlie chooses Do
Not Pay for the fourth DVD if it is sent.
Do Not Send 1
0,0
Send 1
Do Not Pay 1
-1,3
C
1,1
Pay 1
Do Not Send 2
B
Send 2
C
Do Not Pay 2 Pay 2
0,4 B
Do Not Send 2
2,2
Send 3
C
Do Not Pay 3
1,5
Do Not Send 4
3,3
Pay 3
B
Send 4
C
Do Not Pay 4
2,6
Pay 4
4,4
BA 210 Lesson II.7 Repeated Dilemmas 19

Example 3: Buying Online
Rolling back one period from the end of game, Charlie predicts rational responses to alternative strategies.
Blockbuster chooses Do Not
Send the fourth DVD since
Blockbuster predicts Charlie will not pay for that fourth
DVD.
Do Not Send 1
0,0
B
Send 1
C
Do Not Pay 1
-1,3
Do Not Send 2
1,1
Pay 1
B
Send 2
C
Do Not Pay 2
0,4
Do Not Send 2
2,2
Pay 2
B
Send 3
C
Do Not Pay 3
1,5
Do Not Send 4
3,3
Pay 3
B
Send 4
C
Do Not Pay 4
2,6
Pay 4
4,4
BA 210 Lesson II.7 Repeated Dilemmas 20

Example 3: Buying Online
B
Rolling back one more period from the end of game,
Blockbuster predicts rational responses to alternative strategies. Charlie chooses Do
Not Pay for the third DVD if it is sent since Charlie predicts
Blockbuster will not send the fourth DVD.
Do Not Send 1
0,0
Send 1
Do Not Pay 1
-1,3
C
Pay 1
Do Not Send 2
1,1
B
Send 2
Do Not Pay 2
0,4
C
Pay 2
Do Not Send 2
B
2,2
Send 3
C
Do Not Pay 3
1,5
Do Not Send 4
3,3
Pay 3
B
Send 4
C
Do Not Pay 4
2,6
Pay 4
4,4
BA 210 Lesson II.7 Repeated Dilemmas 21

Example 3: Buying Online
B
Rolling back one more period from the end of game, Charlie predicts rational responses to alternative strategies.
Blockbuster chooses Do Not
Send the third DVD since
Blockbuster predicts Charlie will not pay for that third DVD.
Do Not Send 1
0,0
Send 1
Do Not Pay 1
-1,3
C
Pay 1
Do Not Send 2
1,1
B
0,4
Send 2
Do Not Pay 2
C
Do Not Send 2
Pay 2
B
Send 3
2,2 C
Do Not Pay 3
1,5
Do Not Send 4
3,3
Pay 3
B
Send 4
C
Do Not Pay 4
2,6
Pay 4
4,4
BA 210 Lesson II.7 Repeated Dilemmas 22

Example 3: Buying Online
B
Rolling back one more period from the end of game,
Blockbuster predicts rational responses to alternative strategies. Charlie chooses Do
Not Pay for the second DVD if it is sent since Charlie predicts
Blockbuster will not send the third DVD.
Do Not Send 1
0,0
Send 1
Do Not Pay 1
-1,3
C
Pay 1
Do Not Send 2
1,1
B
Send 2
Do Not Pay 2
0,4
C
Pay 2
Do Not Send 2
B
2,2
Send 3
C
Do Not Pay 3
1,5
Do Not Send 4
3,3
Pay 3
B
Send 4
C
Do Not Pay 4
2,6
Pay 4
4,4
BA 210 Lesson II.7 Repeated Dilemmas 23

Example 3: Buying Online
Rolling back one more period from the end of game, Charlie predicts rational responses to alternative strategies.
Blockbuster chooses Do Not
Send the second DVD since
Blockbuster predicts Charlie will not pay for that second
DVD.
Do Not Send 1
0,0
B
Send 1
C
Do Not Pay 1
-1,3
Do Not Send 2
1,1
Pay 1
B
Send 2
C
Do Not Pay 2
0,4
Do Not Send 2
2,2
Pay 2
B
Send 3
C
Do Not Pay 3
1,5
Do Not Send 4
3,3
Pay 3
B
Send 4
C
Do Not Pay 4
2,6
Pay 4
4,4
BA 210 Lesson II.7 Repeated Dilemmas 24

Example 3: Buying Online
Rolling back one more period from the end of game,
Blockbuster predicts rational responses to alternative strategies. Charlie chooses Do
Not Pay for the first DVD if it is sent since Charlie predicts
Blockbuster will not send the second DVD.
Do Not Send 1
0,0
B
Send 1
C
Do Not Pay 1
-1,3
Do Not Send 2
1,1
Pay 1
B
Send 2
C
Do Not Pay 2
0,4
Do Not Send 2
2,2
Pay 2
B
Send 3
C
Do Not Pay 3
1,5
Do Not Send 4
3,3
Pay 3
B
Send 4
C
Do Not Pay 4
2,6
Pay 4
4,4
BA 210 Lesson II.7 Repeated Dilemmas 25

Example 3: Buying Online
Rolling back to the beginning of game, Blockbuster chooses
Do Not Send the first DVD since Blockbuster predicts
Charlie will not pay for that first DVD.
Do Not Send 1
0,0
B
Send 1
C
Do Not Pay 1
-1,3
Do Not Send 2
1,1
Pay 1
B
Send 2
C
Do Not Pay 2
0,4
Do Not Send 2
2,2
Pay 2
B
Send 3
C
Do Not Pay 3
1,5
Do Not Send 4
3,3
Pay 3
B
Send 4
C
Do Not Pay 4
2,6
Pay 4
4,4
BA 210 Lesson II.7 Repeated Dilemmas 26

Example 3: Buying Online
Centipede Game: Should Blockbuster send the first DVD to
Charlie? In the rollback solution, Charlie will steal the first DVD and terminate the relationship. So Blockbuster should not send the first DVD.
There are mutual gains if, say, Charlie pays for every DVD and
Blockbuster sends every DVD.
But Blockbuster cannot trust Charlie to cooperate because
Charlie paying for every DVD, including the last DVD, is not a best response to Blockbuster sending every DVD.
BA 210 Lesson II.7 Repeated Dilemmas 27

Example 4: Solving a Dilemma with Pre-Commitment
BA 210 Lesson II.7 Repeated Dilemmas 28

Example 4: Solving a Dilemma with Pre-Commitment
Question: Consider ways Pepperdine University can get better Teaching or
Research from its faculty. Suppose Pepperdine chooses whether to spend
$1,000 to send Prof. X to a conference in Las Vegas over Christmas break, and simultaneously Prof. X chooses whether to spend $2,000 of effort to Work over Christmas break. If Pepperdine chooses the conference, then both
Pepperdine and Prof. X gain $3,000 of benefit if Prof. X chooses to work
(since he is working more effectively) but Prof. X alone gains $3,000 if Prof.
X chooses to not work (since he is on a free holiday).
Should Pepperdine send Prof. X to the conference? Are there mutual gains from cooperation? Can Pepperdine trust Prof. X to cooperate? Can Prof. X trust Pepperdine to cooperate? Can the two cooperate by having Pepperdine pre-commit to its choice before Prof. X chooses? Or by having Prof. X precommit (say, by agreeing to present his results after Christmas break)?
BA 210 Lesson II.7 Repeated Dilemmas 29

Example 5: Solving a Dilemma with Pre-Commitment
Answer: To begin, fill out the normal form for this game of simultaneous moves. On the one hand, if Pepperdine chooses to send Prof. X to the conference (first row), then both Pepperdine and Prof. X gain $3,000 of benefit if Prof. X chooses to work, resulting in net payoffs of $3,000-$1,000 = 2
(thousand) to Pepperdine and $3,000-$2,000 = 1 (thousand) to Prof. X, but
Prof. X alone gains $3,000 if Prof. X chooses to not work, resulting in net payoffs of $0-$1,000 = -1 (thousand) to Pepperdine and $3,000 = 3 (thousand) to Prof. X. On the other hand, if Pepperdine chooses to send Prof. X (second row), then Pepperdine has no gains or costs, and Prof. X has no gains but
$2,000 cost if he chooses Work.
Conf.
No Conf.
Work No Work
2,1
0,-2
BA 210 Lesson II.7 Repeated Dilemmas
-1,3
0,0
30

Example 4: Solving a Dilemma with Pre-Commitment
Prof. X should choose No Work since it is the dominate strategy.
Pepperdine should then choose
No Conference as the best
Pepperdine
Work No Work
Conf.
2,1
No Conf.
0,-2
Prof. X
-1,3
0,0 response to Prof. X choosing No Work. {No Conference, No
Work} is thus the dominance solution.
There are mutual gains if both Pepperdine and Prof. X cooperate with Pepperdine choosing Conference and Prof. X choosing
Work. But Pepperdine cannot trust Prof. X to cooperate because
Prof. X cooperating and choosing Work is not a best response to
Pepperdine cooperating and choosing Conference. However,
Prof. X can trust Pepperdine to cooperate because Pepperdine cooperating and choosing conference is a best response to Prof. X cooperating and choosing work.
BA 210 Lesson II.7 Repeated Dilemmas 31

Example 4: Solving a Dilemma with Pre-Commitment
Can the two cooperate by having Pepperdine pre-commit to its choice before Prof. X chooses? If Pepperdine
Pepperdine
Work No Work
Conf.
2,1
No Conf.
0,-2
Prof. X
-1,3
0,0 pre-commits to Conference, then the two do not both cooperate since Prof. X cooperating and choosing Work is not a best response to Pepperdine cooperating and choosing Conference.
Can the two cooperate by having Prof. X pre-commit to its choice before Pepperdine chooses? If Prof. X pre-commits to Work, then the two do both cooperate since Pepperdine cooperating and choosing Conference is a best response to Prof. X cooperating and choosing Work.
BA 210 Lesson II.7 Repeated Dilemmas 32

Example 5: Solving a Dilemma with Immediate Punishment
BA 210 Lesson II.7 Repeated Dilemmas 33

Example 5: Solving a Dilemma with Immediate Punishment
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? Are there mutual gains from cooperation? Can Costco trust Sam’s to cooperate? Can Sam’s trust Costco to cooperate?
Reconsider your answers if there is a third strategy of price matching --- charging $95 but matching a competitors $85 price.
BA 210 Lesson II.7 Repeated Dilemmas 34

Example 5: Solving a Dilemma with Immediate Punishment
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.
$85 $95
$85
$95
500,500
0,1000
BA 210 Lesson II.7 Repeated Dilemmas
1000,0
800,800
35

Example 5: Solving a Dilemma with Immediate Punishment
Each player should choose $85 since it is the dominate strategy for each player: $85 it gives better payoffs for that player
Sam's
$85
$95
$85
Costco
$95
500,500 1000,0
0,1000 800,800 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.
BA 210 Lesson II.7 Repeated Dilemmas 36

Example 5: Solving a Dilemma with Immediate Punishment
Reconsider those answers if there is a third strategy of price matching --- charging $95 but matching a competitors $85 price.
To begin, fill out the normal form for this game of simultaneous moves. For example, at Sam's Club Match and Costco price $85, profits are the same as at Sam's Club price $85 and Costco price
$85. And at Sam's Club Match and Costco price $95, profits are the same as at Sam's Club price $95 and Costco price $95.
$85 $95 Match
$85 500,500 1000,0 500,500
$95 0,1000 800,800 800,800
Match 500,500 800,800 800,800
BA 210 Lesson II.7 Repeated Dilemmas 37

Example 5: Solving a Dilemma with Immediate Punishment
There are no dominate or weakly-dominate strategies in the original game, but $95 is weakly-dominated by Match
Sam's
Costco
$85 $95 Match
$85 500,500 1000,0 500,500
$95 0,1000 800,800 800,800
Match 500,500 800,800 800,800 for each player. After $95 is eliminated for each player, Match is the weakly-dominate strategy for each player, resulting in Payoffs of 800 for each player.
There are no mutual gains if both Sam’s and Costco select alternative strategies.
BA 210 Lesson II.7 Repeated Dilemmas 38

Example 5: Solving a Dilemma with Immediate Punishment
Comment: The original game without price matching was a prisoners’ dilemma, with a dominance solution of low
Sam's
Costco
$85 $95 Match
$85 500,500 1000,0 500,500
$95 0,1000 800,800 800,800
Match 500,500 800,800 800,800 prices that was worse for both players than a cooperative solution of high prices .
The Match strategy solved the dilemma by immediately punishing a player that did not cooperate. The punishment against the non-cooperative player charging low prices was for the cooperative player to also charge low prices. And since that punishment was immediate, there was no period of time that the non-cooperative player benefited from his charging low prices.
BA 210 Lesson II.7 Repeated Dilemmas 39

Review Questions
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 1 and cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exams.
BA 210 Lesson II.7 Repeated Dilemmas 40

BA 210 Introduction to Microeconomics
BA 210 Lesson II.7 Repeated Dilemmas 41