1 1 deep thought ba 210 lesson ii.7 repeated dilemmas the face of a child can say it all, especially...

1 1

Deep ThoughtDeep Thought

BA 210 Lesson II.7 Repeated DilemmasBA 210 Lesson II.7 Repeated Dilemmas

The face of a child The face of a child can say it all, can say it all, especially the mouth part of the face. especially the mouth part of the face. ~ Jack Handey~ Jack Handey..

(Translation: Today’s lesson considers whether (Translation: Today’s lesson considers whether people can people can cooperate or collude when they can communicate but not cooperate or collude when they can communicate but not punishpunish.).)

2 2BA 210 Lesson II.7 Repeated DilemmasBA 210 Lesson II.7 Repeated Dilemmas

OverviewOverview

OverviewOverview

3 3

Lesson OverviewLesson Overview

BA 210 Lesson II.7 Repeated Dilemmas

Lesson II.6 Prisoner DilemmasLesson II.6 Prisoner DilemmasLesson II.7 Repeated DilemmasLesson II.7 Repeated DilemmasExample 1: Bonuses and TippingExample 1: Bonuses and TippingExample 2: Example 2: Stackelberg DuopolyStackelberg DuopolyExample 3: Buying Example 3: Buying OnlineOnlineExample 4: Solving a Dilemma with Pre-CommitmentExample 4: Solving a Dilemma with Pre-CommitmentExample 5: Solving a Dilemma with Immediate PunishmentExample 5: Solving a Dilemma with Immediate PunishmentSummarySummaryReview QuestionsReview Questions


Example 1: Bonuses and TippingExample 1: Bonuses and Tipping


5 5BA 210 Lesson II.7 Repeated Dilemmas

Question: Question: Consider ways for Professor Burke To Insure Consider ways for Professor Burke To Insure Promptness (TIP) when out to lunch at Islands Fine Burgers and Promptness (TIP) when out to lunch at Islands Fine Burgers and Drinks. Suppose Maria, his usual server, chooses whether to offer Drinks. Suppose Maria, his usual server, chooses whether to offer Prompt service or Slow Service, and after being served Prof. B Prompt service or Slow Service, and after being served Prof. B chooses whether to tip $2 or 0. If Maria chooses Prompt, she 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 looses $1 worth of energy because of the extra effort but Prof. B gains $3 worth of time. gains $3 worth of time.

Should Maria be Prompt? Should Prof. B Tip? Are there mutual Should Maria be Prompt? Should Prof. B Tip? Are there mutual gains from cooperation? Can Prof. B trust Maria to cooperate? gains from cooperation? Can Prof. B trust Maria to cooperate? Can Maria trust Prof. B to cooperate? Can Maria trust Prof. B to cooperate?


6 6

Prompt SlowTip $2 1,1 -2,2No Tip 3,-1 0,0

Maria

Professor


Answer: Answer: To begin, fill out the normal form for this game of To begin, fill out the normal form for this game of sequential moves. On the one hand, if Prof. B chooses to Tip $2 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 (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 chooses Prompt; and gain -2=0-2 and 2=2-0 if Maria chooses Slow.Slow.

On the other hand, if Prof. B chooses to No Tip (second row), On the other hand, if Prof. B chooses to No Tip (second row), then Prof. B and Maria gain then Prof. B and Maria gain 3=3-0 and -1=0-1 if Maria 3=3-0 and -1=0-1 if Maria chooses Prompt; and gain 0=0-0 chooses Prompt; and gain 0=0-0 and 0=0-0 if chooses Slow.and 0=0-0 if chooses Slow.



Prof. B should choose No TipProf. B should choose No Tip since he moves second and since he moves second and No Tip is the dominate strategy.No Tip is the dominate strategy.Maria should then choose Slow Maria should then choose Slow as the best response to Prof. B choosing No Tip. {No Tip, Slow} as the best response to Prof. B choosing No Tip. {No Tip, Slow} is thus the is thus the rollback solutionrollback solution..

There are mutual gains if both Prof. B and Maria cooperate with There are mutual gains if both Prof. B and Maria cooperate with Prof. B choosing Tip $2 and Maria X choosing Prompt. But Prof. B choosing Tip $2 and Maria X choosing Prompt. But Maria cannot trust Prof. B to cooperate because Prof. B 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 Tip $2 is not a best response to Maria cooperating and choosing Prompt. cooperating and choosing Prompt.

The question of whether Prof. B can trust Maria to cooperate is The question of whether Prof. B can trust Maria to cooperate is irrelevant because Maria chooses before Prof. B. irrelevant because Maria chooses before Prof. B.


Maria

Professor



Comment: Since No TipComment: Since No Tip is the dominate strategy for Prof. B and is the dominate strategy for Prof. B and Slow is the dominate strategy for Maria, the solution to the game Slow is the dominate strategy for Maria, the solution to the game remains remains {No Tip, Slow} regardless of whether Maria continues {No Tip, Slow} regardless of whether Maria continues to serve first, or whether Prof. B tips first (like he does at the to serve first, or whether Prof. B tips first (like he does at the Bellagio Gourmet Buffet in Vegas), or whether they (somehow) Bellagio Gourmet Buffet in Vegas), or whether they (somehow) serve and tip simultaneously.serve and tip simultaneously.


Maria

Professor



Example 2: Stackelberg DuopolyExample 2: Stackelberg Duopoly

Example 2: Stackelberg DuopolyExample 2: Stackelberg Duopoly


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. While the strongest form of a prisoners’ dilemma is to do so. While the strongest form of a prisoners’ dilemma is when non-cooperation is a dominate strategy for each person (as when non-cooperation is a dominate strategy for each person (as in Example 1), there are weaker forms, like when non-in Example 1), there are weaker forms, like when non-cooperation is the unique dominance solution, or when non-cooperation is the unique dominance solution, or when non-cooperation is the unique rollback solution.cooperation is the unique rollback solution.

Example 2: Example 2: Stackelberg Duopoly


Question: Question: You are a manager of Marvel Comics and you compete You are a manager of Marvel Comics and you compete directly with DC Comics selling comic books. Consumers find directly with DC Comics selling comic books. Consumers find the two products to be indistinguishable. The inverse market the two products to be indistinguishable. The inverse market demand for comic books is P = 5-Q (in dollars). Your marginal demand for comic books is P = 5-Q (in dollars). Your marginal costs of production are $1, and the marginal costs of DC Comics costs of production are $1, and the marginal costs of DC Comics are $1. Suppose you choose your output of comic books before are $1. Suppose you choose your output of comic books before DC Comics, and DC Comics knows your output before they DC Comics, and DC Comics knows your output before they decide their own output. Suppose Marvel Comics and DC decide their own output. Suppose Marvel Comics and DC Comics each consider producing quantities 1.0 or 1.1 or 1.8 or Comics each consider producing quantities 1.0 or 1.1 or 1.8 or 2.0 (in thousands).2.0 (in thousands).

How many comic books should you produce? Are there mutual How many comic books should you produce? Are there mutual gains from cooperation? Can Marvel Comics trust DC Comics to gains from cooperation? Can Marvel Comics trust DC Comics to cooperate? Can DC Comics trust Marvel Comics to cooperate?cooperate? Can DC Comics trust Marvel Comics 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 sequential moves. For example, at Marvel quantity 1.8 and DC 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-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 = 0.41.0)1.8 = 0.36 and DC profits = (1.2-1.0)2.0 = 0.4

1.0 1.1 1.8 2.01.0 2,2 1.9,2.09 1.2,2.16 1,21.1 2.09,1.9 1.98,1.98 1.21,1.98 0.99,1.81.8 2.16,1.2 1.98,1.21 0.72,0.72 0.36,0.42.0 2,1 1.8,0.99 0.4,0.36 0,0

DC

Marvel



Marvel is the leader in a Marvel is the leader in a Stackelberg Duopoly Game.Stackelberg Duopoly Game.Start from the end of the game:Start from the end of the game:Given Marvel’s choice 1.0, Given Marvel’s choice 1.0, DC’s best response is 1.8; given Marvel’s choice 1.1, DC’s best 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 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 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 response is 1.0. Of those four choices, the best payoffs for Marvel are for choosing 2.0 and generating payoff 2. Marvel are for choosing 2.0 and generating payoff 2.

1.0 1.1 1.8 2.01.0 2,2 1.9,2.09 1.2,2.16 1,21.1 2.09,1.9 1.98,1.98 1.21,1.98 0.99,1.81.8 2.16,1.2 1.98,1.21 0.72,0.72 0.36,0.42.0 2,1 1.8,0.99 0.4,0.36 0,0

DC

Marvel



There are mutual gains if both Marvel and DC cooperate and There are mutual gains if both Marvel and DC cooperate and Marvel produces either 1.1 or 1.8 and DC produces 1.0. Marvel produces either 1.1 or 1.8 and DC produces 1.0.

But Marvel cannot trust DC to cooperate because DC cooperating But Marvel cannot trust DC to cooperate because DC cooperating and choosing 1.0 is not a best response to Marvel cooperating and choosing 1.0 is not a best response to Marvel cooperating and choosing either 1.1 or 1.8. and choosing either 1.1 or 1.8.

The question of whether DC can trust Marvel to cooperate is The question of whether DC can trust Marvel to cooperate is irrelevant because Marvel chooses before DC. irrelevant because Marvel chooses before DC.

1.0 1.1 1.8 2.01.0 2,2 1.9,2.09 1.2,2.16 1,21.1 2.09,1.9 1.98,1.98 1.21,1.98 0.99,1.81.8 2.16,1.2 1.98,1.21 0.72,0.72 0.36,0.42.0 2,1 1.8,0.99 0.4,0.36 0,0

DC

Marvel



Example 3: Buying OnlineExample 3: Buying Online



Comment: Buyers and Sellers Comment: Buyers and Sellers trading over the internet face a trading over the internet face a prisoners’ dilemma because they risk sending money or goods prisoners’ dilemma because they risk sending money or goods and not getting what was agreed upon. One attempted solution and not getting what was agreed upon. One attempted solution that reduces their exposure to risk is to trade a little at a time. 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?Does trading a little at a time solve that prisoners’ dilemma?



Question: Question: Suppose Charlie values 4 disposable DVDs (Gladiator, …) at $3 Suppose Charlie values 4 disposable DVDs (Gladiator, …) at $3 each, suppose it costs Blockbuster $1 to provide each DVD, and suppose each, suppose it costs Blockbuster $1 to provide each DVD, and suppose Blockbuster sells DVDs for $2 each. Blockbuster sells DVDs for $2 each. Should Blockbuster send the first DVD Should Blockbuster send the first DVD to Charlie? to Charlie?

•If the first DVD is sent, Charlie (C) faces a decision: steal the DVD and 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.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 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.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 If the second DVD is sent, C faces a decision: steal the DVD and terminate the relationship; or, send $2 for the second DVD.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 If the second $2 is sent, B faces a decision: take the $2 and terminate the relationship; or, send the third DVD to C. relationship; or, send the third DVD to C.

•And so on.And so on.

•If the fourth DVD is sent, C faces a decision: steal the DVD and terminate the If the fourth DVD is sent, C faces a decision: steal the DVD and terminate the relationship; or, send $2 for the fourth DVD.relationship; or, send $2 for the fourth DVD.

Are there mutual gains from cooperation? Can each player trust the other to Are there mutual gains from cooperation? Can each player trust the other to cooperate?cooperate?



Answer: Answer: Here is a Game Tree Here is a Game Tree where payoffs list the gains where payoffs list the gains from trade, with payoffs to the from trade, with payoffs to the first player to act (Blockbuster) first player to act (Blockbuster) listed first. (This game is listed first. (This game is sometimes called the sometimes called the Centipede Centipede Game Game since the game tree looks since the game tree looks like a Centipede.)like a Centipede.)

0 ,0

D o N o t S en d 1

-1 ,3

D o N o t P a y 1

1 ,1

D o N o t S en d 2

0 ,4

D o N o t P a y 2

2 ,2

D o N o t S en d 2

1 ,5

D o N o t P a y 3

3 ,3

D o N o t S en d 4

2 ,6

D o N o t P a y 4

4 ,4

P a y 4

C

S e nd 4

B

P a y 3

C

S e nd 3

B

P a y 2

C

S e nd 2

B

P a y 1

C

S e nd 1

B



Starting at the end of the game, Starting at the end of the game, Blockbuster predicts Blockbuster predicts rational rational responses responses to alternative to alternative strategies. Charlie chooses Do strategies. Charlie chooses Do Not Pay for the fourth DVD if Not Pay for the fourth DVD if it is sent. it is sent.

0 ,0

D o N o t S en d 1

-1 ,3

D o N o t P a y 1

1 ,1

D o N o t S en d 2

0 ,4

D o N o t P a y 2

2 ,2

D o N o t S en d 2

1 ,5

D o N o t P a y 3

3 ,3

D o N o t S en d 4

2 ,6

D o N o t P a y 4

4 ,4

P a y 4

C

S e nd 4

B

P a y 3

C

S e nd 3

B

P a y 2

C

S e nd 2

B

P a y 1

C

S e nd 1

B



Rolling back one period from Rolling back one period from the end of game, the end of game, Charlie Charlie predicts predicts rational responses rational responses to to alternative strategies. alternative strategies. Blockbuster chooses Do Not Blockbuster chooses Do Not Send the fourth DVD since Send the fourth DVD since Blockbuster predicts Charlie Blockbuster predicts Charlie will not pay for that fourth will not pay for that fourth DVD. DVD.

0 ,0

D o N o t S en d 1

-1 ,3

D o N o t P a y 1

1 ,1

D o N o t S en d 2

0 ,4

D o N o t P a y 2

2 ,2

D o N o t S en d 2

1 ,5

D o N o t P a y 3

3 ,3

D o N o t S en d 4

2 ,6

D o N o t P a y 4

4 ,4

P a y 4

C

S e nd 4

B

P a y 3

C

S e nd 3

B

P a y 2

C

S e nd 2

B

P a y 1

C

S e nd 1

B



Rolling back one more period Rolling back one more period from the end of game, from the end of game, Blockbuster predicts Blockbuster predicts rational rational responses responses to alternative to alternative strategies. Charlie chooses Do strategies. Charlie chooses Do Not Pay for the third DVD if it Not Pay for the third DVD if it is sent since Charlie predicts is sent since Charlie predicts Blockbuster will not send the Blockbuster will not send the fourth DVD. fourth DVD.

0 ,0

D o N o t S en d 1

-1 ,3

D o N o t P a y 1

1 ,1

D o N o t S en d 2

0 ,4

D o N o t P a y 2

2 ,2

D o N o t S en d 2

1 ,5

D o N o t P a y 3

3 ,3

D o N o t S en d 4

2 ,6

D o N o t P a y 4

4 ,4

P a y 4

C

S e nd 4

B

P a y 3

C

S e nd 3

B

P a y 2

C

S e nd 2

B

P a y 1

C

S e nd 1

B



Rolling back one more period Rolling back one more period from the end of game, from the end of game, Charlie Charlie predicts predicts rational responses rational responses to to alternative strategies. alternative strategies. Blockbuster chooses Do Not Blockbuster chooses Do Not Send the third DVD since Send the third DVD since Blockbuster predicts Charlie Blockbuster predicts Charlie will not pay for that third DVD. will not pay for that third DVD.

0 ,0

D o N o t S en d 1

-1 ,3

D o N o t P a y 1

1 ,1

D o N o t S en d 2

0 ,4

D o N o t P a y 2

2 ,2

D o N o t S en d 2

1 ,5

D o N o t P a y 3

3 ,3

D o N o t S en d 4

2 ,6

D o N o t P a y 4

4 ,4

P a y 4

C

S e nd 4

B

P a y 3

C

S e nd 3

B

P a y 2

C

S e nd 2

B

P a y 1

C

S e nd 1

B



Rolling back one more period Rolling back one more period from the end of game, from the end of game, Blockbuster predicts Blockbuster predicts rational rational responses responses to alternative to alternative strategies. Charlie chooses Do strategies. Charlie chooses Do Not Pay for the second DVD if Not Pay for the second DVD if it is sent since Charlie predicts it is sent since Charlie predicts Blockbuster will not send the Blockbuster will not send the third DVD. third DVD.

0 ,0

D o N o t S en d 1

-1 ,3

D o N o t P a y 1

1 ,1

D o N o t S en d 2

0 ,4

D o N o t P a y 2

2 ,2

D o N o t S en d 2

1 ,5

D o N o t P a y 3

3 ,3

D o N o t S en d 4

2 ,6

D o N o t P a y 4

4 ,4

P a y 4

C

S e nd 4

B

P a y 3

C

S e nd 3

B

P a y 2

C

S e nd 2

B

P a y 1

C

S e nd 1

B



Rolling back one more period Rolling back one more period from the end of game, from the end of game, Charlie Charlie predicts predicts rational responses rational responses to to alternative strategies. alternative strategies. Blockbuster chooses Do Not Blockbuster chooses Do Not Send the second DVD since Send the second DVD since Blockbuster predicts Charlie Blockbuster predicts Charlie will not pay for that second will not pay for that second DVD. DVD.

0 ,0

D o N o t S en d 1

-1 ,3

D o N o t P a y 1

1 ,1

D o N o t S en d 2

0 ,4

D o N o t P a y 2

2 ,2

D o N o t S en d 2

1 ,5

D o N o t P a y 3

3 ,3

D o N o t S en d 4

2 ,6

D o N o t P a y 4

4 ,4

P a y 4

C

S e nd 4

B

P a y 3

C

S e nd 3

B

P a y 2

C

S e nd 2

B

P a y 1

C

S e nd 1

B



Rolling back one more period Rolling back one more period from the end of game, from the end of game, Blockbuster predicts Blockbuster predicts rational rational responses responses to alternative to alternative strategies. Charlie chooses Do strategies. Charlie chooses Do Not Pay for the first DVD if it Not Pay for the first DVD if it is sent since Charlie predicts is sent since Charlie predicts Blockbuster will not send the Blockbuster will not send the second DVD. second DVD.

0 ,0

D o N o t S en d 1

-1 ,3

D o N o t P a y 1

1 ,1

D o N o t S en d 2

0 ,4

D o N o t P a y 2

2 ,2

D o N o t S en d 2

1 ,5

D o N o t P a y 3

3 ,3

D o N o t S en d 4

2 ,6

D o N o t P a y 4

4 ,4

P a y 4

C

S e nd 4

B

P a y 3

C

S e nd 3

B

P a y 2

C

S e nd 2

B

P a y 1

C

S e nd 1

B



Rolling back to the beginning Rolling back to the beginning of game, of game, Blockbuster chooses Blockbuster chooses Do Not Send the first DVD Do Not Send the first DVD since Blockbuster predicts since Blockbuster predicts Charlie will not pay for that Charlie will not pay for that first DVD. first DVD.

0 ,0

D o N o t S en d 1

-1 ,3

D o N o t P a y 1

1 ,1

D o N o t S en d 2

0 ,4

D o N o t P a y 2

2 ,2

D o N o t S en d 2

1 ,5

D o N o t P a y 3

3 ,3

D o N o t S en d 4

2 ,6

D o N o t P a y 4

4 ,4

P a y 4

C

S e nd 4

B

P a y 3

C

S e nd 3

B

P a y 2

C

S e nd 2

B

P a y 1

C

S e nd 1

B



Centipede Game: Centipede Game: Should Blockbuster send the first DVD to Should Blockbuster send the first DVD to Charlie? In the rollback solution, Charlie will steal the first DVD Charlie? In the rollback solution, Charlie will steal the first DVD and terminate the relationship. So Blockbuster should not send and terminate the relationship. So Blockbuster should not send the first DVD. the first DVD.

There are mutual gains if, say, Charlie pays for every DVD and There are mutual gains if, say, Charlie pays for every DVD and Blockbuster sends every DVD. Blockbuster sends every DVD.

But Blockbuster cannot trust Charlie to cooperate because But Blockbuster cannot trust Charlie to cooperate because Charlie paying for every DVD, including the last DVD, is not a Charlie paying for every DVD, including the last DVD, is not a best response to Blockbuster sending every DVD. best response to Blockbuster sending every DVD.



Example 4: Solving a Dilemma with Example 4: Solving a Dilemma with Pre-CommitmentPre-Commitment

Example 4: Solving a Dilemma with Pre-CommitmentExample 4: Solving a Dilemma with Pre-Commitment


Question: Question: Consider ways Pepperdine University can get better Teaching or Consider ways Pepperdine University can get better Teaching or Research from its faculty. Suppose Pepperdine chooses whether to spend 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, $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 and simultaneously Prof. X chooses whether to spend $2,000 of effort to Work over Christmas break. If Pepperdine chooses the conference, then both 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 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. (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). X chooses to not work (since he is on a free holiday).

Should Pepperdine send Prof. X to the conference? Are there mutual gains Should Pepperdine send Prof. X to the conference? Are there mutual gains from cooperation? Can Pepperdine trust Prof. X to cooperate? Can Prof. X from cooperation? Can Pepperdine trust Prof. X to cooperate? Can Prof. X trust Pepperdine to cooperate? Can the two cooperate by having Pepperdine 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 pre-pre-commit to its choice before Prof. X chooses? Or by having Prof. X pre-commit (say, by agreeing to present his results after Christmas break)? commit (say, by agreeing to present his results after Christmas break)?


30 30

Work No WorkConf. 2,1 -1,3

No Conf. 0,-2 0,0

Prof. X

Pepperdine


Answer: Answer: To begin, fill out the normal form for this game of simultaneous 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 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 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 = 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 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 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) 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 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 row), then Pepperdine has no gains or costs, and Prof. X has no gains but $2,000 cost if he chooses Work.$2,000 cost if he chooses Work.



Prof. X should choose No WorkProf. X should choose No Worksince it is the dominate strategy. since it is the dominate strategy. Pepperdine should then choosePepperdine should then chooseNo Conference as the best No Conference as the best response to Prof. X choosing No Work. {No Conference, No response to Prof. X choosing No Work. {No Conference, No Work} is thus the dominance solution.Work} is thus the dominance solution.

There are mutual gains if both Pepperdine and Prof. X cooperate There are mutual gains if both Pepperdine and Prof. X cooperate with Pepperdine choosing Conference and Prof. X choosing with Pepperdine choosing Conference and Prof. X choosing Work. But Pepperdine cannot trust Prof. X to cooperate becauseWork. But Pepperdine cannot trust Prof. X to cooperate becauseProf. X cooperating and choosing Work is not a best response to Prof. X cooperating and choosing Work is not a best response to Pepperdine cooperating and choosing Conference. However, Pepperdine cooperating and choosing Conference. However, Prof. X can trust Pepperdine to cooperate because Pepperdine Prof. X can trust Pepperdine to cooperate because Pepperdine cooperating and choosing conference is a best response to Prof. X cooperating and choosing conference is a best response to Prof. X cooperating and choosing work. cooperating and choosing work.


No Conf. 0,-2 0,0

Prof. X

Pepperdine



Can the two cooperate by Can the two cooperate by having Pepperdine pre-commit having Pepperdine pre-commit to its choice before Prof. X to its choice before Prof. X chooses? If Pepperdine chooses? If Pepperdine pre-commits to Conference, then the two do not both cooperate pre-commits to Conference, then the two do not both cooperate since Prof. X cooperating and choosing Work is not a best since Prof. X cooperating and choosing Work is not a best response to Pepperdine cooperating and choosing Conference. response to Pepperdine cooperating and choosing Conference.

Can the two cooperate by having Prof. X pre-commit to its Can the two cooperate by having Prof. X pre-commit to its choice before Pepperdine chooses? If Prof. X pre-commits to choice before Pepperdine chooses? If Prof. X pre-commits to Work, then the two do both cooperate since Pepperdine Work, then the two do both cooperate since Pepperdine cooperating and choosing Conference is a best response to Prof. cooperating and choosing Conference is a best response to Prof. X cooperating and choosing Work. X cooperating and choosing Work.


No Conf. 0,-2 0,0

Prof. X

Pepperdine



Example 5: Solving a Dilemma with Example 5: Solving a Dilemma with Immediate PunishmentImmediate Punishment

Example 5: Solving a Dilemma with Immediate PunishmentExample 5: Solving a Dilemma with Immediate Punishment


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

Reconsider your answers if there is a third strategy of Reconsider your answers if there is a third strategy of price price matchingmatching --- charging $95 but matching a competitors $85 price. --- charging $95 but matching a competitors $85 price.



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



$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.



ReconsiderReconsider those answers if there is a third strategy of those answers if there is a third strategy of price price matchingmatching --- charging $95 but matching a competitors $85 price. --- charging $95 but matching a competitors $85 price. To begin, fill out the normal form for this game of simultaneous To begin, fill out the normal form for this game of simultaneous moves. For example, at Sam's Club Match and Costco price $85, 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 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 $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. 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

Costco

Sam's



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

Match 500,500 800,800 800,800

Costco

Sam's

There are no There are no dominate or dominate or weakly-dominate strategies weakly-dominate strategies in the original game, but $95 isin the original game, but $95 isweakly-dominated by Matchweakly-dominated by Matchfor each player. After $95 is eliminated for each player, Match is for each player. After $95 is eliminated for each player, Match is the weakly-dominate strategy for each player, resulting in the weakly-dominate strategy for each player, resulting in Payoffs of 800 for each player. Payoffs of 800 for each player.

There are no mutual gains if both Sam’s and Costco select There are no mutual gains if both Sam’s and Costco select alternative strategies. alternative strategies.



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

Match 500,500 800,800 800,800

Costco

Sam's

Comment: Comment: The original gameThe original gamewithout price matching was awithout price matching was aprisoners’ dilemma, with a prisoners’ dilemma, with a dominance solution of low dominance solution of low prices that was worse for both players than a prices that was worse for both players than a cooperative solution cooperative solution of high pricesof high prices. .

The Match strategy solved the dilemma by immediately The Match strategy solved the dilemma by immediately punishingpunishing a player that did not cooperate. The punishment a player that did not cooperate. The punishment against the non-cooperative player charging low prices was for against the non-cooperative player charging low prices was for the cooperative player to also charge low prices. And since that the cooperative player to also charge low prices. And since that punishment was immediate, there was no period of time that the punishment was immediate, there was no period of time that the non-cooperative player benefited from his charging low prices. non-cooperative player benefited from his charging low prices.


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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 1 and cumulative Final Exam will Your upcoming Exam 1 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.7End of Lesson II.7


BA 210 Introduction to BA 210 Introduction to MicroeconomicsMicroeconomics

1 1 deep thought ba 210 lesson ii.7 repeated dilemmas the face of a child can say it all, especially...

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