1 1 lesson overview ba 592 lesson i.4 sequential move applications chapter 3 games with sequential...

1 1

Lesson overviewLesson overview

BA 592 Lesson I.4 Sequential Move Applications

Chapter 3 Games with Sequential MovesChapter 3 Games with Sequential Moves

Lesson I.3 Sequential Move TheoryLesson I.3 Sequential Move Theory

Lesson I.4 Sequential Move ApplicationsLesson I.4 Sequential Move ApplicationsEach Example Game introduces applications or techniquesEach Example Game introduces applications or techniques•Example 1: Example 1: AdvertisingAdvertising•Example 2: Entry DeterrenceExample 2: Entry Deterrence•Example 3: Car LoanExample 3: Car Loan•Example 4: Example 4: RenegotiationRenegotiation•Example 5: Compatible Web BrowsersExample 5: Compatible Web Browsers•Example 6: Evicting TenantsExample 6: Evicting Tenants•Example 7: Strategic VotingExample 7: Strategic Voting•Example 8: Example 8: Nuisance Suits Nuisance Suits •Review ProblemsReview Problems

2 2BA 592 Lesson I.4 Sequential Move ApplicationsBA 592 Lesson I.4 Sequential Move Applications

Each example gameEach example game in this “Sequential Move Applications” in this “Sequential Move Applications” lesson, or in any of the other “Applications” lessons in the lesson, or in any of the other “Applications” lessons in the course, is presented in the same way as questions on an exam: I course, is presented in the same way as questions on an exam: I describe a game verbally and ask questions about its solution. describe a game verbally and ask questions about its solution. You must formulate the game (identifying players, strategies, You must formulate the game (identifying players, strategies, payoffs, …) then answer those questions by solving the game. payoffs, …) then answer those questions by solving the game.

Example 1: AdvertisingExample 1: Advertising


Question: Question: Incumbant Senator Gray Incumbant Senator Gray will run for reelection. The will run for reelection. The challenger is Congresswoman Green. Senator Gray first decides challenger is Congresswoman Green. Senator Gray first decides whether or not to run advertisements early on. The challenger whether or not to run advertisements early on. The challenger Green must then decide whether or not to enter the race. Issues to Green must then decide whether or not to enter the race. Issues to think about in modeling the game:think about in modeling the game:

Players are Gray and Green. Gray moves first.Players are Gray and Green. Gray moves first. Strategies for Gray are Ads, No Ads; for Green: In or Out.Strategies for Gray are Ads, No Ads; for Green: In or Out. Ads are costly, so Gray would prefer not to run ads.Ads are costly, so Gray would prefer not to run ads. Green will find it possible to win if Gray does not run ads, Green will find it possible to win if Gray does not run ads,

but impossible if Gray does run ads.but impossible if Gray does run ads.

Define a game tree for this Define a game tree for this Advertising GameAdvertising Game, choosing payoff , choosing payoff numbers consistent with the issues above. Then, find the numbers consistent with the issues above. Then, find the rollback solution.rollback solution.



4 ,2

O ut

2 ,4

In

G re en

N o A ds

3 ,3

O ut

1 ,1

In

G re en

A ds

G re yAnswer: Game tree


5 5

4 ,2

O ut

2 ,4

In

G re en

N o A ds

3 ,3

O ut

1 ,1

In

G re en

A ds

G re y

BA 592 Lesson I.4 Sequential Move ApplicationsBA 592 Lesson I.4 Sequential Move Applications

Answer: Rollback solution.Grey plays Ads and gets payoff 3.Green plays {In if No Ads, Out if Ads} and gets payoff 3.


6 6

Supplementary Question: Supplementary Question: Is there a first mover advantage in Is there a first mover advantage in thethe Advertising GameAdvertising Game??



7 7

Instructor’s Note:Instructor’s Note:• To see if the order matters in any game, rearrange the To see if the order matters in any game, rearrange the

sequence of moves.sequence of moves.• Examples in which order may matter:Examples in which order may matter:

Adoption of new technology. Better to be first or last?Adoption of new technology. Better to be first or last? Class presentation of a project. Better to be first or last?Class presentation of a project. Better to be first or last?

• Sometimes order does not matter, such as the Prisoners’ Sometimes order does not matter, such as the Prisoners’ dilemma with Confess the dominate strategy for both players. dilemma with Confess the dominate strategy for both players.

• Is there such a thing as a second-mover advantage? Is there such a thing as a second-mover advantage? Sometimes, for example:Sometimes, for example: Sequential biding by two contractors.Sequential biding by two contractors. Cake-cutting: One person cuts, the other gets to decide Cake-cutting: One person cuts, the other gets to decide

how the two pieces are allocated.how the two pieces are allocated. Poker.Poker.




Answer to Supplementary Answer to Supplementary Question: Question: Suppose the Suppose the sequence of play in the sequence of play in the Advertising Game is changed Advertising Game is changed so that Green gets to first so that Green gets to first commit to enter the race before commit to enter the race before Grey commits to Ads. The Grey commits to Ads. The payoffs for the possible payoffs for the possible outcomes are exactly the same outcomes are exactly the same as before, except now, Green’s as before, except now, Green’s payoff is listed first.payoff is listed first.

2 ,4

N o A ds

3 ,3

A ds

G re y

O ut

4 ,2

N o A ds

1 ,1

A ds

G re y

In

G re en


9 9

2 ,4

N o A ds

3 ,3

A ds

G re y

O ut

4 ,2

N o A ds

1 ,1

A ds

G re y

In

G re en


Rollback Solution:Green plays In and gets payoff 4.Grey plays {No Ads if Out, No Ads if In} and gets payoff 2.There is a first-mover advantage.



Example 2: Entry DeterrenceExample 2: Entry Deterrence

Question: Question: A monopolist faces the prospect of loosing part of its A monopolist faces the prospect of loosing part of its $10M profit by a potential competitor entering the industry. If the $10M profit by a potential competitor entering the industry. If the competitor elects not to enter, it earns profits of $0 and the competitor elects not to enter, it earns profits of $0 and the monopolist maintains its profit of $10M. If the competitor enters, monopolist maintains its profit of $10M. If the competitor enters, the monopolist must either accommodate the entry or fight. If the the monopolist must either accommodate the entry or fight. If the monopolist accommodates, both firms earn $4M. If the monopolist accommodates, both firms earn $4M. If the monopolist fights, both firms lose $4M. monopolist fights, both firms lose $4M.

Should the competitor enter? Should the competitor enter?

11 11

0 ,10

O ut

4 ,4

A cco m .

-4 ,-4

F ig h t

M o n op o list

In

E n tra n t


Answer: Game tree and its rollback solution.Entrant plays In and gets payoff 4.Monopolist plays Accommodate if In and gets payoff 4.


12 12

Supplementary Question: Supplementary Question: Is there a first mover advantage in theIs there a first mover advantage in the Advertising GameAdvertising Game??




Answer to Supplementary Answer to Supplementary Question: Question: Suppose the Suppose the sequence of play is changed so sequence of play is changed so that Monopolist gets to first that Monopolist gets to first commit to Accommodate or commit to Accommodate or Fight before Entrant commits to Fight before Entrant commits to Entry. The payoffs for the four Entry. The payoffs for the four possible outcomes are exactly possible outcomes are exactly the same as before, except now, the same as before, except now, Monopolist’s payoff is listed Monopolist’s payoff is listed first. first.

1 0 ,0

O ut

4 ,4

In

E n tra n t

A cco m .

1 0 ,0

O ut

-4 ,-4

In

E n tra n t

F ig h t

M o n op o list



Rollback Solution:Monopolist plays Fight and gets payoff 10.Entrant plays {In if Accom., Out if Fight} and gets payoff 0.There is a first-mover advantage.

1 0 ,0

O ut

4 ,4

In

E n tra n t

A cco m .

1 0 ,0

O ut

-4 ,-4

In

E n tra n t

F ig h t

M o n op o list



Example 3: Car LoanExample 3: Car Loan

Question: Question: A bank must decide whether to offer Joe an auto loan A bank must decide whether to offer Joe an auto loan or not. The loan would be for $11,000, and the bank must decide or not. The loan would be for $11,000, and the bank must decide on a total amount L of principal and interest that he must repay at on a total amount L of principal and interest that he must repay at the end of the year. If Joe accepts the loan, he can buy a car the end of the year. If Joe accepts the loan, he can buy a car worth $12,000 to him. He then decides whether to work hard, worth $12,000 to him. He then decides whether to work hard, earning $15,000, or loaf, earning $8,000. Joe would pay up to earning $15,000, or loaf, earning $8,000. Joe would pay up to $5,000 to be able to loaf. Joe has no other assets. If he decides $5,000 to be able to loaf. Joe has no other assets. If he decides not to repay the loan, he loses the car and gets value $500 for not to repay the loan, he loses the car and gets value $500 for using the car for a year, and the bank collects $7,000 by reselling using the car for a year, and the bank collects $7,000 by reselling the car. If Joe keeps the car, it retains its value of $12,000 to him the car. If Joe keeps the car, it retains its value of $12,000 to him even if it is a year old. Consider an interest rate of 0%.even if it is a year old. Consider an interest rate of 0%.

Should the bank offer a loan? Should the bank offer a loan? If so, what should be the principal If so, what should be the principal and interest?and interest?



Answer: Answer: The Bank first decides whether to offer a loan, and at The Bank first decides whether to offer a loan, and at what principal and interest L. Since L can be any real number, what principal and interest L. Since L can be any real number, we cannot draw a full game graph because it would have a we cannot draw a full game graph because it would have a continuum of branches coming off it. So first fix L, then graph continuum of branches coming off it. So first fix L, then graph the subgame. The Bank looses money if L < 11 (thousand), so the subgame. The Bank looses money if L < 11 (thousand), so just consider L just consider L >> 11. 11.

The decision nodes in the subgame are in this order. The decision nodes in the subgame are in this order. Bank: Offer loan or or don't offer one. Bank: Offer loan or or don't offer one. Joe: Accept or reject the offer. Joe: Accept or reject the offer. Joe: Work or loaf. (If he loafs, he does not have the money to Joe: Work or loaf. (If he loafs, he does not have the money to pay back the loan.) pay back the loan.) Joe: Repay or lose the car to the bank. Joe: Repay or lose the car to the bank.



Subgame graph given L:If the Bank does not offer a loan, or if Joe turns down the loan, its payoff is 0 and Joe’s is 15 if he works or 13 (8+5) if he loafs. If Joe works and repays, the Bank gets L-11 and Joe gets 15+12 -L; if he does not repay, the Bank gets 7-11 and Joe gets 15. If Joe loafs and so does not repay, the Bank gets 7-11 and Joe gets 8+5.

0 , 13

L oa f

0 , 15

W o rk

Joe

N o O ffe r

0 , 13

L oa f

0 , 15

W o rk

Joe

R e je c t L

-4 , 1 3 .5

D o n 't P ay

Joe

L oa f

-4 , 1 5 .5

D o n 't P ay

L -11 , 27 -L

P a y

Joe

W o rk

Joe

A ccep t L

Joe

O ffe r Lo an

B a nk



Some of Joe’s ChoicesSome of Joe’s Choices are independent of L. are independent of L.

0 , 13

L oa f

0 , 15

W o rk

Joe

N o O ffe r

0 , 13

L oa f

0 , 15

W o rk

Joe

R e je c t L

-4 , 1 3 .5

D o n 't P ay

Joe

L oa f

-4 , 1 5 .5

D o n 't P ay

L -11 , 27 -L

P a y

Joe

W o rk

Joe

A ccep t L

Joe

O ffe r Lo an

B a nk



When When L > 11.5:L > 11.5:The equilibrium path is The equilibrium path is the Bank does not offer the Bank does not offer the loan, and Joe works. the loan, and Joe works. That path ends in That path ends in payoff 0 for the bank. payoff 0 for the bank.

0 , 13

L oa f

0 , 15

W o rk

Joe

N o O ffe r

0 , 13

L oa f

0 , 15

W o rk

Joe

R e je c t L

-4 , 1 3 .5

D o n 't P ay

Joe

L oa f

-4 , 1 5 .5

D o n 't P ay

L -11 , 27 -L

P a y

Joe

W o rk

Joe

A ccep t L

Joe

O ffe r Lo an

B a nk



When When L = 11.5:L = 11.5:There are multiple There are multiple rollback solutions rollback solutions because if the Bank because if the Bank Offers Loan, and Joe Offers Loan, and Joe Accepts Loan, and Joe Accepts Loan, and Joe Works, then Joe is Works, then Joe is indifferent between Not indifferent between Not Paying Back the Loan, Paying Back the Loan, and Paying Back the and Paying Back the Loan.Loan.

Let us avoid this case. Let us avoid this case.

0 , 13

L oa f

0 , 15

W o rk

Joe

N o O ffe r

0 , 13

L oa f

0 , 15

W o rk

Joe

R e je c t L

-4 , 1 3 .5

D o n 't P ay

Joe

L oa f

-4 , 1 5 .5

D o n 't P ay

L -11 , 27 -L

P a y

Joe

W o rk

Joe

A ccep t L

Joe

O ffe r Lo an

B a nk



When When 11 11 << L < 11.5: L < 11.5:The Bank’s strategy The Bank’s strategy is offer the loan, and is offer the loan, and it gets payoff L-11.it gets payoff L-11.

0 , 13

L oa f

0 , 15

W o rk

Joe

N o O ffe r

0 , 13

L oa f

0 , 15

W o rk

Joe

R e je c t L

-4 , 1 3 .5

D o n 't P ay

Joe

L oa f

-4 , 1 5 .5

D o n 't P ay

L -11 , 27 -L

P a y

Joe

W o rk

Joe

A ccep t L

Joe

O ffe r Lo an

B a nk



The Bank’s rollback equilibrium payoffs thus depend on L:• If If L > 11.5, L > 11.5, payoff = 0.payoff = 0.• IfIf L = 11.5, L = 11.5, there are multiple rollback equilibria.there are multiple rollback equilibria.• If If 11 11 << L < 11.5, L < 11.5, payoff = Lpayoff = L11.11.

Should the bank offer a loan? If so, what should be the principal Should the bank offer a loan? If so, what should be the principal and interest? and interest? Yes, offer the loan at principal and interest L = Yes, offer the loan at principal and interest L = 11.5-11.5-, and so earn payoff .5, and so earn payoff .5. Joe earns payoff 15.5+. Joe earns payoff 15.5+, which is , which is .5+.5+ more than if he did not get the loan. more than if he did not get the loan.


Example 4: RenegotiationExample 4: Renegotiation

Supplementary Question: Supplementary Question: Now suppose Joe has another option: if Now suppose Joe has another option: if Joe loafs and so cannot repay the full amount of the loan, he can Joe loafs and so cannot repay the full amount of the loan, he can offer the bank some smaller amount S not to foreclose on the offer the bank some smaller amount S not to foreclose on the loan and repossess the car. loan and repossess the car.

What would that amount S be? What would that amount S be? How does the outcome change if How does the outcome change if both Joe and the bank know that this kind of renegotiation is both Joe and the bank know that this kind of renegotiation is possible? possible?



The bank collects The bank collects $7,000 by reselling the $7,000 by reselling the car, so if Joe loafs and car, so if Joe loafs and offers any S > $7,000, offers any S > $7,000, then the Bank would then the Bank would accept. So offer S = accept. So offer S = $7,000+e. Hence, the $7,000+e. Hence, the game tree changes:game tree changes:

0 , 13

L oa f

0 , 15

W o rk

Joe

N o O ffe r

0 , 13

L oa f

0 , 15

W o rk

Joe

R e je c t L

-4 + e , 1 8 -e

R e ne g o tia te

Joe

L oa f

-4 , 1 5 .5

D o n 't P ay

L -11 , 27 -L

P a y

Joe

W o rk

Joe

A ccep t L

Joe

O ffe r Lo an

B a nk


When When L > 11.5:L > 11.5:The equilibrium path is The equilibrium path is the Bank does not offer the Bank does not offer the loan, and Joe works. the loan, and Joe works. That path ends in That path ends in payoff 0 for the bank. payoff 0 for the bank.

0 , 13

L oa f

0 , 15

W o rk

Joe

N o O ffe r

0 , 13

L oa f

0 , 15

W o rk

Joe

R e je c t L

-4 + e , 1 8 -e

R e ne g o tia te

Joe

L oa f

-4 , 1 5 .5

D o n 't P ay

L -11 , 27 -L

P a y

Joe

W o rk

Joe

A ccep t L

Joe

O ffe r Lo an

B a nk



When When 11 11 << L < 11.5: L < 11.5:The Bank’s strategy The Bank’s strategy is offer the loan, and is offer the loan, and it gets payoff L-11.it gets payoff L-11.

0 , 13

L oa f

0 , 15

W o rk

Joe

N o O ffe r

0 , 13

L oa f

0 , 15

W o rk

Joe

R e je c t L

-4 + e , 1 8 -e

R e ne g o tia te

Joe

L oa f

-4 , 1 5 .5

D o n 't P ay

L -11 , 27 -L

P a y

Joe

W o rk

Joe

A ccep t L

Joe

O ffe r Lo an

B a nk




Summary: Summary: When Joe has the option to loaf and offer the bank When Joe has the option to loaf and offer the bank some smaller amount S not to foreclose on the loan and repossess some smaller amount S not to foreclose on the loan and repossess the car, he would offer S = $7,000+e. But when both Joe and the the car, he would offer S = $7,000+e. But when both Joe and the Bank know that this kind of renegotiation is possible, the Bank Bank know that this kind of renegotiation is possible, the Bank no longer offers the loan, which eliminates the previous gains of no longer offers the loan, which eliminates the previous gains of payoff .5-e to the Bank and .5+e to Joe. payoff .5-e to the Bank and .5+e to Joe.


Example 5: Compatible Web BrowsersExample 5: Compatible Web Browsers

Question: Question: Microsoft and Google are planning to introduce a new Microsoft and Google are planning to introduce a new type of Web browser. They must choose between two platforms, type of Web browser. They must choose between two platforms, ActiveX and Java. If they introduce different platforms, their ActiveX and Java. If they introduce different platforms, their profits are zero. If they introduce the same platform, their profits profits are zero. If they introduce the same platform, their profits are 1, plus Microsoft gets 1 more if the platform is ActiveX and are 1, plus Microsoft gets 1 more if the platform is ActiveX and Google gets 1 more if the platform is Java.Google gets 1 more if the platform is Java.

Which platform should Microsoft choose if it can choose first?Which platform should Microsoft choose if it can choose first?Which platform should Google choose if it can choose first?Which platform should Google choose if it can choose first?Is there a first mover advantage?Is there a first mover advantage?Now suppose Microsoft can choose first unless Google rushes Now suppose Microsoft can choose first unless Google rushes development of their browser. Rushing development cost Google development of their browser. Rushing development cost Google 0.5, and it allows Google to choose their platform first. 0.5, and it allows Google to choose their platform first. Should Google rush their development?Should Google rush their development?


Answer: Answer: Which platform Which platform should Microsoft choose if it should Microsoft choose if it can choose first? ActiveX, can choose first? ActiveX, giving Microsoft 2 and Google giving Microsoft 2 and Google 1.1.Which platform should Google Which platform should Google choose if it can choose first? choose if it can choose first? Java, giving Microsoft 1 and Java, giving Microsoft 1 and Google 2.Google 2.Is there a first mover Is there a first mover advantage? Yes, either firm advantage? Yes, either firm earns 1 more moving first earns 1 more moving first rather than second.rather than second.Should Google rush? Should Google rush? Yes, they Yes, they earn 1 more at a cost of 0.5earn 1 more at a cost of 0.5

2 ,1

A c tiveX

0 ,0

Ja va

G oo g le

A c tiveX

0 ,0

A c tiveX

1 ,2

Ja va

G oo g le

Ja va

M ic ro so ft

Example 5: Compatible Web BrowsersExample 5: Compatible Web Browsers

1 ,2

A c tiveX

0 ,0

Ja va

M ic ro so ft

A c tiveX

0 ,0

A c tiveX

2 ,1

Ja va

M ic ro so ft

Ja va

G oo g le


Example 6: Evicting TenantsExample 6: Evicting Tenants

Question: Question: A landlord has three tenants, Alfred, Betty, and A landlord has three tenants, Alfred, Betty, and Charlie, in a rent-controlled apartment building in New York Charlie, in a rent-controlled apartment building in New York City. A new law says that the landlord has the right to evict one City. A new law says that the landlord has the right to evict one tenant per building. The landlord calculates that the value of a tenant per building. The landlord calculates that the value of a vacant apartment is $15,000, both to the tenant and to her. She vacant apartment is $15,000, both to the tenant and to her. She sends the following letter to each of her tenants: “Tomorrow I sends the following letter to each of her tenants: “Tomorrow I will be visiting your building. I will offer A $1,000 if he agrees will be visiting your building. I will offer A $1,000 if he agrees to vacate his apartment voluntarily; otherwise, I will evict him. If to vacate his apartment voluntarily; otherwise, I will evict him. If A agrees to vacate voluntarily, I will then offer B $1,000 if she A agrees to vacate voluntarily, I will then offer B $1,000 if she agrees to vacate his apartment voluntarily; otherwise, I will evict agrees to vacate his apartment voluntarily; otherwise, I will evict her. If B agrees to vacate voluntarily, I will evict C.”her. If B agrees to vacate voluntarily, I will evict C.”

How many vacant apartments will the landlord have? What How many vacant apartments will the landlord have? What profit will the landlord have?profit will the landlord have?


Answer:Answer: This is a game This is a game between tenants A and B. (The between tenants A and B. (The Landlord has committed to the Landlord has committed to the letter, and C has no choices.) A letter, and C has no choices.) A and B both vacate, and C gets and B both vacate, and C gets evicted.evicted.

The landlord thus gains 3 The landlord thus gains 3 vacant apartments and pays vacant apartments and pays $2,000. So the landlord gains $2,000. So the landlord gains $45,000 = $43,000 $45,000 = $43,000 $2,000. $2,000.

-1 5 , 0

G e t E v ic ted

-1 4 , -15

G e t E v ic ted

-1 4 ,-14

V a ca te

B

V a ca te

A

Example 6: Evicting TenantsExample 6: Evicting Tenants


Example 7: Strategic VotingExample 7: Strategic Voting

Question: Question: Three legislators, Alfred, Betty, and Charlie, are voting Three legislators, Alfred, Betty, and Charlie, are voting on whether to give themselves a pay raise. The raise is worth b, on whether to give themselves a pay raise. The raise is worth b, but each legislator who votes for the raise incurs a cost of voter but each legislator who votes for the raise incurs a cost of voter resentment equal to a < b. The outcome is decided by majority resentment equal to a < b. The outcome is decided by majority rule. A votes first, then B sees A’s choice and votes, then C sees rule. A votes first, then B sees A’s choice and votes, then C sees A’s and B’s choice and votes.A’s and B’s choice and votes.

How should A vote?How should A vote?


Answer:Answer: A should vote A should vote AgainstAgainst, believing that , believing that B and C will then vote B and C will then vote ForFor the raise. the raise.

b -a ,b -a ,b -a

F o r

b -a ,b -a ,b

A g a in st

C

F o r

b -a ,b ,b -a

F o r

-a ,0 ,0

A g a in st

C

A g a in st

B

F o r

b ,b -a ,b -a

F o r

0 ,-a ,0

A g a in st

C

F o r

0 ,0 ,-a

F o r

0 ,0 ,0

A g a in st

C

A g a in st

B

A g a in st

A

Example 7: Strategic VotingExample 7: Strategic Voting


Example 8: Nuisance Suits Example 8: Nuisance Suits

Question: Question: Alfred contemplates suing Betty over the purported Alfred contemplates suing Betty over the purported damage done to Alfred’s son sustained while using the bike jump damage done to Alfred’s son sustained while using the bike jump in Betty’s yard. Suppose A’s court cost for initiating a suit is a, in Betty’s yard. Suppose A’s court cost for initiating a suit is a, his legal costs of going to trial are b, and Betty’s cost of his legal costs of going to trial are b, and Betty’s cost of defending herself is c. Suppose both sides know these costs and defending herself is c. Suppose both sides know these costs and also share the knowledge that the probability that A will win the also share the knowledge that the probability that A will win the suit is p and the expected amount of the settlement is x. Assume suit is p and the expected amount of the settlement is x. Assume px < bpx < b. Finally, suppose that before the case goes to trial (but . Finally, suppose that before the case goes to trial (but after the suit is initiated), the parties can settle out of court for the after the suit is initiated), the parties can settle out of court for the amount s.amount s.

Should A file suit?Should A file suit?


Answer:Answer: There are two There are two rollback solutions, depending rollback solutions, depending on whether A choose on whether A choose Offer to Offer to Settle Settle or or No Offer to SettleNo Offer to Settle. . But in either rollback solution, But in either rollback solution, A does not file suit.A does not file suit.

0 ,0

N o S u it

p x -a -b ,-p x -c

P u rsue S u it

-a ,0

D ro p S .

A

N o O ffe r

p x -a -b ,-p x -c

P u rsue S u it

-a ,0

D ro p S .

A

R e je ct O ffe r

s -a ,-s

A ccep t O .

B

O ffe r S e tt le

A

F ile S u it

A

Example 8: Nuisance Suits Example 8: Nuisance Suits

36 36BA 592 Lesson I.4 Sequential Move Applications

Review ProblemsReview Problems

Mall Location GameMall Location Game

Page 83, Question S8.Page 83, Question S8.

AnswerAnswer

37 37BA 592 Lesson I.4 Sequential Move Applications

Review ProblemsReview Problems

Political GamePolitical Game

Page 85, Question U4.Page 85, Question U4.

AnswerAnswer

38 38

End of Lesson I.4End of Lesson I.4

BA 592 Game BA 592 Game TheoryTheory

BA 592 Lesson I.4 Sequential Move Applications

1 1 lesson overview ba 592 lesson i.4 sequential move applications chapter 3 games with sequential...

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