1 1 Deep Thought BA 445 Lesson C.2 Cheap Talk when Interests Align A verbal contract isn’t worth the paper it’s written on. ~ Yogi Berra (Translation:

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Deep Thought

BA 445 Lesson C.2 Cheap Talk when Interests Align

A verbal contract isn’t worth the paper it’s written on. ~ Yogi Berra

(Translation: Today’s lesson teaches how talk is cheap.)

2 2BA 445 Lesson C.2 Cheap Talk when Interests Align

Readings

Readings

Baye “Coordination Game” (see the index)Dixit Chapter 9


Overview

Overview

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Lesson 2 considers games where players easily reveal information about their own moves when players’ interests align.


Overview

5 5

Overview


Cheap Talk given Minor Conflict is a good way to make your action predictable to your allies (whose interests align). It can change outcomes by changing players’ beliefs about other players’ actions.

Cheap Talk given Major Conflict is disregarded by opponents (whose interests conflict) since, if they believed you, you could exploit that belief. — So, an employer should disregard a shirker’s self assessment.

Cheap Talk given Perfect Conflict is disregarded by opponents since, if they believed you, you could exploit that belief. — So, a goalie should disregard a kicker saying “I’ll kick left”.


Example 1: Cheap Talk given Minor Conflict



Overview

Cheap Talk given Minor Conflict is a good way to make your actions predictable to your allies (whose interests align). It can change outcomes by changing players’ beliefs about other players’ actions.



Comment: The simplest way to give information to others seems to be to tell them, and the simplest way to get information is to ask. But in a game of strategy, players are aware that others may not tell the truth, and there own talk may not be believed by others. It is said that talk is cheap; that is, talk has zero or negligible direct cost. However, it can indirectly affect the outcome and payoffs of a game by changing one player’s beliefs about another player’s actions, and so selecting one equilibrium out of multiple equilibria.



Call talk that has no direct cost cheap talk. For a game with cheap talk, call an equilibrium that is affected by talk a cheap-talk equilibrium. The central question is whether it is possible that the speaker tells the truth, or whether he must be lying. So for each cheap-talk game, ask: Is there a cheap-talk equilibrium with truthful communication?



Question: Consider the Format Game between The Blu-ray Disc Association and Toshiba. Suppose that at the same time each player either adopts the Blu-ray format or the HD format. Suppose if both adopt the same format, then both gain $100 million from customers that value the convenience of having a universal format. Suppose if they both adopt the Blu-ray format, then The Blu-ray Disc Association gains an extra $10 million since their expertise with that format gives them lower production costs. Suppose if they both adopt the HD format, then Toshiba gains an extra $10 million since their expertise with that format gives them lower production costs. Finally, suppose that, before the game is played, The Blu-ray Disc Association is given an opportunity to communicate either “I will choose Blu-ray” or “I will choose HD”.

Is there a cheap-talk equilibrium with truthful communication? If so, find it.



Answer: First, complete the normal form below for the Format Game. For example, if The Blu-ray Disc Association and Toshiba both adopt HD, then both gain $100 million from customers that value the convenience of having a universal format, and Toshiba gains an extra $10 million since their expertise with the HD format gives them lower production costs.

Blu-ray HDBlu-ray 110,100 0,0HD 0,0 100,110

Toshiba

Blu-ray



Define a game tree of this Cheap-Talk-Format Game. Create a first stage to the game where The Blu-ray Disc Association makes one of two statements --- “I will choose Blu-ray” or “I will choose HD”. The second stage is Toshiba’s choice of format --- assuming Toshiba believes Blu-ray’s statement. And the third stage is The Blu-ray Disc Association’s choice of format --- after they deduced Toshiba’s choice based on Toshiba believing Blu-ray’s statement.



Game Tree:

1 1 0,1 00

B lu -ra y

0 ,0

H D

A sso cia tion

B lu -ra y

0 ,0

B lu -ra y

1 0 0,1 10

H D

A sso cia tion

H D

T o sh iba

I w ill ch o ose B lu -ray

1 1 0,1 00

B lu -ra y

0 ,0

H D

A sso cia tion

B lu -ra y

0 ,0

B lu -ra y

1 0 0,1 10

H D

A sso cia tion

H D

T o sh iba

I w ill ch o o se H D

A sso cia tion



Modified Rollback Solution: First, Toshiba’s choice of format --- assuming Toshiba believes Blu-ray’s statement.

1 1 0 ,1 00

B lu -ra y

0 ,0

H D

A s s o c ia tio n

B lu -ra y

0 ,0

B lu -ra y

1 0 0 ,1 10

H D

A s s o c ia tio n

H D

T o s h iba

I w ill c h o o s e B lu -ra y

1 1 0 ,1 00

B lu -ra y

0 ,0

H D

A s s o c ia tio n

B lu -ra y

0 ,0

B lu -ra y

1 0 0 ,1 10

H D

A s s o c ia tio n

H D

T o s h iba

I w ill c h o o s e H D

A s s o c ia tio n



Modified Rollback Solution: Second, Association’s choice of format --- after they deduced Toshiba’s choice.

1 1 0 ,1 00

B lu -ra y

0 ,0

H D

A s s o c ia tio n

B lu -ra y

0 ,0

B lu -ra y

1 0 0 ,1 10

H D

A s s o c ia tio n

H D

T o s h iba


1 1 0 ,1 00

B lu -ra y

0 ,0

H D

A s s o c ia tio n

B lu -ra y

0 ,0

B lu -ra y

1 0 0 ,1 10

H D

A s s o c ia tio n

H D

T o s h iba


A s s o c ia tio n



Modified Rollback Solution: Finally, Association’s choice of statement. Was communication truthful? Yes.

1 1 0 ,1 00

B lu -ra y

0 ,0

H D

A s s o c ia tio n

B lu -ra y

0 ,0

B lu -ra y

1 0 0 ,1 10

H D

A s s o c ia tio n

H D

T o s h iba


1 1 0 ,1 00

B lu -ra y

0 ,0

H D

A s s o c ia tio n

B lu -ra y

0 ,0

B lu -ra y

1 0 0 ,1 10

H D

A s s o c ia tio n

H D

T o s h iba


A s s o c ia tio n



Example 2: Cheap Talk given Major Conflict



Overview

Cheap Talk given Major Conflict is disregarded by opponents (whose interests conflict) since, if they believed you, you could exploit that belief. — So, an employer should disregard a shirker’s self assessment.



Question: Consider the Work-Shirk Game for an employee and an employer. Suppose that at the same time the employee chooses to either work or shirk (not work) and the employer chooses to either monitor the employee or not monitor the employee. Suppose if the employee chooses to work, he looses $100 of happiness from the effort of working, but he yields $400 to his employer. Suppose the employer can monitor the employee at a cost of $80. Suppose if the employee chooses to not work and the employer chooses to monitor, then the employee is not paid, but in every other case (“work” or “not monitor”), then the employee is paid $150. Finally, suppose that, before the game is played, the employer is given an opportunity to communicate either “I will monitor” or “I will not monitor”.




Answer: First, complete the normal form below for the Work-Shirk Game. For example, if the employee chooses to work and the employer chooses to monitor, then the employee looses $100 of happiness from the effort of working but is paid $150, and the employer gain $400 from his employer but pays $80 for monitoring and pays $150 to his employee.

Monitor TrustWork 50,170 50,250Shirk 0,-80 150,-150

Employer

Employee



Define a game tree of this Cheap-Talk-Work-Shirk Game. Create a first stage to the game where the employer makes one of two statements --- “I will monitor” or “I will not monitor”. The second stage is the employee’s choice of work --- assuming the employee believes the employer’s statement. And the third stage is the employer’s choice of monitoring --- after they deduced the employee’s choice based on the employee believing the employer’s statement.



Game Tree:

5 0 ,1 70

M o n ito r

5 0 ,2 50

T ru s t

E m p lo ye r

W o rk

0 ,-80

M o n ito r

1 5 0 ,-1 50

T ru s t

E m p lo ye r

S h irk

E m p lo yee

I w ill ch o ose m o n ito r

5 0 ,1 70

M o n ito r

5 0 ,2 50

T ru s t

E m p lo ye r

W o rk

0 ,-80

M o n ito r

1 5 0 ,-1 50

T ru s t

E m p lo ye r

S h irk

E m p lo yee

I w ill ch oo se tru st

E m p lo ye r


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Modified Rollback Solution: First, Employee’s choice of work -- assuming Employee believes Employer’s statement.

5 0 ,1 70

M o n ito r

5 0 ,2 50

T ru s t

E m p lo ye r

W o rk

0 ,-80

M o n ito r

1 5 0 ,-1 50

T ru s t

E m p lo ye r

S h irk

E m p lo yee


5 0 ,1 70

M o n ito r

5 0 ,2 50

T ru s t

E m p lo ye r

W o rk

0 ,-80

M o n ito r

1 5 0 ,-1 50

T ru s t

E m p lo ye r

S h irk

E m p lo yee


E m p lo ye r


Modified Rollback Solution: Second, Employer’s choice of monitor --- after they deduced Employee’s choice.

5 0 ,1 70

M o n ito r

5 0 ,2 50

T ru s t

E m p lo ye r

W o rk

0 ,-80

M o n ito r

1 5 0 ,-1 50

T ru s t

E m p lo ye r

S h irk

E m p lo yee


5 0 ,1 70

M o n ito r

5 0 ,2 50

T ru s t

E m p lo ye r

W o rk

0 ,-80

M o n ito r

1 5 0 ,-1 50

T ru s t

E m p lo ye r

S h irk

E m p lo yee


E m p lo ye r



Modified Rollback Solution: Finally, Employer’s choice of statement. Was communication truthful? No. So ignore the original message.

5 0 ,1 70

M o n ito r

5 0 ,2 50

T ru s t

E m p lo ye r

W o rk

0 ,-80

M o n ito r

1 5 0 ,-1 50

T ru s t

E m p lo ye r

S h irk

E m p lo yee


5 0 ,1 70

M o n ito r

5 0 ,2 50

T ru s t

E m p lo ye r

W o rk

0 ,-80

M o n ito r

1 5 0 ,-1 50

T ru s t

E m p lo ye r

S h irk

E m p lo yee


E m p lo ye r



Comment: Since there is no cheap-talk equilibrium with truthful communication, the original message should be ignored, and the game reduces to the original work-shirk game.

The Nash equilibrium strategy for the Employee is the mixed strategy for which the Employer would not benefit if he could predict the Employee’s mixed strategy. Suppose the Employer predicts p and (1-p) are the probabilities the Employee chooses Work or Shirk. The Employer expects 170p - 80(1-p) from playing Monitor, and 250p - 150(1-p) from Trust. The Employer does not benefit if those payoffs equal, 170p - 80(1-p) = 250p - 150(1-p), or -80 + 250p = -150 + 400p,or p = 70/150 = 0.467


Employer

Employee



The Nash equilibrium strategy for the Employer is the mixed strategy for which the Employee would not benefit if he could predict the Employer’s mixed strategy. Suppose the Employee predicts q and (1-q) are the probabilities the Employer chooses Monitor or Trust. The Employee expects 50q + 50(1-q) from playing Work, and 0q + 150(1-q) from Shirk. The Employee does not benefit if those payoffs equal, 50q + 50(1-q) = 0q + 150(1-q), or 50 = 150 – 150q,or q = 100/150 = 0.667


Employer

Employee



Example 3: Cheap Talk given Perfect Conflict



Overview

Cheap Talk given Perfect Conflict is disregarded by opponents since, if they believed you, you could exploit that belief. — So, a goalie should disregard a kicker saying “I’ll kick left”.


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Left RightLeft .1,.9 .8,.2Right .4,.6 .3,.7

Goalie

Kicker


Question: Consider a penalty kick in soccer. The goalie either jumps left or right at the same time that the kicker either kicks left or right. The kicker’s payoffs are the probability of him scoring, and the goalie’s payoffs are the probability of the kicker not scoring. Those actions and payoffs define a normal form for this Penalty Kick Game. Finally, suppose that, before the game is played, the kicker is given an opportunity to communicate either “I will kick left” or “I will kick right”.



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Answer: Define a game tree of this Cheap-Talk-Penalty-Kick Game. Create a first stage to the game where the kicker makes one of two statements --- “I will kick left” or “I will kick right”. The second stage is the goalie’s choice of jumping left or right --- assuming the goalie believes the kicker’s statement. And the third stage is the kicker’s choice of kicking left or right --- after he deduced the goalie’s choice based on the goalie believing the kicker’s statement.

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0 .1 ,0 .9

L e ft

0 .4 ,0 .6

R ig h t

K icke r

L e ft

0 .8 ,0 .2

L e ft

0 .3 ,0 .7

R ig h t

K icke r

R ig h t

G o a lie

I w ill k ic k L e ft

0 .1 ,0 .9

L e ft

0 .4 ,0 .6

R ig h t

K icke r

L e ft

0 .8 ,0 .2

L e ft

0 .3 ,0 .7

R ig h t

K icke r

R ig h t

G o a lie

I w ill k ic k R ig h t

K icke r


Game Tree:


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0 .1 ,0 .9

L e ft

0 .4 ,0 .6

R ig h t

K icke r

L e ft

0 .8 ,0 .2

L e ft

0 .3 ,0 .7

R ig h t

K icke r

R ig h t

G o a lie


0 .1 ,0 .9

L e ft

0 .4 ,0 .6

R ig h t

K icke r

L e ft

0 .8 ,0 .2

L e ft

0 .3 ,0 .7

R ig h t

K icke r

R ig h t

G o a lie


K icke r



Modified Rollback Solution: First, Goalie’s choice --- assuming Goalie believes Kicker’s statement. Goalie eliminates the choices in black.


0 .1 ,0 .9

L e ft

0 .4 ,0 .6

R ig h t

K icke r

L e ft

0 .8 ,0 .2

L e ft

0 .3 ,0 .7

R ig h t

K icke r

R ig h t

G o a lie


0 .1 ,0 .9

L e ft

0 .4 ,0 .6

R ig h t

K icke r

L e ft

0 .8 ,0 .2

L e ft

0 .3 ,0 .7

R ig h t

K icke r

R ig h t

G o a lie


K icke r


Modified Rollback Solution: Second, Kicker’s choice --- after he deduced Goalie’s choice. Kicker eliminates the choices in black.

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0 .1 ,0 .9

L e ft

0 .4 ,0 .6

R ig h t

K icke r

L e ft

0 .8 ,0 .2

L e ft

0 .3 ,0 .7

R ig h t

K icke r

R ig h t

G o a lie


0 .1 ,0 .9

L e ft

0 .4 ,0 .6

R ig h t

K icke r

L e ft

0 .8 ,0 .2

L e ft

0 .3 ,0 .7

R ig h t

K icke r

R ig h t

G o a lie


K icke r


Finally, Kicker’s choice of statement. Kicker says “I will kick Right” but he actually kicks Left. Was communication truthful? No. So ignore the original message.



Comment: Since there is no cheap-talk equilibrium with truthful communication, the original message should be ignored, and the game reduces to the original penalty-kick game.

The Nash equilibrium strategy for the Kicker is the mixed strategy for which the Goalie would not benefit if he could predict the Kicker’s mixed strategy. Suppose the Goalie predicts p and (1-p) are the probabilities the Kicker chooses Left or Right. The Goalie expects .9p + .6(1-p) from playing Left, and .2p + .7(1-p) from Right. The Goalie does not benefit if those payoffs equal, .9p + .6(1-p) = .2p + .7(1-p), or .6 + .3p = .7 - .5p, or p = 1/8 = 0.125


Goalie

Kicker



The Nash equilibrium strategy for the Goalie is the mixed strategy for which the Kicker would not benefit if he could predict the Goalie’s mixed strategy. Suppose the Kicker predicts q and (1-q) are the probabilities the Goalie chooses Left or Right. The Kicker expects .1q + .8(1-q) from playing Left, and .4q + .3(1-q) from Right. The Kicker does not benefit if those payoffs equal, .1q + .8(1-q) = .4q + .3(1-q), or .8 - .7q = .3 + .1q, orq = 5/8 = 0.625


Goalie

Kicker


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Review Questions


Review Questions You should try to answer some of the review questions

(see the online syllabus) 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 cumulative Final Exam will contain

some similar questions, so you should eventually consider every review question before taking your exams.

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End of Lesson C.2


BA 445 Managerial Economics

1 1 Deep Thought BA 445 Lesson C.2 Cheap Talk when Interests Align A verbal contract isn’t worth the paper it’s written on. ~ Yogi Berra (Translation:

Documents

overview cheap talk

direct cost cheap talk

interests conflict

players interests

minor conflict slide

players actions

todays lesson

players beliefs