1 1 deep thought ba 445 lesson c.3 signaling worker quality to recommend a lazy job candidate: in my...

1 1

Deep Thought

BA 445 Lesson C.3 Signaling Worker Quality

To recommend a lazy job candidate: In my opinion, you will be very fortunate to get this person to work for you.To recommend a person who is totally inept: I most enthusiastically recommend this candidate with no qualifications whatsoever.To describe an ex-employee who had problems getting along with fellow workers: I am pleased to say that this candidate is a former colleague of mine.To describe a candidate who is so unproductive that the job would be better left unfilled: I can assure you that no person would be better for the job.

(Translation: Today’s lesson teaches how to access a job applicant when cheap talk is worthless.)

2 2BA 445 Lesson C.3 Signaling Worker Quality

Readings

Readings

Baye “Signaling” (see the index)Dixit Chapter 9


Overview

Overview

4 4

Lessons 3 and 4 consider games where players want to reveal information about themselves (not just about their actions, as in Lessons 1 and 2) but they find it hard because their interests conflict. In particular, cheap talk is not believable.

For example, consider King Solomon’s Dilemma:

Two women came before King Solomon, disputing who was the true mother of a child. The Bible takes up the story in 1 Kings 3:24-28 …


Overview

5 5

Then the king said, “Bring me a sword.” So they brought a sword for the king. He then gave an order: “Cut the living child in two and give half to one and half to the other.” The woman whose son was alive was filled with compassion for her son and said to the king, “Please, my lord, give her the living baby! Don’t kill him!” But the other said, “Neither I nor you shall have him. Cut him in two!” Then the king gave his ruling: “Give the living baby to the first woman. Do not kill him; she is the mother.” When all Israel heard the verdict the king had given, they held the king in awe, because they saw that he had wisdom from God to administer justice.


Overview

6 6

King Solomon was indeed wise. But he was also lucky. How would the story have been different if the second woman had studied game theory?


Overview

7 7

Overview


Adverse Selection and Market Failure can result from asymmetric information. — So, good workers may not be offered a worthy pooled wage if they cannot distinguish themselves from bad workers.

Signaling and Screening can cure market failure but at a cost. — So, good workers may distinguish themselves from bad workers at the cost of enduring hard college courses that bad workers avoid.

The Dilemma of Pooling is a type of prisoners’ dilemma that makes costly signaling and screening persist even when all parties to a trade prefer to trading at a common pooled price.


Example 1: Adverse Selection and Market Failure



Overview

Adverse Selection and Market Failure can result from asymmetric information. — So, good workers may not be offered a worthy pooled wage if they cannot distinguish themselves from bad workers.



Comment: Employers know less about the skills of potential employees than does the employee, with other important matters like work attitude and collegiality even harder to observe. Buyers of used cars know less about a car than do the sellers. And insurance companies know less about the heath and driving skills of insurance applicants than do the applicants.

In those examples, cheap talk cannot be screened for information by the less informed player. Unskilled, lazy, and obnoxious potential employees will claim to have skills and will act hard working and collegial during interviews to get higher pay. Sellers of used cars will withhold any problems about their cars. And insurance applicants who are bad risks will claim good health and driving habits to get lower rates. For those same reasons, cheap talk cannot signal information by the more informed player since the other player knows there are incentives to lie.



If there are no other ways to screen or signal information, then insurance companies would have to offer the same rates to all applicants, say 5 cents per dollar of coverage. That rate would be especially attractive to applicants who know there own risk (of illness or car crash) exceeds 5%. Hence, the pool of applicants for that insurance policy will have a larger proportion of poorer risks than the proportion of those risks in the population as a whole. The insurance company thus selectively attracts an unfavorable, or adverse, group of customers. That phenomenon is common in transactions involving asymmetric information (one player knows more than the other) and is known as adverse selection.

Adverse selection can exclude some mutually-beneficial agreements.



Question: Suppose Employer Earl has use for two kinds of employees. Skilled and hard working Type A (impatient, time-conscious, status-conscious, ambitious) employees contribute $160,000 per year to profits. And Type B (patient, easy-going, apathetic) employees contribute $60,000 per year to profits.

Suppose Type A workers have existing jobs paying $125,000 per year, and Type B have existing jobs paying $30,000 per year. Suppose there is no way for the employer to tell Type A workers from Type B workers and, so, must offer each the same wage. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter).

Determine the wage demand, and which types work for Employer Earl.



Answer: The wage demand depends on the positive fraction f of Type A workers and the remaining positive fraction (1-f ) of Type B workers in the general population. A random worker in the general population is thus Type A with probability f and Type B with probability (1-f ). The expected value of a random worker is $160,000 x f + $60,000 x (1-f ) = $60,000 + $100,000 x f .

In particular, $60,000 + $100,000 x f is the best acceptable wage demand from a random worker in the general population.

But is that wage enough for both types to gain from employment?

Type A Type Bto Employer $160K $60K

of Self $125K $30K

The Worker is a

Value/Cost



On the one hand, if $60,000 + $100,000 x f > $125,000, or f > 0.65, then both types of workers gain from Employment with Earl. So $60,000 + $100,000 x f is, indeed, the wage demand, and both types work for Employer Earl.

On the other hand, if $60,000 + $100,000 x f < $125,000, or f < 0.65, then Type A workers would loose from Employment with Earl. So only Type B workers make wage demands. Anticipating that, the expected value of a random job applicant falls to $60,000, which is now is the best acceptable wage demand. So $60,000 is the wage demand, and only Type B works for Employer Earl.


of Self $125K $30K

The Worker is a

Value/Cost



Comment: When $60,000 + $100,000 x f < $125,000, or f < 0.65, Type B works for Employer Earl. So, markets fail to bring about an agreement between Employer Earl and Type A workers. That is unlike the bargaining problems in Part II where every possible mutually-beneficial gain from an agreement was realized. The only issue for our analysis was how to divide that gain.


of Self $125K $30K

The Worker is a

Value/Cost



Example 2: Signaling and Screening



Overview:

Signaling and Screening can cure market failure but at a cost. — So, good workers may distinguish themselves from bad workers at the cost of enduring hard college courses that bad workers avoid.



Comment: In games where cheap talk (costless communication) cannot be screened for information by the less informed player and cheap talk cannot signal information by the more informed player, costly communication can be used for screening and signaling. What about costly communication?

Can an employer screen for information by investigating a potential employee’s college record? Or can a potential employee signal for information by taking college courses that he would not take otherwise?



Question: Suppose Employer Earl has use for two kinds of employees. Skilled and hard working Type A employees contribute $160,000 per year to profits. And Type B employees contribute $60,000 per year to profits.

Suppose Type A workers have existing jobs paying $125,000 per year, and Type B have existing jobs paying $30,000 per year. Suppose Type A workers regard the cost of completing a hard college course as $3,000 a year of salary, and Type B workers as $15,000. Suppose there is no way for the employer to directly tell Type A workers from Type B workers, but the employer can confirm the number of completed hard courses. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter).

For each type of worker, determine wage demands and the number of completed classes.



Answer: Consider finding an appropriate integer number N so the Employer knows that anyone who has completed at least N courses must be a Type A worker (and so should be granted a wage demand of $160,000), and anyone who has not must be Type B (and so should be granted a wage demand of $60,000).

There are two types of constraints on N: incentive compatibility and participation.



of Self $125K $30Kof Courses $3K $15K

The Worker is a

Value/Cost


Incentive compatibility constrains the number N of courses to be high enough so Type B workers (to be paid $60,000) do not bother to meet it, and low enough so Type A workers (to be paid $160,000) will meet it.

Incentive compatibility for Type B requires$60,000 > $160,000 - $15,000 x N, or N > 6.67, meaning N > 7.

Incentive compatibility for Type A requires$160,000 - $3,000 x N > $60,000, or N < 33.33, meaning N < 33.




The Worker is a

Value/Cost


Participation constrains the number N of courses so Type B and Type A workers each benefit from job agreements of $60,000 to Type B workers and $160,000 to Type A workers.

Participation for Type B requires$60,000 > $30,000, which is true regardless of N.

Participation for Type A requires$160,000 - $3,000 x N > $125,000, or N < 11.67, meaning N < 11.




The Worker is a

Value/Cost


Putting it all together, the Employer should pick any number N between 7 and 11 and accept a wage demand of $160K per year for workers that have completed at least N courses, and accept a wage demand of $60K per year for the other workers, who would complete 0 courses.

Comment: Those acceptances separate Type A from Type B workers, but it comes at the communication cost of $3,000 x N per year paid by the Type A workers. Even if the smallest number of courses were picked (N = 7), the cost of the information asymmetry is $3,000 x 7 = $21,000 per year.




The Worker is a

Value/Cost


Example 3: The Dilemma of Pooling


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Overview

The Dilemma of Pooling is a type of prisoners’ dilemma that makes costly signaling and screening persist even when all parties to a trade prefer to trading at a common pooled price.

26 26




Suppose Type A workers have existing jobs paying $125,000 per year, and Type B have existing jobs paying $30,000 per year. Suppose Type A workers regard the cost of completing a hard college course as $3,000 a year of salary, and Type B workers as $15,000. Suppose there is no way for the employer to directly tell Type A workers from Type B workers, but the employer can confirm the number of completed hard courses. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter).

Would all workers be better off if Employer Earl did not use the number of completed courses to screen job candidates?


Answer: From previous calculations, if Employer Earl does use the number of completed courses to screen job candidates, then Employer Earl should pick any number of courses between 7 and 11 and accept a wage demand of $160K per year for workers that have completed at least N courses, and accept a wage demand of $60K per year for the other workers.



The Worker is a

Value/Cost



Those acceptances separate Type A from Type B workers, but it comes at the communication cost of $3,000 x N per year paid by the Type A workers. Even if the smallest number of courses were picked (N = 7), the cost of the information asymmetry is $3,000 x 7 = $21,000 per year, leaving Type A workers with $160,000-$21,000 = $139,000 net wages.




The Worker is a

Value/Cost


Dropping the screening by course selection avoids the $21,000 per year cost of the information asymmetry but means pooling all workers together, paying them the same.

From previous calculations, $60,000 + $100,000 x f is the best acceptable wage demand from a random worker in the general population, which depends on the positive fraction f of Type A workers in the general population. In particular, all workers would be better off if Employer Earl dropped screening job candidates if $60,000 + $100,000 x f > $139,000, or f > 0.79.




The Worker is a

Value/Cost


For example, if 80% of the population were Type A, and 20% Type B. Then the common salary is .8 x $160,000 + .2 x $60,000 = $140,000. Type B workers prefer the pooling equilibrium (salary $140,000) to the screening equilibrium (salary $60,000). And Type A workers also prefer the pooling equilibrium (salary $140,000) to the screening equilibrium (net salary $139,000).




The Worker is a

Value/Cost


Comment: That pooling equilibrium creates a Prisoner’s dilemma for Type A workers.

Working with the 80%-20% of types, all Type A workers are best off by accepting the pooling equilibrium, but individually each worker could signal by offering to complete 1 course and work for $140,000 + $10,000 per year.




The Worker is a

Value/Cost


Employers would agree to pay $140,000 + $10,000 per year for a worker that completes 1 course because only Type A workers would be willing to take 1 course for an extra $10,000 per year.

As more Type A workers take 1 course to signal their type, the average value of the pooled workers decreases, which increases the salary gap between Type A workers and pooled workers, which requires more courses to signal. This process continues until all Type A workers signal by taking 7 courses, and we are back at the equilibrium with separation of types based on screening (or signaling).




The Worker is a

Value/Cost


Summary

Summary


In any screening or signaling problem we consider, there is a good (labor, cars, wrenches, …) that is either High Quality or Low Quality, where the High Quality good has higher value to the Buyer ($160 > $60), and higher opportunity or production cost to the seller ($125 > $30). The seller of either quality makes a take-it-or-leave-it offer to the buyer. Quality is known to the seller, but not to the buyer. The only way for the Seller of the high quality good to credibly communicate to the buyer is for the Seller to pay for units of a signal (education, a service warranty, a replacement warranty, …).

High Q. Low Q.to Buyer $160 $60to Seller $125 $30of Signal $3 $15

The Good is a

Value/Cost

Summary


For that signal to communication credibly, the signal quantity N must satisfy incentive compatibility constraints that Sellers with Low Quality (to be paid $60 if his good is known to be Low Quality) do not bother to signal (60 > 160-15N), and low enough so Sellers with High Quality (to be paid $160 if his good is known to be High Quality) will signal. In particular, it must be true that the signal is cheaper for the Seller of the High Quality good than for the Seller of the Low Quality good ($3 < $15).


The Good is a

Value/Cost

Summary


The signal must also satisfy the participation constraint that the transaction benefits the Seller of the High Quality good after paying for the signal (160 - 3N > 125).

The Seller of the Low Quality good always benefits from a transaction since he does not pay for the signal ($60 > $30).

Finally, we only consider the cases where the potential gain from transacting the High Quality good ($160-$125) is higher than the potential gain from the Low Quality good ($60-$30).


The Good is a

Value/Cost

Summary

37 37

Review Questions


Review Questions You should try to answer some of the following

questions 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.


Review 1: Adverse Selection and Market Failure



Question: Suppose Employer Earl has use for two kinds of employees. Skilled and hard working Type A (impatient, time-conscious, status-conscious, ambitious) employees contribute $130,000 per year to profits. And Type B (patient, easy-going, apathetic) employees contribute $80,000 per year to profits.

Suppose Type A workers have existing jobs paying $70,000 per year, and Type B have existing jobs paying $40,000 per year. Suppose there is no way for the employer to tell Type A workers from Type B workers and, so, must offer each the same wage. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter).

Determine the wage demand, and which types work for Employer Earl.



Answer: The wage demand may depend on the positive fraction f of Type A workers and the remaining positive fraction (1-f ) of Type B workers in the general population. A random worker in the general population is thus Type A with probability f and Type B with probability (1-f ). The expected value of a random worker is $130,000 x f + $80,000 x (1-f ) = $80,000 + $50,000 x f .

In particular, $80,000 + $50,000 x f is the best acceptable wage demand from a random worker in the general population.

But is that wage enough for both types to gain from employment?


of Self $70K $40K

The Worker is a

Value/Cost



If $80,000 + $50,000 x f > $70,000, which is true for every f > 0, then both types of workers gain from Employment with Earl. So $80,000 + $50,000 x f is, indeed, the wage demand, and both types work for Employer Earl, regardless of the value of f > 0.


of Self $70K $40K

The Worker is a

Value/Cost



Review 2: The Dilemma of Pooling




Suppose Type A workers have existing jobs paying $125,000 per year, and Type B have existing jobs paying $30,000 per year. Suppose Type A workers regard the cost of completing a hard college class as $3,000 a year of salary, and Type B workers as $15,000 a year of salary. Suppose there is no way for the employer to directly tell Type A workers from Type B workers, but the employer can confirm the number of completed classes. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter).

Would all workers be better off if Employer Earl did not use the number of completed classes to screen job candidates?



Answer: First, suppose Employer Earl does use the number of completed classes to screen job candidates. Consider finding an appropriate integer number N so the Employer should accept a wage demand of $120K per year for workers that have completed at least N courses, and a wage demand of $70K per year to the other workers. There are two constraints on N, incentive compatibility and participation.



The Worker is a

Value/Cost



Incentive compatibility constrains the number N of courses to be high enough so Type B workers do not bother to meet it, and low enough so Type A workers will meet it.

Incentive compatibility for Type B requires$70,000 > $120,000 - $12,000 x N, or N > 4.16, meaning N > 5.

Incentive compatibility for Type A requires$120,000 - $4,000 x N > $70,000, or N < 12.5, meaning N < 12.



The Worker is a

Value/Cost



Participation constrains the number N of courses so Type B and Type A workers both accept the job offers of $70,000 to Type B workers and $120,000 to Type A workers.


Participation for Type A requires$120,000 - $4,000 x N > $40,000, or N < 20.



The Worker is a

Value/Cost



Putting it all together, the Employer should pick any number between 5 and 12 and accept a wage demand of $120K per year for workers that have completed at least N courses, and accept a wage demand of $70K per year for the other workers.




The Worker is a

Value/Cost




The expected value of a random worker is $120,000 x f + $70,000 x (1-f ) = $70,000 + $50,000 x f , so $70,000 + $50,000 x f is the best acceptable wage demand from a random worker in the general population. In particular, all workers would be better off if Employer Earl dropped screening job candidates if $70,000 + $50,000 x f > $100,000, or f > 0.6.



The Worker is a

Value/Cost




Suppose Type A workers have existing jobs paying $125,000 per year, and Type B have existing jobs paying $30,000 per year. Suppose Type A workers regard the cost of completing a hard college class as $3,000 a year of salary, and Type B workers as $15,000 a year of salary. Suppose there is no way for the employer to directly tell Type A workers from Type B workers, but the employer can confirm the number of completed classes. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter).

Would all workers be better off if Employer Earl did not use the number of completed classes to screen job candidates?



Answer: First, suppose Employer Earl does use the number of completed classes to screen job candidates. Consider finding an appropriate integer number N so the Employer should accept a wage demand of $140K per year for workers that have completed at least N courses, and a wage demand of $80K per year to the other workers. There are two constraints on N, incentive compatibility and participation.



The Worker is a

Value/Cost



Incentive compatibility constrains the number N of courses to be high enough so Type B workers do not bother to meet it, and low enough so Type A workers will meet it.

Incentive compatibility for Type B requires$80,000 > $140,000 - $20,000 x N, or N > 3.

Incentive compatibility for Type A requires$140,000 - $2,000 x N > $80,000, or N < 30.



The Worker is a

Value/Cost



Participation constrains the number N of courses so Type B and Type A workers both accept the job offers of $80,000 to Type B workers and $140,000 to Type A workers.


Participation for Type A requires$140,000 - $2,000 x N > $100,000, or N < 20.



The Worker is a

Value/Cost



Putting it all together, the Employer should pick any number between 3 and 20 and accept a wage demand of $140K per year for workers that have completed at least N courses, and accept a wage demand of $80K per year for the other workers.




The Worker is a

Value/Cost




The expected value of a random worker is $140,000 x f + $80,000 x (1-f ) = $80,000 + $60,000 x f , so $80,000 + $60,000 x f is the best acceptable wage demand from a random worker in the general population. In particular, all workers would be better off if Employer Earl dropped screening job candidates if $80,000 + $60,000 x f > $134,000, or f > 0.9.



The Worker is a

Value/Cost


56 56

End of Lesson C.3


BA 445 Managerial Economics

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