Game Theory 11 – chap22. Job-market signaling

5. Dynamic Bayesian Games
5.3 Dynamic Bayesian Games: Signaling
Application I : Job-Market Signaling (Chapter 29, Spence (1973))

Job-Market Signaling, Michael Spence (1973)

In most job markets, a job hunter’s productive capability on the job is not perfectly observable when an employer makes a hiring decision

Instead, the employer is able to observe a plethora of personal data and certain attributes such as:
education, previous work experiences, race, age, sex, etc

Michael Spence – Nobel laureate in 2001

MICHAEL SPENCE (1973) classifies the set of attributes into indices and signals according to its alterability

In his pioneering work, a job hunter is represented by a pair of his productivity and one signal,

(\(\theta\),e),

where \(\theta\) his unobservable innate talent and e is the level of education

The textbook presents a simple version of his job-market signaling model:

• The worker’s type 0 is either high or low
• The common prior is Pr(\(\theta\) = H) =1/3
• After observing \(\theta\), the worker decides whether to obtain an education or not
• Education is costly, 4 to the high type and 7 to the low type
• After observing the worker’s choice, the firm decides whether to appoint him as a manager or a clerk
• The firm earns a profit of 10 (0) by putting the high (low) type in the management position
• When appointed as a clerk, both types yield a profit of 4 to the firm
• The manager receives a wage of 10, whereas the clerk receives 4

The dynamic game can be put in the extensive form:

separate equilibrium: High Type E, Low Type N’
(Since there is no intensive debated, because of M for q and C’ for p)

pooling equilibrium: High Type N, Low Type N’
expected payoff: 10/3 < 4 so C’ is Best Response

<(NN’, C’C), p = 1/3, q <= 2/5>

This signaling game has a unique PBE in separating strategies satisfying the Cho-Kreps criterion:
⟨(\(E^H N^L, C^N M^E\)), p = 0, q = 1⟩

This highlights the signaling role of education in job markets

• Although it does not improve productivity, education could still have economic value to the worker
• High-type workers are willing to obtain more education in order to signal their productivity, and this costly signaling is compensated with high pay in the market

“the sheepskin (diploma) effect”

Spence’s work sparked subsequent empirical research investigating whether this effect indeed exists in the real world

We study how to compute a PBE by going through the next classic example

EXAMPLE 5.7 (THE BEER-QUICHE GAME, CHO AND KREPS (1987)).

• Player 1 can be weak (w) or strong (s), and let Pr(\(t_1\) = w) = 0.1. The strong type likes beer for breakfast, while the weak likes quiche.
• Player 1 is ordering his breakfast, and player 2 is watching and contemplating whether to pick a fight with player 1. Player 2 wants to fight with the weak type but walk away from the strong type.
• Player 1 likes to avoid a fight: he gets a payoff of one from the preferred breakfast, and a payoff of two from avoiding the fight.

• Reference: Chang-Koo Chi, (40/50) Game Theory and Applications 11 – Job-market signaling, Jul 15, 2020, https://youtu.be/O19madhZ2rE