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Unformatted text preview: Spence’s Signaling Game In Spence’s model, workers know whether their produc—
tivity is low or high, and must choose education, y. Next,
firms (who do not observe a worker’s productivity) offer
a wage as a function of the education level. We will as—
sume that firms are risk neutral and competitive, so that
the wage will be the expected productivity level. An index is an unalterable characteristic of a worker, like
age, race, or gender. A signal is a characteristic subject to manipulation, like
education. We assume that signaling costs are negatively correlated
with productivity. This is not really an assumption, be—
cause for this model the only effective signals will have
this property. Type 1 workers: have productivity 6 = 1, constitute
a fraction ql of the population, and have signaling cost C1(9) = 9 Type 2 workers: have productivity 9 = 2, constitute a
fraction 1 —q1 of the population, and have signaling cost 02(9) = The timing is
1) Workers receive education 2) Firms choose wage contracts As part of a
WPBE, firms must form beliefs about the probability that
a worker with education y is type 1, even for off the
equilibrium path choices of y. 3) Workers choose a contract. Note: In his classic paper, Spence talks about the timing
as 1) Firms select wage contracts w(y) and select their be—
liefs about which types of workers will choose which ed—
ucation levels. 2) Workers choose education levels.
3) Firms’ beliefs must be rational (correct). This description does not make sense, because beliefs are
not a strategic choice variable. If the timing is that firms
choose w(y) and then workers choose y, then we have a
screening game (like Rothschild—Stiglitz) that should be
studied using game theoretic concepts like WPBE. If a
firm deviates to another wage contract, this will affect
workers’ incentives to acquire education, so the beliefs should not be held fixed. if [A 1; («cumming/rs c.(’\ L C ' I, \k W L égpmmﬁf ? V10, E2 LC , 5’ V 714. (if: jive. ,\
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«Cth PPOdWL’HUﬂ'y Consider the separating equilibrium with y* z 1.9, sup—
ported by beliefs that anyone with lower education is type
1. Suppose a worker deviates to y : 1.1, which is
inconsistent with the equilibrium. Who is more likely
to make this “mistake”? A type 1 worker prefers to
choose 3/ = 0, even if she would receive a wage of 2 with
y = 1.1. Under the "intuitive criterion” we rule out
beliefs on information sets following a deviation that as—
sign positive probability to types that would never make
such a deviation (because that type is worse off for all
continuation strategies). Then the only WPBE satisfy—
ing the intuitive criterion is the most efficient separating
equilibrium, y* = 1. Timing makes a big difference. Consider the Rothschild—
Stiglitz timing, where 1) Firms choose w(y) 2) Workers choose y and accept a contract. The only candidate separating equilibria involve 111(0) 2
1 and 111(1) 2 2. The wages offered for other education
levels are arbitrary, as long as no worker is induced to
choose that education. If ql is small, a pooling contract will break the candidate
separating equilibrium. w(y) : 2 — ql for ally will be
accepted by both types if we have 1
2— >2——
Q1 2 or q1 < lf q1 > % holds, then the condidate sepa— rating equilibrium is an equilibrium (subgame perfect or
WPBE). Under the Rothschild—Stiglitz timing, there is no pooling
equilibrium. Consider the best pooling contract, =
2 — ql. A new firm could offer the contract, = 2
for y 2 y*. This contract is accepted by type 2 workers
(who choose y = y*) if >l< y
2*—— > 2— or
2 (11 y* < 2q1. The contract is rejected by type 1 workers (who choose
the pooling contract with y = 0) if 2—q1 > 2—y* or
34* > (11 Thus, any y* E [q1,2q1] breaks the candidate pooling
equilibrium. ...
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This note was uploaded on 07/17/2008 for the course ECON 805 taught by Professor Peck during the Spring '08 term at Ohio State.
 Spring '08
 PECK

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