Lesson overview
Chapter 9 Uncertainty and Information
Lesson II.3 Cheap Talk and Adverse Selection Theory
Lesson II.4 Signaling and Screening Theory
Each Example Game Introduces some Game Theory
• Example 1: Signaling and Screening
• Example 2: Pooling
• Example 3: Separating Equilibrium
• Example 4: Pooling Equilibrium
• Example 5: Semiseparating Equilibrium
Lesson II.5 Signaling and Screening Applications
BA 592 Lesson II.4 Signaling and Screening Theory
1
Example 1: Signaling and Screening
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.
For example, employers know less about the skills and work
attitude of potential employees than do the employees. Because
unskilled and lazy potential employees will claim to have skills
and will act hard working during interviews to get higher pay,
employers cannot use costless communication to screen
applicants. What about costly communication? Does that screen
or signal information?
BA 592 Lesson II.4 Signaling and Screening Theory
2
Example 1: Signaling and Screening
Suppose employers have two kinds of jobs. Skilled and hard
working Type A (impatient, time-conscious, status-conscious,
ambitious) employees can do Type A jobs, which contribute
$160,000 per year to profits. And Type B (patient, easy-going,
apathetic) employees can do Type B jobs, which contribute
$60,000 per year to profits.
Suppose Type A workers have existing jobs paying $125,000 per
year, and Type B have 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 are more jobs than workers.
Determine whether the employer can use the differential cost of
completing hard college courses to screen Type A workers from
Type B workers. Or, whether workers can signal.
BA 592 Lesson II.4 Signaling and Screening Theory
3
Example 1: Signaling and Screening
The Worker is a
Type A
to Employer $160K
Value/Cost
of Self
$125K
of Courses
$3K
Type B
$60K
$30K
$15K
Consider finding an appropriate integer number N so the
Employer should offer $160K per year for workers that have
completed at least N courses, and $60K per year to the other
workers. There are two constraints on N, incentive compatibility
and participation.
BA 592 Lesson II.4 Signaling and Screening Theory
4
Example 1: Signaling and Screening
The Worker is a
Type A
to Employer $160K
Value/Cost
of Self
$125K
of Courses
$3K
Type B
$60K
$30K
$15K
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
$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.
BA 592 Lesson II.4 Signaling and Screening Theory
5
Example 1: Signaling and Screening
The Worker is a
Type A
to Employer $160K
Value/Cost
of Self
$125K
of Courses
$3K
Type B
$60K
$30K
$15K
Participation constrains the number N of courses so Type B and
Type A workers both accept the job offers 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.
BA 592 Lesson II.4 Signaling and Screening Theory
6
Example 1: Signaling and Screening
The Worker is a
Type A
to Employer $160K
Value/Cost
of Self
$125K
of Courses
$3K
Type B
$60K
$30K
$15K
Putting it all together, the Employer should pick any number
between 7 and 11 and offer $160K per year for workers that have
completed at least N courses, and $60K per year to the other
workers. Those job offers 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.
BA 592 Lesson II.4 Signaling and Screening Theory
7
Example 2: Pooling
The Worker is a
Type A
to Employer $160K
Value/Cost
of Self
$125K
of Courses
$3K
Type B
$60K
$30K
$15K
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. In particular, you
overpay Type B workers.
Determine whether the employer should use college courses to
screen Type A workers from Type B workers, or whether the
employer should pool workers.
BA 592 Lesson II.4 Signaling and Screening Theory
8
Example 2: Pooling
The Worker is a
Type A
to Employer $160K
Value/Cost
of Self
$125K
of Courses
$3K
Type B
$60K
$30K
$15K
Dropping the screening by course selection and pooling workers
requires, in a competitive market, the common salary under
pooling equals the population average of what the types are worth
to the Employer, and that average depends on the proportions of
the types in the population.
On the one hand, if 60% of the population were Type A, and 40%
Type B. Then the common salary is .6 x $160,000 + .4 x $60,000
= $120,000. Type B workers thus prefer the pooling equilibrium.
Type A workers find the pooling salary $120,000 inferior to the
$160,000-$21,000 = $139,000 net from screening.
BA 592 Lesson II.4 Signaling and Screening Theory
9
Example 2: Pooling
The Worker is a
Type A
to Employer $160K
Value/Cost
of Self
$125K
of Courses
$3K
Type B
$60K
$30K
$15K
On the other hand, 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 still prefer the pooling
equilibrium to the screening equilibrium. And now Type A
workers prefer the pooling equilibrium. However, 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.
BA 592 Lesson II.4 Signaling and Screening Theory
10
Example 2: Pooling
The Worker is a
Type A
to Employer $160K
Value/Cost
of Self
$125K
of Courses
$3K
Type B
$60K
$30K
$15K
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).
BA 592 Lesson II.4 Signaling and Screening Theory
11
Example 3: Separating Equilibrium
Signaling and screening in the asymmetric information games
above had many informed players and many uninformed players.
Asymmetric information games with just two players allow the
previous separating equilibrium and pooling equilibrium, and the
new possibility of semiseparating equilibrium.
BA 592 Lesson II.4 Signaling and Screening Theory
12
Example 3: Separating Equilibrium
Ford currently enjoys a monopoly in the market for the most
economical-but-fun car, the Ford Mustang Convertible. Pontiac
has a competing redesign of the Pontiac Solstice (to make it more
economical) and is deciding whether to enter the market. But
Pontiac does not know how tough a competitor Ford will prove to
be. Specifically, Ford’s production cost is unknown to Pontiac,
and may be high or low. If it is high, Pontiac can enter and
compete profitably; if it is low, Pontiac’s entry and development
costs cannot be recouped by subsequent operating profits, and it
will make a net loss if it enters.
BA 592 Lesson II.4 Signaling and Screening Theory
13
Example 3: Separating Equilibrium
The two firms interact in a three-stage sequential move game. In
each stage, the per-unit costs and prices are in thousands of
dollars, and the number of cars sold is in hundreds of thousands,
so total costs and profits are in hundreds of millions.
BA 592 Lesson II.4 Signaling and Screening Theory
14
Example 3: Separating Equilibrium
In the first stage, Nature chooses with probability probLow Ford to
have Low cost cLow (thousand dollars) and with probability
(1-probLow) Ford to have High cost cHigh. Ford observes Nature’s
choice but Pontiac only knows only the probabilities and the
possible cost values cLow and cHigh.
In the second stage, Ford sets a price PLow or PHigh (thousand
dollars) knowing that it is the only manufacturer in the market in
Period 1, and that the selling price of cars depends on the total
output of cars, P = 25-Q. Specifically, if Ford is Low cost cLow, it
sets its monopoly price PLow. But if Ford is High cost cHigh, it
chooses to either set its monopoly price PHigh or falsely signal
Low cost by choosing PLow.
BA 592 Lesson II.4 Signaling and Screening Theory
15
Example 3: Separating Equilibrium
In the third stage, Pontiac makes its entry decision in Period 2. To
enter the market, Pontiac must pay 40 to build its plant, advertise,
and so on. If Pontiac enters the market, its costs of producing and
delivering each of its cars to the market is 10, and it becomes a
Cournot duopolist with Ford, with the selling price of cars again
depends on the total output of cars, P = 25-Q.
BA 592 Lesson II.4 Signaling and Screening Theory
16
Example 3: Separating Equilibrium
Ford prefers Pontiac not enter the market. It might try to use its
price in the second stage to signal a low cost. A low-cost firm
would charge a lower Monopoly price than a high-cost firm.
Pontiac is aware that Ford might falsely signal a low cost with a
low price. Can Ford profitably signal low cost and keep Pontiac
from entering?
The answer depends on the probability probLow and cost cLow and
cHigh parameters.
We consider three possible cases.
BA 592 Lesson II.4 Signaling and Screening Theory
17
Example 3: Separating Equilibrium
In the first case:
 the probability that Ford is Low cost is probLow = 0.4
 the probability of High cost is (1-probLow) = 0.6
 the Low cost level is cLow = 5
 the High cost level is cHigh = 15
Use those parameters to define the game tree for the Market
Entry Game #1, and find all rollback solutions.
BA 592 Lesson II.4 Signaling and Screening Theory
18
Example 3: Separating Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
First stage: Nature determines low
unit cost of 5 for Ford with probability
0.4, and cost 15 with probability 0.6
Second stage: If Ford costs are Low,
Ford sets the monopoly price,
PLow=15 and earns 100. If costs are
High, either set price PLow=15 and
earn 0, or set the monopoly price
PHigh=20 and earn 25.
Nature
Cost Low
prob = 0.4
Cost High
prob = 0.6
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
169,-29
200,0
3,4
25,0
28,4
50,0
Third stage: Pontiac Enters In or Stays
Out. If Stays Out, Ford sets
monopoly price according to its true
costs, earning 100 if Ford’s costs are
low or 25 if high. If Enters In, Ford
and Pontiac are Cournot Duopolists,
earning 69.4 and 11.1 if Ford’s costs
are low, or 2.7 and 44.4 if Ford’s costs
are high.
BA 592 Lesson II.4 Signaling and Screening Theory
19
Example 3: Separating Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Partial rollback solution: If Ford
prices High, then Pontiac Enters In.
Nature
Cost Low
prob = 0.4
Cost High
prob = 0.6
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
169,-29
200,0
3,4
25,0
28,4
50,0
Remaining decisions: Ford prices Low
or High if costs are High. Pontiac
Enters In or Stays out if Ford chooses
to price Low.
Pontiac
In
Out
Low
Ford
High
In stage two, Ford’s two branches for
Price Low are in the same information
set for Pontiac, meaning Pontiac does
not know which branch it is on when
Ford prices Low. Pontiac is thus
limited to choosing the same strategy
(Enter In or Stay Out or a mixture) for
each branch in the information set.
BA 592 Lesson II.4 Signaling and Screening Theory
20
Example 3: Separating Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Expected value of payoffs if Ford
prices Low if costs are High and
Pontiac Enters In if Ford chooses to
price Low:
0.4(169,-29) + 0.6(3,4) = (69.4,-9.2)
Nature
Pontiac
Cost Low
prob = 0.4
Cost High
prob = 0.6
Ford
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
169,-29
200,0
3,4
25,0
28,4
50,0
Low
High
In
69.4,-9.2
BA 592 Lesson II.4 Signaling and Screening Theory
Out
21
Example 3: Separating Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Expected value of payoffs if Ford
prices Low if costs are High and
Pontiac Stays Out if Ford chooses to
price Low:
0.4(200,0) + 0.6(25,0) = (95,0)
Nature
Pontiac
Cost Low
prob = 0.4
Cost High
prob = 0.6
Ford
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
169,-29
200,0
3,4
25,0
28,4
50,0
Low
High
In
69.4,-9.2
BA 592 Lesson II.4 Signaling and Screening Theory
Out
95,0
22
Example 3: Separating Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Expected value of payoffs if Ford
prices High if costs are High and
Pontiac Enters In if Ford chooses to
price Low:
0.4(169,-29) + 0.6(28,4) = (84.4,-9.2)
Nature
Pontiac
Cost Low
prob = 0.4
Cost High
prob = 0.6
Ford
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
169,-29
200,0
3,4
25,0
28,4
50,0
Low
High
In
69.4,-9.2
84.4,-9.2
BA 592 Lesson II.4 Signaling and Screening Theory
Out
95,0
23
Example 3: Separating Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Expected value of payoffs if Ford
prices High if costs are High and
Pontiac Stays Out if Ford chooses to
price Low:
0.4(200,0) + 0.6(28,4) = (96.8,2.4)
Nature
Pontiac
Cost Low
prob = 0.4
Cost High
prob = 0.6
Ford
Ford
Price Low
Price Low
Pontiac
Ford
Low
High
In
Out
69.4,-9.2
95,0
84.4,-9.2 96.8,2.4
Price High
Pontiac
Pontiac
In
Out
In
Out
In
Out
169,-29
200,0
3,4
25,0
28,4
50,0
The completed Normal form has High
Price the dominate strategy for Ford,
making Pontiac respond with Stay
Out. That is the case pictured in the
tree on the left. Ford signals its true
type in the Separating Equilibrium.
BA 592 Lesson II.4 Signaling and Screening Theory
24
Example 4: Pooling Equilibrium
In the second case, cLow = 10 rather than cLow = 5:
 the probability that Ford is Low cost is probLow = 0.4
 the probability of High cost is (1-probLow) = 0.6
 the Low cost level is cLow = 10
 the High cost level is cHigh = 15
Use those parameters to define the game tree for the Market
Entry Game #2, and find all rollback solutions.
BA 592 Lesson II.4 Signaling and Screening Theory
25
Example 4: Pooling Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
First stage: Nature determines cLow =
10 for Ford with probability 0.4, and
cost 15 with probability 0.6
Second stage: If Ford costs are Low,
Ford sets the monopoly price,
PLow=17.5 and earns 56. If costs are
High, either set price PLow=17.5 and
earn 2.5x7.5 = 18.8, or set the
monopoly price PHigh=20 and earn 25.
Nature
Cost Low
prob = 0.4
Cost High
prob = 0.6
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
81,-15
112,0
22,4
44,0
28,4
50,0
Third stage: Pontiac Enters In or Stays
Out. If Stays Out, Ford sets
monopoly price according to its true
costs, earning 56 if Ford’s costs are
low or 25 if high. If Enters In, Ford
and Pontiac are Cournot Duopolists,
earning 25 and 25 if Ford’s costs are
low, or 2.7 and 44.4 if Ford’s costs are
high.
BA 592 Lesson II.4 Signaling and Screening Theory
26
Example 4: Pooling Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Partial rollback solution: If Ford
prices High, then Pontiac Enters In.
Remaining decisions: Ford prices Low
or High if costs are High. Pontiac
Enters In or Stays out if Ford chooses
to price Low.
Pontiac
In
Out
Low
Ford
High
Nature
Cost Low
prob = 0.4
Cost High
prob = 0.6
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
81,-15
112,0
22,4
44,0
28,4
50,0
BA 592 Lesson II.4 Signaling and Screening Theory
27
Example 4: Pooling Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Expected value of payoffs if Ford
prices Low if costs are High and
Pontiac Enters In if Ford chooses to
price Low:
0.4(81,-15) + 0.6(22,4) = (45.6,-3.6)
Nature
Pontiac
Cost Low
prob = 0.4
Cost High
prob = 0.6
Ford
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
81,-15
112,0
22,4
44,0
28,4
50,0
Low
High
In
45.6,-3.6
BA 592 Lesson II.4 Signaling and Screening Theory
Out
28
Example 4: Pooling Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Expected value of payoffs if Ford
prices High if costs are High and
Pontiac Enters In if Ford chooses to
price Low:
0.4(81,-15) + 0.6(28,4) = (49.2,-3.6)
Nature
Pontiac
Cost Low
prob = 0.4
Cost High
prob = 0.6
Ford
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
81,-15
112,0
22,4
44,0
28,4
50,0
Low
High
In
45.6,-3.6
49.2,-3.6
BA 592 Lesson II.4 Signaling and Screening Theory
Out
29
Example 4: Pooling Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Expected value of payoffs if Ford
prices High if costs are High and
Pontiac Stays Out if Ford chooses to
price Low:
0.4(112,0) + 0.6(28,4) = (61.6,2.4)
Nature
Pontiac
Cost Low
prob = 0.4
Cost High
prob = 0.6
Ford
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
81,-15
112,0
22,4
44,0
28,4
50,0
Low
High
In
Out
45.6,-3.6
49.2,-3.6 61.6,2.4
BA 592 Lesson II.4 Signaling and Screening Theory
30
Example 4: Pooling Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Expected value of payoffs if Ford
prices Low if costs are High and
Pontiac Stays Out if Ford chooses to
price Low:
0.4(112,0) + 0.6(44,0) = (71.2,0)
Nature
Pontiac
Cost Low
prob = 0.4
Cost High
prob = 0.6
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
81,-15
112,0
22,4
44,0
28,4
50,0
In
Out
Low
45.6,-3.6 71.2,0
Ford
High
49.2,-3.6 61.6,2.4
The completed Normal form has Stay
Out the dominate strategy for Pontiac,
making Pontiac respond with Price
Low. That is the case pictured in the
tree on the left. Ford signals Low
Cost in the Pooling Equilibrium.
BA 592 Lesson II.4 Signaling and Screening Theory
31
Example 5: Semiseparating Equilibrium
In the third case, probLow = 0.1 rather than probLow = 0.4:
 the probability that Ford is Low cost is probLow = 0.1
 the probability of High cost is (1-probLow) = 0.9
 the Low cost level is cLow = 10
 the High cost level is cHigh = 15
Use those parameters to define the game tree for the Market
Entry Game #3, and find all rollback solutions.
BA 592 Lesson II.4 Signaling and Screening Theory
32
Example 5: Semiseparating Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
First stage: Nature determines cLow =
10 for Ford with probability 0.4, and
cost 15 with probability 0.6
Second stage: If Ford costs are Low,
Ford sets the monopoly price,
PLow=17.5 and earns 56. If costs are
High, either set price PLow=17.5 and
earn 2.5x7.5 = 18.8, or set the
monopoly price PHigh=20 and earn 25.
Nature
Cost Low
prob = 0.1
Cost High
prob = 0.9
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
81,-15
112,0
22,4
44,0
28,4
50,0
Third stage: Pontiac Enters In or Stays
Out. If Stays Out, Ford sets
monopoly price according to its true
costs, earning 56 if Ford’s costs are
low or 25 if high. If Enters In, Ford
and Pontiac are Cournot Duopolists,
earning 25 and 25 if Ford’s costs are
low, or 2.7 and 44.4 if Ford’s costs are
high.
BA 592 Lesson II.4 Signaling and Screening Theory
33
Example 5: Semiseparating Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Partial rollback solution: If Ford
prices High, then Pontiac Enters In.
Nature
Cost Low
prob = 0.1
Cost High
prob = 0.9
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
81,-15
112,0
22,4
44,0
28,4
50,0
Remaining decisions: Ford prices Low
or High if costs are High. Pontiac
Enters In or Stays out if Ford chooses
to price Low.
Pontiac
In
Out
Low
Ford
High
Complete the normal form just as in
Example 4, but with new
probabilities.
BA 592 Lesson II.4 Signaling and Screening Theory
34
Example 5: Semiseparating Equilibrium
Expected value of payoffs if Ford
prices Low if costs are High and
Pontiac Enters In if Ford chooses to
price Low:
0.1(81,-15) + 0.9(22,4) = (27.9,2.1)
Expected value of payoffs if Ford
prices High if costs are High and
Pontiac Enters In if Ford chooses to
price Low:
0.1(81,-15) + 0.9(28,4) = (33.3,2.1)
Expected value of payoffs if Ford
prices Low if costs are High and
Pontiac Stays Out if Ford chooses to
price Low:
0.1(112,0) + 0.9(44,0) = (50.8,0)
Pontiac
Ford
Low
High
In
27.9,2.1
33.3,2.1
Out
50.8,0
36.4,3.6
Expected value of payoffs if Ford
prices High if costs are High and
Pontiac Stays Out if Ford chooses to
price Low:
0.1(112,0) + 0.9(28,4) = (36.4,3.6)
BA 592 Lesson II.4 Signaling and Screening Theory
35
Example 5: Semiseparating Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Nature
Cost Low
prob = 0.1
Cost High
prob = 0.9
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
81,-15
112,0
22,4
44,0
28,4
50,0
The completed Normal form has no
Nash equilibrium in pure strategies.
In mixed strategies, with probability p
Ford prices Low if costs are High and
with probability q Pontiac Stays Out if
Ford chooses to price Low:
Pontiac
In
Out
Low
27.9,2.1 50.8,0
Ford
High
33.3,2.1 36.4,3.6
Ford’s p-mix must make Pontiac
indifferent between its pure strategies:
2.1p+2.1(1-p) = 0p+3.6(1-p),
or p = 1.5/3.6 = .42
And Pontiac’s q-mix must make Ford
indifferent between its pure strategies:
27.9q+50.8(1-q) = 33.3q+36.4(1-q),
or q = 14.4/19.8 = .73
BA 592 Lesson II.4 Signaling and Screening Theory
36
Example 5: Semiseparating Equilibrium
Common Data
Demand
P = 25-Q
Pontiac entry
40
Pontiac unit cost
10
Putting it all together, with
probability p = .42 Ford prices
Low if costs are High, and with
q = .73 Pontiac Stays Out if
Ford chooses to price Low.
Nature
Cost Low
prob = 0.1
Cost High
prob = 0.9
Ford
Ford
Price Low
Price Low
Price High
Pontiac
Pontiac
Pontiac
In
Out
In
Out
In
Out
81,-15
112,0
22,4
44,0
28,4
50,0
Ford’s types are thus only
partially separated. The low
cost type always prices low, but
the high price type mixes and
will also price low with 42%
probability. A high price thus
conveys full information, but a
low price conveys only partial
information about type in this
Semiseparating Equilibrium.
BA 592 Lesson II.4 Signaling and Screening Theory
37
Lesson overview
Chapter 9 Uncertainty and Information
Lesson II.4 Signaling and Screening
Each Example Game Introduces some Game Theory
• Example 1: Signaling and Screening
• Example 2: Pooling
• Example 3: Separating Equilibrium
• Example 4: Pooling Equilibrium
• Example 5: Semiseparating Equilibrium
Lesson II.1 Mixed Strategy Applications
BA 592 Lesson II.4 Signaling and Screening Theory
38
BA 592
Game Theory
End of Lesson II.1
BA 592 Lesson II.4 Signaling and Screening Theory
39