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UNIT III: MONOPOLY & OLIGOPOLY Monopoly Oligopoly Strategic Competition 7/30 Strategic Competition Prisoner s Dilemma Repeated Games Discounting The Folk Theorem ... – PowerPoint PPT presentation

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Title: UNIT III: MONOPOLY

1
UNIT III MONOPOLY OLIGOPOLY
• Monopoly
• Oligopoly
• Strategic Competition

7/30
2
Strategic Competition
• Prisoners Dilemma
• Repeated Games
• Discounting
• The Folk Theorem
• Cartel Enforcement

3
The Prisoners Dilemma
• In years in jail Player 2
• Confess Dont
• Confess
• Player 1
• Dont

-10, -10 0, -20 -20, 0 -1, -1
GAME 1.
4
The Prisoners Dilemma
The pair of dominant strategies (Confess,
Confess) is a Nash Eq.
• In years in jail Player 2
• Confess Dont
• Confess
• Player 1
• Dont

-10, -10 0, -20 -20, 0 -1, -1
GAME 1.
5
The Prisoners Dilemma
• Each player has a dominant strategy. Yet the
outcome (-10, -10) is pareto inefficient.
• Is this a result of imperfect information? What
would happen if the players could communicate?
• What would happen if the game were repeated? A
finite number of times? An infinite or unknown
number of times?
• What would happen if rather than 2, there were
many players?

6
Repeated Games
• Some Questions
• What happens when a game is repeated?
• Can threats and promises about the future
influence behavior in the present?
• Cheap talk
• Finitely repeated games Backward induction
• Indefinitely repeated games Trigger strategies

7
Repeated Games
• Examples of Repeated Prisoners Dilemma
• Cartel enforcement
• Transboundary pollution
• Common property resources
• Arms races

The Tragedy of the Commons
Free-rider Problems
8
Repeated Games
• Can threats and promises about future actions
influence behavior in the present?
• Consider the following game, played 2X

C D
C 3,3 0,5
See Gibbons 82-104.
D 5,0 1,1
9
Repeated Games
• Draw the extensive form game

(3,3) (0,5) (5,0) (1,1)
(6,6) (3,8) (8,3) (4,4) (3,8)(0,10)(5,5)(1,6)(8,3)
(5,5)(10,0) (6,1) (4,4) (1,6) (6,1) (2,2)
10
Repeated Games
• Now, consider three repeated game strategies
• D (ALWAYS DEFECT) Defect on every move.
• C (ALWAYS COOPERATE) Cooperate on every
move.
• T (TRIGGER) Cooperate on the first move,
then cooperate after the other cooperates.
If the other defects, then defect
forever.

11
Repeated Games
• If the game is played twice, the V(alue) to a
player using ALWAYS DEFECT (D) against an
opponent using ALWAYS DEFECT(D) is
• V (D/D) 1 1 2, and so on. . .
• V (C/C) 3 3 6
• V (T/T) 3 3 6
• V (D/C) 5 5 10
• V (D/T) 5 1 6
• V (C/D) 0 0 0
• V (C/T) 3 3 6
• V (T/D) 0 1 1
• V (T/C) 3 3 6

12
Repeated Games
• And 3x
• V (D/D) 1 1 1 3
• V (C/C) 3 3 3 9
• V (T/T) 3 3 3 9
• V (D/C) 5 5 5 15
• V (D/T) 5 1 1 7
• V (C/D) 0 0 0 0
• V (C/T) 3 3 3 9
• V (T/D) 0 1 1 2
• V (T/C) 3 3 3 9

13
Repeated Games
• Time average payoffs
• n3
• V (D/D) 1 1 1 3 /3 1
• V (C/C) 3 3 3 9 /3 3
• V (T/T) 3 3 3 9 /3 3
• V (D/C) 5 5 5 15 /3 5
• V (D/T) 5 1 1 7 /3 7/3
• V (C/D) 0 0 0 0 /3 0
• V (C/T) 3 3 3 9 /3 3
• V (T/D) 0 1 1 2 /3 2/3
• V (T/C) 3 3 3 9 /3 3

14
Repeated Games
• Time average payoffs
• n
• V (D/D) 1 1 1 ... /n 1
• V (C/C) 3 3 3 ... /n 3
• V (T/T) 3 3 3 ... /n 3
• V (D/C) 5 5 5 ... /n 5
• V (D/T) 5 1 1 ... /n 1 e
• V (C/D) 0 0 0 ... /n 0
• V (C/T) 3 3 3 /n 3
• V (T/D) 0 1 1 ... /n 1 -
e
• V (T/C) 3 3 3 ... /n 3

15
Repeated Games
• Now draw the matrix form of this game
• 1x

C D T
C 3,3 0,5 3,3
D 5,0 1,1 5,0
T 3,3 0,5 3,3
16
Repeated Games

Time Average Payoffs
C D T
C 3,3 0,5 3,3
If the game is repeated, ALWAYS DEFECT is no
longer dominant.
D 5,0 1,1 1e,1-e
T 3,3 1-e,1e 3,3
17
Repeated Games

C D T
C 3,3 0,5 3,3
and TRIGGER achieves a NE with itself.
D 5,0 1,1 1e,1-e
T 3,3 1-e,1e 3,3
18
Repeated Games
• Time Average
• Payoffs
• T(emptation) gt
• R(eward) gt
• P(unishment)gt
• S(ucker)

C D T
C R,R S,T R,R
D T,S P,P Pe,P-e
T R,R P-e,Pe R,R
19
Discounting
• The discount parameter, d, is the weight of the
next payoff relative to the current payoff.
• In a indefinitely repeated game, d can also be
interpreted as the likelihood of the game
continuing for another round (so that the
expected number of moves per game is 1/(1-d)).
•
• The V(alue) to someone using ALWAYS DEFECT (D)
when playing with someone using TRIGGER (T) is
the sum of T for the first move, d P for the
second, d2P for the third, and so on (Axelrod
13-4)
•
• V (D/T) T dP d2P

20
Discounting
• Writing this as V (D/T) T dP d 2P ..., we
have the following
• V (D/D) P dP d2P P/(1-d)
• V (C/C) R dR d2R R/(1-d)
• V (T/T) R dR d2R R/(1-d)
• V (D/C) T dT d2T T/(1-d)
• V (D/T) T dP d2P T dP/(1-d)
• V (C/D) S dS d2S S/(1-d)
• V (C/T) R dR d2R R/(1- d)
• V (T/D) S dP d2P S dP/(1-d)
• V (T/C) R dR d2R R/(1- d)

21
Discounting

C D T
R/(1-d) S/(1-d) R/(1-d)
R/(1-d) T/(1-d) R/(1-d)
C
Discounted Payoffs T gt R gt P gt S 0 gt d gt 1 T
weakly dominates C
T/(1-d) P/(1-d) T dP/(1-d)
S/(1-d) P/(1-d) S
dP/(1-d)
D
R/(1-d) S dP/(1-d) R/(1- d)
R/(1-d) T dP/(1-d) R/(1-d)
T
22
Discounting
Now consider what happens to these values as d
varies (from 0-1) V (D/D) P dP
d2P P/(1-d) V (C/C) R dR
d2R R/(1-d) V (T/T) R dR d2R
R/(1-d) V (D/C) T dT d2T
T/(1-d) V (D/T) T dP d2P
T dP/(1-d) V (C/D) S dS d2S
S/(1-d) V (C/T) R dR d2R R/(1-
d) V (T/D) S dP d2P S
dP/(1-d) V (T/C) R dR d2R R/(1-
d)
23
Discounting
Now consider what happens to these values as d
varies (from 0-1) V (D/D) P dP
d2P P dP/(1-d) V (C/C) R dR
d2R R/(1-d) V (T/T) R dR d2R
R/(1-d) V (D/C) T dT d2T
T/(1-d) V (D/T) T dP d2P
T dP/(1-d) V (C/D) S dS d2S
S/(1-d) V (C/T) R dR d2R R/(1-
d) V (T/D) S dP d2P S
dP/(1-d) V (T/C) R dR d2R R/(1-
d)
V(D/D) gt V(T/D) D is a best response to D
24
Discounting
Now consider what happens to these values as d
varies (from 0-1) V (D/D) P dP
d2P P dP/(1-d) V (C/C) R dR
d2R R/(1-d) V (T/T) R dR d2R
R/(1-d) V (D/C) T dT d2T
T/(1-d) V (D/T) T dP d2P
T dP/(1-d) V (C/D) S dS d2S
S/(1-d) V (C/T) R dR d2R R/(1-
d) V (T/D) S dP d2P S
dP/(1-d) V (T/C) R dR d2R R/(1-
d)
2 1 3
?
25
Discounting
• Now consider what happens to these values as d
varies (from 0-1)
•
• For all values of d V(D/T) gt V(D/D) gt
V(T/D)
• V(T/T) gt V(D/D) gt V(T/D)
•
• Is there a value of d s.t., V(D/T) V(T/T)?
Call this d.
• If d lt d, the following ordering hold
•
• V(D/T) gt V(T/T) gt V(D/D) gt V(T/D)
•
• D is dominant GAME SOLVED

?
V(D/T) V(T/T) TdP(1-d) R/(1-d)
T-dtdP R T-R d(T-P) d
(T-R)/(T-P)
26
Discounting
• Now consider what happens to these values as d
varies (from 0-1)
•
• For all values of d V(D/T) gt V(D/D) gt
V(T/D)
• V(T/T) gt V(D/D) gt V(T/D)
•
• Is there a value of d s.t., V(D/T) V(T/T)?
Call this d.
• d (T-R)/(T-P)
• If d gt d, the following ordering hold
•
• V(T/T) gt V(D/T) gt V(D/D) gt V(T/D)
•

D is a best response to D T is a best response
to T multiple NE.
27
Discounting
Graphically The V(alue) to a player using
ALWAYS DEFECT (D) against TRIGGER (T), and the
V(T/T) as a function of the discount parameter
(d)
V T R
V(D/T) T dP/(1-d)
V(T/T) R/(1-d)
d 1
28
The Folk Theorem
The payoff set of the repeated PD is the convex
closure of the points (T,S) (R,R) (S,T)
(P,P).
(S,T)
(R,R)
(P,P)
(T,S)
29
The Folk Theorem
The shaded area is the set of payoffs that
Pareto-dominate the one-shot NE (P,P).
(S,T)
(R,R)
(P,P)
(T,S)
30
The Folk Theorem
Theorem Any payoff that pareto-dominates the
one-shot NE can be supported in a SPNE of the
repeated game, if the discount parameter is
sufficiently high.
(S,T)
(R,R)
(P,P)
(T,S)
31
The Folk Theorem
In other words, in the repeated game, if the
future matters enough i.e., (d gt d), there are
zillions of equilibria!
(S,T)
(R,R)
(P,P)
(T,S)
32
The Folk Theorem
• The theorem tells us that in general, repeated
games give rise to a very large set of Nash
equilibria. In the repeated PD, these are
pareto-rankable, i.e., some are efficient and
some are not.
• In this context, evolution can be seen as a
process that selects for repeated game strategies
with efficient payoffs.

Survival of the Fittest
33
Cartel Enforcement
Consider a market in which two identical firms
can produce a good with a marginal cost of 1 per
unit. The market demand function is given by P
7 Q Assume that the firms choose prices. If
the two firms choose different prices, the one
with the lower price gets all the customers if
they choose the same price, they split the market
demand. What is the Nash Equilibrium of this
game?
34
Cartel Enforcement
Consider a market in which two identical firms
can produce a good with a marginal cost of 1 per
unit. The market demand function is given by P
7 Q Now suppose that the firms compete
repeatedly, and each firm attempts to maximize
the discounted value of its profits (? lt 1).
What if this pair of Bertrand duopolists try to
behave as a monopolist (w/2 plants)?
35
Cartel Enforcement
• What if a pair of Bertrand duopolists try to
behave as a monopolist (w/2 plants)?
• P 7 Q TCi qi
• Monopoly Bertrand Duopoly
• TR TC Q q1 q2
• PQ Q Pb MC 1 Qb 6
• (7-Q)Q - Q
• 7Q - Q2 - Q
• FOC 7-2Q-1 0 gt Qm 3 Pm 4
• w/2 plants q1 q2 1.5 q1 q2 3
• P1 P2 4.5 P1 P2 0

36
Cartel Enforcement
• What if a pair of Bertrand duopolists try to
behave as a monopolist (w/2 plants)?
• Promise Ill charge Pm 4, if you do.
• Threat Ill charge Pb 1, forever, if you
deviate.
• 4.5 4.5 4.5 4.5 4.5 4.5 4.5
(4.5)/(1-d) 4.5 4.5 4.5 9 0 0
0
• If d is sufficiently high, the threat will be
credible, and the pair of trigger strategies is a
Nash equilibrium.
• d 0.5

Trigger Strategy
Current gain from deviation 4.5
Future gain from cooperation d(4.5)/(1-d)
37
UNIT IV INFORMATION WELFARE
• Decision under Uncertainty
• Externalities Public Goods
• Review

38
Decision under Uncertainty
• In UNIT I we assumed that consumers have perfect
information about the possible options they face
(their income and prices) and about the utility
consequences of their choices (their
preferences).
• Now, we will ask whether our model can be
extended to deal with more realistic cases in
which decisions are made without perfect
information.
• We will also ask how imperfect (asymmetric)
information affects market outcomes and their
welfare consequences.

39
Decision under Uncertainty
• The Economics of Information How can I maximize
utility given incomplete info? How much info
should I gather? We can distinguish between 2
sources of uncertainty
• The behavior of other actors (strategic
uncertainty)
• states of nature (natural uncertainty)
• Will it rain? Or not?
• Is there oil in the drilling hole?
• Will the roulette wheel come up red? (1 -- 35)
• Is the car a lemon?

40
Decision under Uncertainty
• The Economics of Information How can I maximize
utility given incomplete info? How much info
should I gather? We can distinguish between 2
sources of uncertainty
• states of nature (natural uncertainty)
• Will it rain? Or not?
• Is there oil in the drilling hole?
• Will the roulette wheel come up red? (1 -- 35)
• Is the car a lemon?

41
Decision under Uncertainty
• Expected Value v. Expected Utility
• Risk Preferences
• Reducing Risk Insurance
• Contingent Consumption
• Adverse Selection (and Moral Hazard)

42
Expected Value Expected Utility
• Which would you prefer?
• A) 50-50 chance of winning 30,000 or losing
5,000
• B) Sure thing of 10,000
• How much would you be willing to pay for the
chance to win 2n if the head comes up on nth
flip?
• 2(1/2) 4(1/4) 1 1

43
Expected Value Expected Utility
• How much would you be willing to pay for the
chance to win 2n if a heads comes up on nth
flip?
• Expected Value (EV) the sum of the value (V) of
each possible state, weighted by the probability
(p) of that state occurring.
• On 1 flip
• p(H) ½ (2) 4(1/4) 1 1

44
Expected Value Expected Utility
• How much would you be willing to pay for the
chance to win 2n if a heads comes up on nth
flip?
• Expected Value (EV) the sum of the value (V) of
each possible state, weighted by the probability
(p) of that state occurring.
• On 1 flip
• EV p(V)H (½)2 4(1/4) 1 1

45
Expected Value Expected Utility
• How much would you be willing to pay for the
chance to win 2n if a heads comes up on nth
flip?
• Expected Value (EV) the sum of the value (V) of
each possible state, weighted by the probability
(p) of that state occurring.
• On nth flip
• EV(Hn) ½n(2n) 4(1/4) 1 1

46
Expected Value Expected Utility
• How much would you be willing to pay for the
chance to win 2n if a heads comes up on nth
flip?
• Expected Value (EV) the sum of the value (V) of
each possible state, weighted by the probability
(p) of that state occurring.
• On nth flip
• EV(Hn) ½n(2n) 4(1/4) 1 1

EV(H)½(2)(1/4)4(1/8)8
H T
Flip 1 Win 2
½ ½
H T
Flip 2 Win 4
¼ ¼
H T
Flip 3 Win 8
½ ¼
8
8
47
Expected Value Expected Utility
• How much would you be willing to pay for the
chance to win 2n if a heads comes up on nth
flip?
• Expected Value (EV) the sum of the value (V) of
each possible state, weighted by the probability
(p) of that state occurring.
• On n flips
• EV(H)(½)2(1/4)4(1/8)8111 infinity
• So, youd be willing to pay an awful lot?

Whats going on here?
48
Expected Value Expected Utility
• With examples such as these, David Bernoulli
(1738) observed that rational agents often behave
contrary to expected value maximization.
• Expected Utility (EU) the sum of the utility of
each possible state, weighted by the probability
of that state occurring.
• EU p1(U(s1)) p2(U(s2)) pn(U(sn))
• Where p is the probability of that state
occurring. arise because utility will be a
non-linear function of wealth.

49
Expected Value Expected Utility
• With examples such as these, David Bernoulli
(1738) observed that rational agents often behave
contrary to expected value maximization.
• Expected Utility (EU) the sum of the utility of
each possible state, weighted by the probability
of that state occurring.
• Rankings of expected values and expected
utilities need not be the same! Differences
arise because utility will be a non-linear
function of wealth and will depend on
endowments.

or income or consumption
50
Expected Value Expected Utility
• Diminishing Marginal Utility The intrinsic worth
of wealth increases with wealth, but at a
diminishing rate.

U U(15) U(10) U(5)
von Neumann-Morgenstern Utility Indexes MU ½W-½
U W½ MU 1/W U lnW For 2 states EU
p(U(Wi)) (1-p)(U(Wj)) MRS (p/(1-p))MUi/MUj
5 10 15 W
51
Risk Preferences
• A risk averse consumer will prefer a certain
income to a risky income with the same expected
value.

U U(15) U(10) U(5)
The chord represents the chance to win 5 or
15.
.5U(5) .5U(15)
5 CE 10 15 W
52
Risk Preferences
• A risk averse consumer will prefer a certain
income to a risky income with the same expected
value.

U U(15) U(10) U(5)
Certainty Equivalent (CE) of an equal chance of
winning 5 and 15 Risk Premium 10 CE
.5U(5) .5U(15)
5 CE 10 15 W
53
Risk Preferences
• A risk loving consumer will prefer a risky income
to a certain income with the same expected value.

U U(15) .5U(5) .5U(15) U(5)
U(10)
5 CE 10 15 W
54
Risk Preferences
• A risk neutral consumer is indifferent between a
risky income and a certain income with the same
expected value.

U U(15) U(10) U(5)
5 CE 10 15 W
55
Risk Preferences
• A risk neutral consumer is indifferent between a
risky income and a certain income with the same
expected value.

Do any of these cases violate any of our
Draw a set of indifference curves for each
case.
U U(15) U(10) U(5)
5 CE 10 15 W
56
Risk and Insurance
• A risk averse consumer will prefer a certain
income to a risky income with the same expected
value. Given the opportunity, therefore, she
will attempt to smooth the variability of her
wealth, by spreading (or diversifying) her risks
across states.
• Insurance offers a way to buy wealth in the event
of a low wealth (or bad) state, by transferring
some wealth from the good to the bad state.

57
Risk and Insurance
• A risk averse consumer has wealth of 35,000,
including a car worth 10,000. There is a 1/100
chance that the car will be stolen.
• So there is a 0.01 chance his wealth will be
25,000 and a 0.99 chance it will be 35,000.
• EW 0.01(25000) 0.99(35000)
• Buying insurance can change this distribution.

58
Risk and Insurance
• If his car is stolen, his wealth will be 25,000
if it is not stolen, his wealth will be 35,000.
Buying insurance is transferring wealth from the

Wg 35,000
Suppose he can by 1000 insurance at a premium of
1/100. g .01 How much insurance will he
?
25,000 Wb
59
Risk and Insurance
• If his car is stolen, his wealth will be 25,000
if it is not stolen, his wealth will be 35,000.
Buying insurance is transferring wealth from the

Wg 35,000
Given the chance to buy insurance at an
actuarily fair price (i.e., g p), a risk
averse consumer will fully insure. Equalizing
Certainty Line
34,900
25,000 Wb
34,900
60
Risk and Insurance
• Insurance is a way to allocate wealth across
possible states of the world. In essence, he is
(wealth) in the two states. So we can solve in
the usual way

Wg Eg
Endowment
More generally E Endowment K dollars of
Eg - gK
Eb Wb
Eb K - gK
61
Contingent Consumption
• If his car is stolen, his wealth will be 25,000
if it is not stolen, his wealth will be 35,000.
Buying insurance is transferring wealth from the

Wg 35,000
Endowment
Now suppose the premium rises to 1.10/100 (g
.011). His vN-M Index U lnW How much
35000 - gk
25,000 Wb
25,000 K - gK
62
Contingent Consumption
• If his car is stolen, his wealth will be 25,000
if it is not stolen, his wealth will be 35,000.
Buying insurance is transferring wealth from the

Wg 35,000
Slope(m) DWg/DWb -gK/(K-gK) -g/(1-g)
g Pb 1-g Pg
m -Pb/Pg
25,000 Wb
Not to scale
63
Contingent Consumption
• If his car is stolen, his wealth will be 25,000
if it is not stolen, his wealth will be 35,000.
Buying insurance is transferring wealth from the

Wg 35,000
Budget Constraint Wg m(Wb) Wg(int) Wg
-(.011/.989)Wb 35278
Wg
m -.0111
25,000 Wb
Wb
Not to scale
64
Contingent Consumption
• If his car is stolen, his wealth will be 25,000
if it is not stolen, his wealth will be 35,000.
Buying insurance is transferring wealth from the

Wg 35,000
U lnW EU p(U(Wb)) (1-p)(U(Wg)) MRS
(p/(1-p))MUb/MUg (.01/.99)(Wg/Wb)
P(Wb)/P(Wg) g/(1-g)
Wg
25,000 Wb
Wb
Not to scale
65
Contingent Consumption
• If his can is stolen, his wealth will be 25,000
if it is not stolen, his wealth will be 35,000.
Buying insurance is transferring wealth from the

Wg 35,000
MRS (.01/.99)(Wg/Wb) Pb/Pg g/(1-g) MRS
Pb/Pg gt Wb .909Wg Wg -(.011/.989)Wb
35278 Wg 34925
Wg
25,000 Wb
Wb
Not to scale
66
Contingent Consumption
• If his can is stolen, his wealth will be 25,000
if it is not stolen, his wealth will be 35,000.
Buying insurance is transferring wealth from the

Wg 35,000
Wg 34925 So he pays 75 for 6818 of ins
Wg34925
25,000 Wb
Wb31743
Not to scale
67
Contingent Consumption
• How would the answer change for a risk lover?

Wg Eg

A risk lover will maximize utility (reach her
highest indifference curve) in a corner solution.
In this case, remaining at the endowment.
Eb Wb
68
• Consider the market for drivers insurance
• Good drivers have accidents with prob 0.2
• Good and bad drivers are equally distributed in
population.
• At the actuarially fair price of 0.50/1
coverage
• for good drivers price is too high -gt dont
insure
• for bad too low -gt insure
• Bad drivers are selected in good are selected
out

What price would an actuarially fair insurance
company charge?
69
• Consider the market for drivers insurance
• Good drivers have accidents with prob 0.2
• Good and bad drivers are equally distributed in
population.
• At the actuarially fair price of 0.50/1
coverage
• for good drivers price is too high -gt dont
insure
• for bad too low -gt insure
• Bad drivers are selected in good are selected
out

Driver quality is a hidden characteristic
70
• Consider the market for drivers insurance
• Good drivers have accidents with prob 0.2
• Good and bad drivers are equally distributed in
population.
• At the actuarially fair price of 0.50/1
coverage
• for good drivers price is too high -gt dont
insure
• for bad too low -gt insure
• Bad drivers are selected in good are selected
out

Asymmetric Information
71
Acquiring a Company
• BUYER represents Company A (the Acquirer), which
is currently considering make a tender offer to
acquire Company T (the Target) from SELLER.
BUYER and SELLER are going to be meeting to
negotiate a price.
• Company T is privately held, so its true value is
known only to SELLER. Whatever the value,
Company T is worth 50 more in the hands of the
acquiring company, due to improved management and
corporate synergies. BUYER only knows that its
value is somewhere between 0 and 100 (/share),
with all values equally likely.

Source M. Bazerman
72
Acquiring a Company
73
Acquiring a Company
45
123 BU MBA Students Similar results from MIT
Masters Candidates CPA CEOs.
Source Bazerman, 1992
27
18
9
7
5
4
4
1
0
0 10-15 20-25 30-35 40-45 50-55 60-65
70-75 80-85 90-95
Offers
74
Acquiring a Company
• OFFER VALUE ACCEPT OR VALUE
GAIN OR
• TO SELLER REJECT TO BUYER
LOSS
• (O) (s) (3/2 s b) (b - O)
• 60 0 A 0 -60
• 10 A 15 -45
• 20 A 30 -30
• 30 A 45 -15
• 40 A 60 0
• 50 A 75 15
• 60 R -
-
• 70 R -
-

75
Acquiring a Company
• The key to the problem is the asymmetric
information structure of the game. SELLER knows
the true value of the company (s). BUYER knows
only the upper and lower limits (0 lt s lt 100).
Therefore, buyer must form an expectation on s
(s').
• BUYER also knows that the company is worth 50
more under the new management, i.e., b' 3/2 s'.
BUYER makes an offer (O). The expected payoff
of the offer, EP(O), is the difference between
the offer and the expected value of the company
• EP(O) b O 3/2s O.

76
Acquiring a Company
• BUYER wants to maximize her payoff by offering
the smallest amount (O) she expects will be
accepted
• EP(O) b O 3/2s O.
• O s' e. Seller accepts if O gt s.
• Now consider this Buyer has formed her
expectation based on very little information. If
Buyer offers O and Seller accepts, this
she can now update her expectation on s.
• How should Buyer update her expectation,
conditioned on the new information that s lt O?
•

77
Acquiring a Company
• BUYER wants to maximize her payoff by offering
the smallest amount (O) she expects will be
accepted
• EP(O) b O 3/2s O.
• O s' e. Seller accepts if O gt s.
• Lets say BUYER offers 50. If SELLER accepts,
BUYER knows that s cannot be greater than (or
equal to) 50, that is 0 lt s lt 50. Since all
values are equally likely, s''/(s lt O) 25.
The expected value of the company to BUYER (b''
3/2s'' 37.50), which is less than the 50 she
just offered to pay. (EP(O) - 12.5.) When
SELLER accepts, BUYER gets a sinking feeling in
the pit of her stomach.
• THE WINNERS CURSE!

78
Acquiring a Company
• BUYER wants to maximize her payoff by offering
the smallest amount (O) she expects will be
accepted
• EP(O) b O 3/2s O.
• O s' e. Seller accepts if O gt s.
• Generally EP(O) O - ¼s' (-e). EP is
negative for all values of O.
• THE WINNERS CURSE!

79
Acquiring a Company
• The high level of uncertainty swamps the
potential gains available, such that value is
often left on the table, i.e., on average the
outcome is inefficient.
• Under these particular conditions, BUYER should
not make an offer.
• SELLER has an incentive to reveal some
the uncertainty, she may make an offer that
leaves both players better off.

80
• Lemons (Akerlof 1970) Buyers of used cars cant
distinguish between high and low quality cars
(lemons) the price of used cars reflects this
uncertainty and the price is lower than high
quality cars are worth. Thus owners of high
quality cars wont choose to sell their cars at
the market price eventually, only (mostly)
lemons will be sold on the used car market.
• Sellers of high-quality products can use means to
certify their value Appraisals audits
reputable agents brand names.
•

81
Moral Hazard
• Buying insurance may make drivers take more
risks. Measures to prevent damage or theft are
costly, so drivers may decide to avoid these
costs, e.g., why lock the car, if Im insured
against theft?
• If insurance companies cannot monitor drivers
habits, they will respond by charging higher
prices to all, so good drivers leave the market
.
• The result is an inefficient allocation of
insurance and a net loss to society, b/c the
price of insurance does not reflect the true
social cost.