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UNIT III: MONOPOLY

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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

The Shadow of the Future
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.
    Instead, they maximize
  • 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.
    Instead, they maximize
  • 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
assumptions about well-behaved preferences?
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
    good to the bad state.

Wg 35,000
Suppose he can by 1000 insurance at a premium of
1/100. g .01 How much insurance will he
buy?he buy?
?
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
    good to the bad state.

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
wealth across states. he buy?
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
    purchasing contingent claims on consumption
    (wealth) in the two states. So we can solve in
    the usual way

Wg Eg
Endowment
More generally E Endowment K dollars of
insurance g premium ?
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
    good to the bad state.

Wg 35,000
Endowment
Now suppose the premium rises to 1.10/100 (g
.011). His vN-M Index U lnW How much
insurance will he buy?
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
    good to the bad state.

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
    good to the bad state.

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
    good to the bad state.

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
    good to the bad state.

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
    good to the bad state.

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
Adverse Selection
  • Consider the market for drivers insurance
  • Good drivers have accidents with prob 0.2
  • Bad 0.8
  • 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
Adverse Selection
  • Consider the market for drivers insurance
  • Good drivers have accidents with prob 0.2
  • Bad 0.8
  • 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
Adverse Selection
  • Consider the market for drivers insurance
  • Good drivers have accidents with prob 0.2
  • Bad 0.8
  • 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
What offer should Buyer make?
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
    in the hands of BUYER
  • 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
    considerably increases Buyers information, so
    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
    information to BUYER, because if BUYER can reduce
    the uncertainty, she may make an offer that
    leaves both players better off.

80
Adverse Selection
  • 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.
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