Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Managerial Economics &
Business Strategy
Chapter 10
Game Theory,
Inside Oligopoly
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Overview
I,Introduction to Game Theory
II,Simultaneous-Move,One-Shot Games
III,Infinitely Repeated Games
IV,Finitely Repeated Games
V,Multistage Games
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Game
? A Normal Form Game consists of,
? Players
? Strategies or feasible actions
? Payoffs
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
A Normal Form Game
S t r a t e g y A B C
a
b
c
Player 2
Pla
ye
r 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Game,
Scenario Analysis
? Suppose 1 thinks 2 will choose,A”,
S t r a t e g y A B C
a
b
c
Player 2
Play
er 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Game,
Scenario Analysis
? Then 1 should choose,a”,
? Player 1’s best response to,A” is,a”,
S t r a t e g y A B C
a
b
c
Player 2
Pla
ye
r 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Game,
Scenario Analysis
? Suppose 1 thinks 2 will choose,B”,
S t r a t e g y A B C
a
b
c
Player 2
Pla
ye
r 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Game,
Scenario Analysis
? Then 1 should choose,a”,
? Player 1’s best response to,B” is,a”,
S t r a t e g y A B C
a
b
c
Player 2
Pla
ye
r 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Game
Scenario Analysis
? Similarly,if 1 thinks 2 will choose C…
? Player 1’s best response to,C” is,a”,
S t r a t e g y A B C
a
b
c
Player 2
Play
er 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Dominant Strategy
? Regardless of whether Player 2 chooses A,B,or
C,Player 1 is better off choosing,a”!
?,a” is Player 1’s Dominant Strategy!
S t r a t e g y A B C
a
b
c
Player 2
Pla
ye
r 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Putting Yourself in your Rival’s
Shoes
? What should player 2 do?
? 2 has no dominant strategy!
? But 2 should reason that 1 will play,a”,
? Therefore 2 should choose,C”,
S t r a t e g y A B C
a
b
c
Player 2
Play
er 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
The Outcome
? This outcome is called a Nash equilibrium,
?,a” is player 1’s best response to,C”,
?,C” is player 2’s best response to,a”,
S t r a t e g y A B C
a
b
c
Player 2
Pla
ye
r 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Key Insights
? Look for dominant strategies
? Put yourself in your rival’s shoes
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
A Market Share Game
? Two managers want to maximize market
share
? Strategies are pricing decisions
? Simultaneous moves
? One-shot game
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
The Market-Share Game
in Normal Form
S t r a t e g y P = $ 1 0 P = $ 5 P = $ 1
P = $ 1 0, 5,,5, 2,,8, 1,,9
P = $ 5, 8,,2, 5,,5, 2,,8
P = $ 1, 9,,1, 8,,2, 5,,5
Manager 2
M
an
age
r 1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Market-Share Game
Equilibrium
S t r a t e g y P = $ 1 0 P = $ 5 P = $ 1
P = $ 1 0, 5,,5, 2,,8, 1,,9
P = $ 5, 8,,2, 5,,5, 2,,8
P = $ 1, 9,,1, 8,,2, 5,,5
Manager 2
M
an
age
r 1
Nash Equilibrium
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Key Insight,
? Game theory can be used to analyze
situations where,payoffs” are non
monetary!
? We will,without loss of generality,focus on
environments where businesses want to
maximize profits,
? Hence,payoffs are measured in monetary units,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Examples of Coordination
Games
? Industry standards
? size of floppy disks
? size of CDs
? etc,
? National standards
? electric current
? traffic laws
? etc,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
A Coordination Game in
Normal Form
S t r a t e g y A B C
1 0,0 0,0 $ 1 0,$ 1 0
2 $ 1 0,$ 1 0 0,0 0,0
3 0,0 $ 1 0,$ 1 0 0,0
Player 2
Pl
ay
er 1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
A Coordination Problem,
Three Nash Equilibria!
S t r a t e g y A B C
1 0,0 0,0 $ 1 0,$ 1 0
2 $ 1 0,$ 1 0 0,0 0,0
3 0,0 $ 1 0,$ 1 0 0,0
Player 2
Pl
ay
er 1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Key Insights,
? Not all games are games of conflict,
? Communication can help solve coordination
problems,
? Sequential moves can help solve coordination
problems,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
An Advertising Game
? Two firms (Kellogg’s & General Mills)
managers want to maximize profits
? Strategies consist of advertising campaigns
? Simultaneous moves
? One-shot interaction
? Repeated interaction
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
A One-Shot Advertising Game
S t r a t e g y N o n e M o d e r a t e H i g h
N o n e 1 2,1 2 1,2 0 - 1,1 5
M o d e r a t e 2 0,1 6,6 0,9
H i g h 1 5,- 1 9,0 2,2
General Mills
Ke
llogg’
s
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Equilibrium to the One-Shot
Advertising Game
S t r a t e g y N o n e M o d e r a t e H i g h
N o n e 1 2,1 2 1,2 0 - 1,1 5
M o d e r a t e 2 0,1 6,6 0,9
H i g h 1 5,- 1 9,0 2,2
General Mills
Ke
llogg’
s
Nash Equilibrium
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Can collusion work if the game
is repeated 2 times?
S t r a t e g y N o n e M o d e r a t e H i g h
N o n e 1 2,1 2 1,2 0 - 1,1 5
M o d e r a t e 2 0,1 6,6 0,9
H i g h 1 5,- 1 9,0 2,2
General Mills
Ke
llogg’
s
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
No (by backwards induction),
? In period 2,the game is a one-shot game,so
equilibrium entails High Advertising in the
last period,
? This means period 1 is,really” the last
period,since everyone knows what will
happen in period 2,
? Equilibrium entails High Advertising by
each firm in both periods,
? The same holds true if we repeat the game
any known,finite number of times,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Can collusion work if firms play the
game each year,forever?
? Consider the following,trigger strategy”
by each firm,
?,Don’t advertise,provided the rival has not advertised
in the past,If the rival ever advertises,“punish” it by
engaging in a high level of advertising forever after.”
? In effect,each firm agrees to,cooperate”
so long as the rival hasn’t,cheated” in the
past.,Cheating” triggers punishment in all
future periods,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Suppose General Mills adopts this
trigger strategy,Kellogg’s profits?
?Cooperate = 12 +12/(1+i) + 12/(1+i)2 + 12/(1+i)3 + …
= 12 + 12/i
S t r a t e g y N o n e M o d e r a t e H i g h
N o n e 1 2,1 2 1,2 0 - 1,1 5
M o d e r a t e 2 0,1 6,6 0,9
H i g h 1 5,- 1 9,0 2,2
General Mills
Ke
llog
g’s
Value of a perpetuity of $12 paid
at the end of every year
?Cheat = 20 +2/(1+i) + 2/(1+i)2 + 2/(1+i)3 +
= 20 + 2/i
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Kellogg’s Gain to Cheating,
? ?Cheat - ?Cooperate = 20 + 2/i - (12 + 12/i) = 8 - 10/i
? Suppose i =,05
? ?Cheat - ?Cooperate = 8 - 10/.05 = 8 - 200 = -192
? It doesn’t pay to deviate,
? Collusion is a Nash equilibrium in the infinitely repeated
game!
S t r a t e g y N o n e M o d e r a t e H i g h
N o n e 1 2,1 2 1,2 0 - 1,1 5
M o d e r a t e 2 0,1 6,6 0,9
H i g h 1 5,- 1 9,0 2,2
General Mills
Ke
llogg’
s
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Benefits & Costs of Cheating
? ?Cheat - ?Cooperate = 8 - 10/i
? 8 = Immediate Benefit (20 - 12 today)
? 10/i = PV of Future Cost (12 - 2 forever after)
? If Immediate Benefit > PV of Future Cost
? Pays to,cheat”,
? If Immediate Benefit ? PV of Future Cost
? Doesn’t pay to,cheat”,
S t r a t e g y N o n e M o d e r a t e H i g h
N o n e 12,1 2 1,2 0 - 1,1 5
M o d e r a t e 20,1 6,6 0,9
H i g h 1 5,- 1 9,0 2,2
General Mills
Ke
llogg’
s
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Key Insight
? Collusion can be sustained as a Nash
equilibrium when there is no certain,end”
to a game,
? Doing so requires,
? Ability to monitor actions of rivals
? Ability (and reputation for) punishing defectors
? Low interest rate
? High probability of future interaction
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Real World Examples of
Collusion
? Garbage Collection Industry
? OPEC
? NASDAQ
? Airlines
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Garbage Collection Industry
? Homogeneous products
? Bertrand oligopoly
? Identity of customers is known
? Identity of competitors is known
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Bertrand Game
S t r a t e g y L o w P r i c e H i g h P r i c e
L o w P r i c e 0,0 2 0,- 1
H i g h P r i c e - 1,2 0 1 5,1 5Firm 1
Firm 2
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
One-Shot Bertrand
(Nash) Equilibrium
S t r a t e g y L o w P r i c e H i g h P r i c e
L o w P r i c e 0,0 2 0,- 1
H i g h P r i c e - 1,2 0 1 5,1 5Firm 1
Firm 2
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Potential Repeated Game
Equilibrium Outcome
S t r a t e g y L o w P r i c e H i g h P r i c e
L o w P r i c e 0,0 2 0,- 1
H i g h P r i c e - 1,2 0 1 5,1 5Firm 1
Firm 2
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
2,OPEC
? Cartel founded in 1960 by Iran,Iraq,Kuwait,Saudi
Arabia,and Venezuela
? Currently has 11 members
?,OPEC’s objective is to co-ordinate and unify
petroleum policies among Member Countries,in
order to secure fair and stable prices for petroleum
producers…” (www.opec.com)
? Cournot oligopoly
? Absent collusion,PCompetition < PCournot < PMonopoly
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Current OPEC Members
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cournot Game in Normal
Form
S t r a t e g y H i g h Q M e d Q L o w Q
H i g h Q 5,3 9,4 3,6
M e d Q 6,7 1 2,1 0 2 0,8
L o w Q 8,1 1 0,1 8 1 8,1 5
Venezuela
Sau
di
Ar
ab
ia
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
One-Shot Cournot
(Nash) Equilibrium
S t r a t e g y H i g h Q M e d Q L o w Q
H i g h Q 5,3 9,4 3,6
M e d Q 6,7 1 2,1 0 2 0,8
L o w Q 8,1 1 0,1 8 1 8,1 5
Venezuela
Sau
di
Ar
ab
ia
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Repeated Game Equilibrium*
Venezuela
S t r a t e g y H i g h Q M e d Q L o w Q
H i g h Q 5,3 9,4 3,6
M e d Q 6,7 1 2,1 0 2 0,8
L o w Q 8,1 1 0,1 8 1 8,1 5
* (Assuming a Low Interest Rate)
Sau
di
Ar
ab
ia
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Effect of Collusion on Oil
Prices
Quantity of Oil
Price
World Demand
for Oil
Medium
$15
Low
$30
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
OPEC’s Demise
-5
0
5
10
15
20
25
30
35
40
1970 1972 1974 1976 1978 1980 1982 1984 1986
R e a l I n te r e s t R a te Pr i c e o f O i l
Low Interest
Rates
High Interest
Rates
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Caveat
? Collusion is a felony under Section 2 of the
Sherman Antitrust Act,
? Conviction can result in both fines and jail-
time (at the discretion of the court),
? Some NASDAQ dealers and airline companies
have been charged with violations
? OPEC isn’t illegal; US laws don’t apply
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Simultaneous-Move Bargaining
? Management and a union are negotiating a wage increase,
? Strategies are wage offers & wage demands
? Successful negotiations lead to $600 million in surplus,
which must be split among the parties
? Failure to reach an agreement results in a loss to the firm
of $100 million and a union loss of $3 million
? Simultaneous moves,and time permits only one-shot at
making a deal,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
The Bargaining Game
in Normal Form
S t r a t e g y W = $ 1 0 W = $ 5 W = $ 1
W = $ 1 0 1 0 0,5 0 0 - 1 0 0,- 3 - 1 0 0,- 3
W = $ 5 - 1 0 0,- 3 3 0 0,3 0 0 - 1 0 0,- 3
W = $ 1 - 1 0 0,- 3 - 1 0 0,- 3 5 0 0,1 0 0
Union
M
an
age
me
nt
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Three Nash Equilibria!
S t r a t e g y W = $ 1 0 W = $ 5 W = $ 1
W = $ 1 0 1 0 0,5 0 0 - 1 0 0,- 3 - 1 0 0,- 3
W = $ 5 - 1 0 0,- 3 3 0 0,3 0 0 - 1 0 0,- 3
W = $ 1 - 1 0 0,- 3 - 1 0 0,- 3 5 0 0,1 0 0
Union
M
an
age
me
nt
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Fairness,The,Natural” Focal
Point
S t r a t e g y W = $ 1 0 W = $ 5 W = $ 1
W = $ 1 0 1 0 0,5 0 0 - 1 0 0,- 3 - 1 0 0,- 3
W = $ 5 - 1 0 0,- 3 3 0 0,3 0 0 - 1 0 0,- 3
W = $ 1 - 1 0 0,- 3 - 1 0 0,- 3 5 0 0,1 0 0
Union
M
an
age
me
nt
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Lessons in
Simultaneous Bargaining
? Simultaneous-move bargaining results in a
coordination problem
? Experiments suggests that,in the absence of
any,history,” real players typically
coordinate on the,fair outcome”
? When there is a,bargaining history,” other
outcomes may prevail
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Single Offer Bargaining
? Now suppose the game is sequential in nature,and
management gets to make the union a,take-it-or-
leave-it” offer,
? Analysis Tool,Write the game in extensive form
? Summarize the players
? Their potential actions
? Their information at each decision point
? The sequence of moves and
? Each player’s payoff
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Firm
10
5
1
Step 1,Management’s Move
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Firm
10
5
1
Union
Union
Union
Accept
Reject
Accept
Accept
Reject
Reject
Step 2,Add the Union’s
Move
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Firm
10
5
1
Union
Union
Union
Accept
Reject
100,500
-100,-3
Accept
Accept
300,300
-100,-3 Reject
Reject
500,100
-100,-3
Step 3,Add the Payoffs
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
The Game in Extensive Form
Firm
10
5
1
Union
Union
Union
Accept
Reject
100,500
-100,-3
Accept
Accept
300,300
-100,-3 Reject
Reject
500,100
-100,-3
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Step 4,Identify the Firm’s
Feasible Strategies
? Management has one information set and
thus three feasible strategies,
? Offer $10
? Offer $5
? Offer $1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Step 5,Identify the Union’s
Feasible Strategies
? Accept $10,Accept $5,Accept $1
? Accept $10,Accept $5,Reject $1
? Accept $10,Reject $5,Accept $1
? Reject $10,Accept $5,Accept $1
? Accept $10,Reject $5,Reject $1
? Reject $10,Accept $5,Reject $1
? Reject $10,Reject $5,Accept $1
? Reject $10,Reject $5,Reject $1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Step 6,Identify Nash
Equilibrium Outcomes,
? Outcomes such that neither the firm nor the
union has an incentive to change its strategy,
given the strategy of the other
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Finding Nash
Equilibrium Outcomes
A c c e p t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
U n i o n ' s S t r a t e g y F i r m ' s B e s t
R e s p o n s e
M u t u a l B e s t
R e s p o n s e?
$1 Yes
$5
$1
$1
$10
Yes
Yes
Yes
Yes
$5 Yes
$1
No
Yes
$10,$5,$1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Step 7,Find the Subgame
Perfect Nash Equilibrium
Outcomes
? Outcomes where no player has an incentive
to change its strategy,given the strategy of
the rival,and
? The outcomes are based on,credible
actions;” that is,they are not the result of
“empty threats” by the rival,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Checking for Credible Actions
A c c e p t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
U n i o n ' s S t r a t e g y
A r e a l l
A c t i o n s
C r e d i b l e?
Yes
No
No
No
No
No
No
No
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
The,Credible” Union Strategy
A c c e p t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
U n i o n ' s S t r a t e g y
A r e a l l
A c t i o n s
C r e d i b l e?
Yes
No
No
No
No
No
No
No
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Finding Subgame Perfect Nash
Equilibrium Strategies
A c c e p t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
U n i o n ' s S t r a t e g y F i r m ' s B e s t
R e s p o n s e
M u t u a l B e s t
R e s p o n s e?
$1 Yes
$5
$1
$1
$10
Yes
Yes
Yes
Yes
$5 Yes
$1
No
Yes
$10,$5,$1
Nash and Credible Nash Only Neither Nash Nor Credible
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
To Summarize,
? We have identified many combinations of
Nash equilibrium strategies
? In all but one the union does something that
isn’t in its self interest (and thus entail
threats that are not credible)
? Graphically,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Firm
10
5
1
Union
Union
Union
Accept
Reject
100,500
-100,-3
Accept
Accept
300,300
-100,-3 Reject
Reject
500,100
-100,-3
There are 3 Nash
Equilibrium Outcomes!
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Firm
10
5
1
Union
Union
Union
Accept
Reject
100,500
-100,-3
Accept
Accept
300,300
-100,-3 Reject
Reject
500,100
-100,-3
Only 1 Subgame-Perfect Nash
Equilibrium Outcome!
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Re-Cap
? In take-it-or-leave-it bargaining,there is a
first-mover advantage,
? Management can gain by making a take-it
or leave-it offer to the union,But..,
? Management should be careful,however;
real world evidence suggests that people
sometimes reject offers on the the basis of
“principle” instead of cash considerations,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Pricing to Prevent Entry,An
Application of Game Theory
? Two firms,an incumbent and potential
entrant
? The game in extensive form,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
The Entry Game in Extensive
Form
Entrant
Out
Enter
Incumbent
Hard
Soft
-1,1
5,5
0,10
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Identify Nash and Subgame
Perfect Equilibria
Entrant
Out
Enter
Incumbent
Hard
Soft
-1,1
5,5
0,10
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Two Nash Equilibria
Entrant
Out
Enter
Incumbent
Hard
Soft
-1,1
5,5
0,10
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
One Subgame Perfect Equilibrium
Entrant
Out
Enter
Incumbent
Hard
Soft
-1,1
5,5
0,10
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Insights
? Establishing a reputation for being unkind
to entrants can enhance long-term profits
? It is costly to do so in the short-term,so
much so that it isn’t optimal to do so in a
one-shot game,
Managerial Economics &
Business Strategy
Chapter 10
Game Theory,
Inside Oligopoly
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Overview
I,Introduction to Game Theory
II,Simultaneous-Move,One-Shot Games
III,Infinitely Repeated Games
IV,Finitely Repeated Games
V,Multistage Games
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Game
? A Normal Form Game consists of,
? Players
? Strategies or feasible actions
? Payoffs
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
A Normal Form Game
S t r a t e g y A B C
a
b
c
Player 2
Pla
ye
r 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Game,
Scenario Analysis
? Suppose 1 thinks 2 will choose,A”,
S t r a t e g y A B C
a
b
c
Player 2
Play
er 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Game,
Scenario Analysis
? Then 1 should choose,a”,
? Player 1’s best response to,A” is,a”,
S t r a t e g y A B C
a
b
c
Player 2
Pla
ye
r 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Game,
Scenario Analysis
? Suppose 1 thinks 2 will choose,B”,
S t r a t e g y A B C
a
b
c
Player 2
Pla
ye
r 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Game,
Scenario Analysis
? Then 1 should choose,a”,
? Player 1’s best response to,B” is,a”,
S t r a t e g y A B C
a
b
c
Player 2
Pla
ye
r 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Game
Scenario Analysis
? Similarly,if 1 thinks 2 will choose C…
? Player 1’s best response to,C” is,a”,
S t r a t e g y A B C
a
b
c
Player 2
Play
er 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Dominant Strategy
? Regardless of whether Player 2 chooses A,B,or
C,Player 1 is better off choosing,a”!
?,a” is Player 1’s Dominant Strategy!
S t r a t e g y A B C
a
b
c
Player 2
Pla
ye
r 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Putting Yourself in your Rival’s
Shoes
? What should player 2 do?
? 2 has no dominant strategy!
? But 2 should reason that 1 will play,a”,
? Therefore 2 should choose,C”,
S t r a t e g y A B C
a
b
c
Player 2
Play
er 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
The Outcome
? This outcome is called a Nash equilibrium,
?,a” is player 1’s best response to,C”,
?,C” is player 2’s best response to,a”,
S t r a t e g y A B C
a
b
c
Player 2
Pla
ye
r 1
12,11 11,12
14,13
11,10
10,11
12,12
10,15
10,13
13,14
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Key Insights
? Look for dominant strategies
? Put yourself in your rival’s shoes
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
A Market Share Game
? Two managers want to maximize market
share
? Strategies are pricing decisions
? Simultaneous moves
? One-shot game
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
The Market-Share Game
in Normal Form
S t r a t e g y P = $ 1 0 P = $ 5 P = $ 1
P = $ 1 0, 5,,5, 2,,8, 1,,9
P = $ 5, 8,,2, 5,,5, 2,,8
P = $ 1, 9,,1, 8,,2, 5,,5
Manager 2
M
an
age
r 1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Market-Share Game
Equilibrium
S t r a t e g y P = $ 1 0 P = $ 5 P = $ 1
P = $ 1 0, 5,,5, 2,,8, 1,,9
P = $ 5, 8,,2, 5,,5, 2,,8
P = $ 1, 9,,1, 8,,2, 5,,5
Manager 2
M
an
age
r 1
Nash Equilibrium
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Key Insight,
? Game theory can be used to analyze
situations where,payoffs” are non
monetary!
? We will,without loss of generality,focus on
environments where businesses want to
maximize profits,
? Hence,payoffs are measured in monetary units,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Examples of Coordination
Games
? Industry standards
? size of floppy disks
? size of CDs
? etc,
? National standards
? electric current
? traffic laws
? etc,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
A Coordination Game in
Normal Form
S t r a t e g y A B C
1 0,0 0,0 $ 1 0,$ 1 0
2 $ 1 0,$ 1 0 0,0 0,0
3 0,0 $ 1 0,$ 1 0 0,0
Player 2
Pl
ay
er 1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
A Coordination Problem,
Three Nash Equilibria!
S t r a t e g y A B C
1 0,0 0,0 $ 1 0,$ 1 0
2 $ 1 0,$ 1 0 0,0 0,0
3 0,0 $ 1 0,$ 1 0 0,0
Player 2
Pl
ay
er 1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Key Insights,
? Not all games are games of conflict,
? Communication can help solve coordination
problems,
? Sequential moves can help solve coordination
problems,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
An Advertising Game
? Two firms (Kellogg’s & General Mills)
managers want to maximize profits
? Strategies consist of advertising campaigns
? Simultaneous moves
? One-shot interaction
? Repeated interaction
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
A One-Shot Advertising Game
S t r a t e g y N o n e M o d e r a t e H i g h
N o n e 1 2,1 2 1,2 0 - 1,1 5
M o d e r a t e 2 0,1 6,6 0,9
H i g h 1 5,- 1 9,0 2,2
General Mills
Ke
llogg’
s
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Equilibrium to the One-Shot
Advertising Game
S t r a t e g y N o n e M o d e r a t e H i g h
N o n e 1 2,1 2 1,2 0 - 1,1 5
M o d e r a t e 2 0,1 6,6 0,9
H i g h 1 5,- 1 9,0 2,2
General Mills
Ke
llogg’
s
Nash Equilibrium
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Can collusion work if the game
is repeated 2 times?
S t r a t e g y N o n e M o d e r a t e H i g h
N o n e 1 2,1 2 1,2 0 - 1,1 5
M o d e r a t e 2 0,1 6,6 0,9
H i g h 1 5,- 1 9,0 2,2
General Mills
Ke
llogg’
s
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
No (by backwards induction),
? In period 2,the game is a one-shot game,so
equilibrium entails High Advertising in the
last period,
? This means period 1 is,really” the last
period,since everyone knows what will
happen in period 2,
? Equilibrium entails High Advertising by
each firm in both periods,
? The same holds true if we repeat the game
any known,finite number of times,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Can collusion work if firms play the
game each year,forever?
? Consider the following,trigger strategy”
by each firm,
?,Don’t advertise,provided the rival has not advertised
in the past,If the rival ever advertises,“punish” it by
engaging in a high level of advertising forever after.”
? In effect,each firm agrees to,cooperate”
so long as the rival hasn’t,cheated” in the
past.,Cheating” triggers punishment in all
future periods,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Suppose General Mills adopts this
trigger strategy,Kellogg’s profits?
?Cooperate = 12 +12/(1+i) + 12/(1+i)2 + 12/(1+i)3 + …
= 12 + 12/i
S t r a t e g y N o n e M o d e r a t e H i g h
N o n e 1 2,1 2 1,2 0 - 1,1 5
M o d e r a t e 2 0,1 6,6 0,9
H i g h 1 5,- 1 9,0 2,2
General Mills
Ke
llog
g’s
Value of a perpetuity of $12 paid
at the end of every year
?Cheat = 20 +2/(1+i) + 2/(1+i)2 + 2/(1+i)3 +
= 20 + 2/i
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Kellogg’s Gain to Cheating,
? ?Cheat - ?Cooperate = 20 + 2/i - (12 + 12/i) = 8 - 10/i
? Suppose i =,05
? ?Cheat - ?Cooperate = 8 - 10/.05 = 8 - 200 = -192
? It doesn’t pay to deviate,
? Collusion is a Nash equilibrium in the infinitely repeated
game!
S t r a t e g y N o n e M o d e r a t e H i g h
N o n e 1 2,1 2 1,2 0 - 1,1 5
M o d e r a t e 2 0,1 6,6 0,9
H i g h 1 5,- 1 9,0 2,2
General Mills
Ke
llogg’
s
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Benefits & Costs of Cheating
? ?Cheat - ?Cooperate = 8 - 10/i
? 8 = Immediate Benefit (20 - 12 today)
? 10/i = PV of Future Cost (12 - 2 forever after)
? If Immediate Benefit > PV of Future Cost
? Pays to,cheat”,
? If Immediate Benefit ? PV of Future Cost
? Doesn’t pay to,cheat”,
S t r a t e g y N o n e M o d e r a t e H i g h
N o n e 12,1 2 1,2 0 - 1,1 5
M o d e r a t e 20,1 6,6 0,9
H i g h 1 5,- 1 9,0 2,2
General Mills
Ke
llogg’
s
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Key Insight
? Collusion can be sustained as a Nash
equilibrium when there is no certain,end”
to a game,
? Doing so requires,
? Ability to monitor actions of rivals
? Ability (and reputation for) punishing defectors
? Low interest rate
? High probability of future interaction
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Real World Examples of
Collusion
? Garbage Collection Industry
? OPEC
? NASDAQ
? Airlines
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Garbage Collection Industry
? Homogeneous products
? Bertrand oligopoly
? Identity of customers is known
? Identity of competitors is known
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Normal Form Bertrand Game
S t r a t e g y L o w P r i c e H i g h P r i c e
L o w P r i c e 0,0 2 0,- 1
H i g h P r i c e - 1,2 0 1 5,1 5Firm 1
Firm 2
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
One-Shot Bertrand
(Nash) Equilibrium
S t r a t e g y L o w P r i c e H i g h P r i c e
L o w P r i c e 0,0 2 0,- 1
H i g h P r i c e - 1,2 0 1 5,1 5Firm 1
Firm 2
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Potential Repeated Game
Equilibrium Outcome
S t r a t e g y L o w P r i c e H i g h P r i c e
L o w P r i c e 0,0 2 0,- 1
H i g h P r i c e - 1,2 0 1 5,1 5Firm 1
Firm 2
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
2,OPEC
? Cartel founded in 1960 by Iran,Iraq,Kuwait,Saudi
Arabia,and Venezuela
? Currently has 11 members
?,OPEC’s objective is to co-ordinate and unify
petroleum policies among Member Countries,in
order to secure fair and stable prices for petroleum
producers…” (www.opec.com)
? Cournot oligopoly
? Absent collusion,PCompetition < PCournot < PMonopoly
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Current OPEC Members
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cournot Game in Normal
Form
S t r a t e g y H i g h Q M e d Q L o w Q
H i g h Q 5,3 9,4 3,6
M e d Q 6,7 1 2,1 0 2 0,8
L o w Q 8,1 1 0,1 8 1 8,1 5
Venezuela
Sau
di
Ar
ab
ia
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
One-Shot Cournot
(Nash) Equilibrium
S t r a t e g y H i g h Q M e d Q L o w Q
H i g h Q 5,3 9,4 3,6
M e d Q 6,7 1 2,1 0 2 0,8
L o w Q 8,1 1 0,1 8 1 8,1 5
Venezuela
Sau
di
Ar
ab
ia
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Repeated Game Equilibrium*
Venezuela
S t r a t e g y H i g h Q M e d Q L o w Q
H i g h Q 5,3 9,4 3,6
M e d Q 6,7 1 2,1 0 2 0,8
L o w Q 8,1 1 0,1 8 1 8,1 5
* (Assuming a Low Interest Rate)
Sau
di
Ar
ab
ia
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Effect of Collusion on Oil
Prices
Quantity of Oil
Price
World Demand
for Oil
Medium
$15
Low
$30
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
OPEC’s Demise
-5
0
5
10
15
20
25
30
35
40
1970 1972 1974 1976 1978 1980 1982 1984 1986
R e a l I n te r e s t R a te Pr i c e o f O i l
Low Interest
Rates
High Interest
Rates
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Caveat
? Collusion is a felony under Section 2 of the
Sherman Antitrust Act,
? Conviction can result in both fines and jail-
time (at the discretion of the court),
? Some NASDAQ dealers and airline companies
have been charged with violations
? OPEC isn’t illegal; US laws don’t apply
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Simultaneous-Move Bargaining
? Management and a union are negotiating a wage increase,
? Strategies are wage offers & wage demands
? Successful negotiations lead to $600 million in surplus,
which must be split among the parties
? Failure to reach an agreement results in a loss to the firm
of $100 million and a union loss of $3 million
? Simultaneous moves,and time permits only one-shot at
making a deal,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
The Bargaining Game
in Normal Form
S t r a t e g y W = $ 1 0 W = $ 5 W = $ 1
W = $ 1 0 1 0 0,5 0 0 - 1 0 0,- 3 - 1 0 0,- 3
W = $ 5 - 1 0 0,- 3 3 0 0,3 0 0 - 1 0 0,- 3
W = $ 1 - 1 0 0,- 3 - 1 0 0,- 3 5 0 0,1 0 0
Union
M
an
age
me
nt
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Three Nash Equilibria!
S t r a t e g y W = $ 1 0 W = $ 5 W = $ 1
W = $ 1 0 1 0 0,5 0 0 - 1 0 0,- 3 - 1 0 0,- 3
W = $ 5 - 1 0 0,- 3 3 0 0,3 0 0 - 1 0 0,- 3
W = $ 1 - 1 0 0,- 3 - 1 0 0,- 3 5 0 0,1 0 0
Union
M
an
age
me
nt
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Fairness,The,Natural” Focal
Point
S t r a t e g y W = $ 1 0 W = $ 5 W = $ 1
W = $ 1 0 1 0 0,5 0 0 - 1 0 0,- 3 - 1 0 0,- 3
W = $ 5 - 1 0 0,- 3 3 0 0,3 0 0 - 1 0 0,- 3
W = $ 1 - 1 0 0,- 3 - 1 0 0,- 3 5 0 0,1 0 0
Union
M
an
age
me
nt
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Lessons in
Simultaneous Bargaining
? Simultaneous-move bargaining results in a
coordination problem
? Experiments suggests that,in the absence of
any,history,” real players typically
coordinate on the,fair outcome”
? When there is a,bargaining history,” other
outcomes may prevail
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Single Offer Bargaining
? Now suppose the game is sequential in nature,and
management gets to make the union a,take-it-or-
leave-it” offer,
? Analysis Tool,Write the game in extensive form
? Summarize the players
? Their potential actions
? Their information at each decision point
? The sequence of moves and
? Each player’s payoff
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Firm
10
5
1
Step 1,Management’s Move
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Firm
10
5
1
Union
Union
Union
Accept
Reject
Accept
Accept
Reject
Reject
Step 2,Add the Union’s
Move
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Firm
10
5
1
Union
Union
Union
Accept
Reject
100,500
-100,-3
Accept
Accept
300,300
-100,-3 Reject
Reject
500,100
-100,-3
Step 3,Add the Payoffs
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
The Game in Extensive Form
Firm
10
5
1
Union
Union
Union
Accept
Reject
100,500
-100,-3
Accept
Accept
300,300
-100,-3 Reject
Reject
500,100
-100,-3
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Step 4,Identify the Firm’s
Feasible Strategies
? Management has one information set and
thus three feasible strategies,
? Offer $10
? Offer $5
? Offer $1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Step 5,Identify the Union’s
Feasible Strategies
? Accept $10,Accept $5,Accept $1
? Accept $10,Accept $5,Reject $1
? Accept $10,Reject $5,Accept $1
? Reject $10,Accept $5,Accept $1
? Accept $10,Reject $5,Reject $1
? Reject $10,Accept $5,Reject $1
? Reject $10,Reject $5,Accept $1
? Reject $10,Reject $5,Reject $1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Step 6,Identify Nash
Equilibrium Outcomes,
? Outcomes such that neither the firm nor the
union has an incentive to change its strategy,
given the strategy of the other
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Finding Nash
Equilibrium Outcomes
A c c e p t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
U n i o n ' s S t r a t e g y F i r m ' s B e s t
R e s p o n s e
M u t u a l B e s t
R e s p o n s e?
$1 Yes
$5
$1
$1
$10
Yes
Yes
Yes
Yes
$5 Yes
$1
No
Yes
$10,$5,$1
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Step 7,Find the Subgame
Perfect Nash Equilibrium
Outcomes
? Outcomes where no player has an incentive
to change its strategy,given the strategy of
the rival,and
? The outcomes are based on,credible
actions;” that is,they are not the result of
“empty threats” by the rival,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Checking for Credible Actions
A c c e p t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
U n i o n ' s S t r a t e g y
A r e a l l
A c t i o n s
C r e d i b l e?
Yes
No
No
No
No
No
No
No
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
The,Credible” Union Strategy
A c c e p t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
U n i o n ' s S t r a t e g y
A r e a l l
A c t i o n s
C r e d i b l e?
Yes
No
No
No
No
No
No
No
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Finding Subgame Perfect Nash
Equilibrium Strategies
A c c e p t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,A c c e p t $ 1
A c c e p t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,A c c e p t $ 5,R e j e c t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,A c c e p t $ 1
R e j e c t $ 1 0,R e j e c t $ 5,R e j e c t $ 1
U n i o n ' s S t r a t e g y F i r m ' s B e s t
R e s p o n s e
M u t u a l B e s t
R e s p o n s e?
$1 Yes
$5
$1
$1
$10
Yes
Yes
Yes
Yes
$5 Yes
$1
No
Yes
$10,$5,$1
Nash and Credible Nash Only Neither Nash Nor Credible
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
To Summarize,
? We have identified many combinations of
Nash equilibrium strategies
? In all but one the union does something that
isn’t in its self interest (and thus entail
threats that are not credible)
? Graphically,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Firm
10
5
1
Union
Union
Union
Accept
Reject
100,500
-100,-3
Accept
Accept
300,300
-100,-3 Reject
Reject
500,100
-100,-3
There are 3 Nash
Equilibrium Outcomes!
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Firm
10
5
1
Union
Union
Union
Accept
Reject
100,500
-100,-3
Accept
Accept
300,300
-100,-3 Reject
Reject
500,100
-100,-3
Only 1 Subgame-Perfect Nash
Equilibrium Outcome!
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Re-Cap
? In take-it-or-leave-it bargaining,there is a
first-mover advantage,
? Management can gain by making a take-it
or leave-it offer to the union,But..,
? Management should be careful,however;
real world evidence suggests that people
sometimes reject offers on the the basis of
“principle” instead of cash considerations,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Pricing to Prevent Entry,An
Application of Game Theory
? Two firms,an incumbent and potential
entrant
? The game in extensive form,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
The Entry Game in Extensive
Form
Entrant
Out
Enter
Incumbent
Hard
Soft
-1,1
5,5
0,10
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Identify Nash and Subgame
Perfect Equilibria
Entrant
Out
Enter
Incumbent
Hard
Soft
-1,1
5,5
0,10
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Two Nash Equilibria
Entrant
Out
Enter
Incumbent
Hard
Soft
-1,1
5,5
0,10
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
One Subgame Perfect Equilibrium
Entrant
Out
Enter
Incumbent
Hard
Soft
-1,1
5,5
0,10
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Insights
? Establishing a reputation for being unkind
to entrants can enhance long-term profits
? It is costly to do so in the short-term,so
much so that it isn’t optimal to do so in a
one-shot game,
