Game Theory
1
Game Theory Definition
The study of strategic decision making.
More formally, it is the study of
mathematical models of conflict and
cooperation between intelligent rational
decision-makers.
Game Theory is used to analyze how firms
interact but has many other applications.
2
Other Applications of Game Theory



National Defense – Terrorism and Cold War
Movie Release Dates and Program
Scheduling
Auctions http://en.wikipedia.org/wiki/Spectrum_auction
http://en.wikipedia.org/wiki/United_States_2008_wireless_spectrum_auction





Sports – Cards, Cycling, and race car driving
Politics – positions taken and $$/time spent
on campaigning
Nanny Monitoring
Group of Birds Feeding
Mating Habits
3
Grey’s Anatomy vs. The Donald
NBC delays 'Apprentice' premiere
By Nellie Andreeva
NBC is taking the premiere of "Celebrity
Apprentice" out of the cross-hairs of the last
original episode of ABC's "Grey's Anatomy"... or
so it seems.
NBC on Wednesday said that it will push the
launch of "Apprentice" from Jan. 3 to Jan. 10,
expanding "Deal or No Deal" to two hours on
Thursday, Jan. 3.
The move follows ABC's midseason schedule
announcement Friday that included the last
original episode of "Grey's" airing Jan. 3,…
4
Grey’s Anatomy vs. The Donald
'Grey' move has NBC red Peacock shifts 'Apprentice' back
By Nellie Andreeva
The Thursday night scheduling tango between NBC and
ABC continued Thursday morning when ABC officially
announced that it will move the last original episode of
"Grey's Anatomy" from Jan. 3 to Jan. 10.
That led to a reversal in NBC's Wednesday decision to
push the premiere of "Celebrity Apprentice" from Jan. 3
toJan. 10 to avoid the first-run "Grey's."
NBC said Thursday afternoon that "Apprentice," hosted
by Donald Trump, will now launch Jan. 3 as originally
planned.
5
Game Theory and Movie Release Dates
The Imperfect Science of Release Dates
New York Times
On Dec. 25, which this year happens to be a Thursday, five
new movies will be released in theaters -- six, if you count a
new Disney IMAX film called ''Young Black Stallion.'' As with
the Fourth of July and Thanksgiving, there is a special cachet to
opening a film on Christmas Day…. The casual moviegoer
rarely ponders why a particular bubbly romantic comedy, serialkiller thriller, literary costume drama or animated talking-farmanimals movie opens on the day it does. Movies come; movies
go; movies wind up on video. To those responsible for putting
those films on the screen, however, nothing about the timing of
their releases is arbitrary.
6
Game Theory and Movie Release Dates
(cont.)
Last December featured one of the most dramatic games of
chicken in recent memory, when two films starring Leonardo
DiCaprio were both slated to open on Christmas weekend.
Ultimately, Miramax blinked first, moving the release of Martin
Scorsese's ''Gangs of New York'' five days earlier and ceding
the holiday to the other DiCaprio film, DreamWorks' ''Catch Me
if You Can.'' ''We didn't think about moving,'' says Terry Press,
the head of marketing for DreamWorks. ''We had been there
first, and 'Catch Me if You Can' was perfect for that date.'' This
year, DreamWorks chose to schedule a somber psychological
drama, ''House of Sand and Fog,'' for the day after Christmas,
deferring a bit to Miramax. ''I don't want our reviews to run on
the same day as 'Cold Mountain,''' Press says.
Ever wonder why a movie theater shows a preview of an
7
upcoming movie that is to be released in 2 years?
Other Applications of Game Theory



National Defense – Terrorism and Cold War
Movie Release Dates and Program
Scheduling
Auctions http://en.wikipedia.org/wiki/Spectrum_auction
http://en.wikipedia.org/wiki/United_States_2008_wireless_spectrum_auction






Sports – Cards, Cycling, and race car driving
Politics – positions taken and $$/time spent
on campaigning
Nanny Monitoring
Group of Birds Feeding
Mating Habits
Parenting
8
Game Theory Secrets for Parents
Wall Street Journal July, 2014
The party is over, and you're down to the last bit of cake. All three of your children want it.
If you're familiar with game theory, you might think of the classic strategy in which one
person cuts the cake and the other chooses the slice. But how do you divide it three ways
without anyone throwing a fit?
Game theory is, in essence, the science of strategic thinking—a way of making the best
decision possible based on the way you expect other people to act. It was once the
domain of Nobel Prize-winning economists and big thinkers on geopolitics, but now
parents are getting in on the act. Though game theory assumes, as a technical matter,
that its players are rational, it applies just as well to not-always-rational children.
A key lesson in game theory, says Barry Nalebuff, a professor at the Yale School of
Management, is to understand the perspective of the other players. It isn't about what
you would do in another person's shoes, he says; it's about what they would do in their
shoes. "Good game theory," he says, "appreciates the quirks and features that make us
unique and takes us as we are." The same could be said of good parenting.
So how to deal with the problem of dividing a piece of cake into three equal shares? Try
this: After the first child cuts and the second one chooses, each child further cuts his or
her own slice into thirds. The third child then chooses a third of a slice from each plate. It
might get messy, but all three should feel fairly treated.
9
Game Theory Secrets for Parents
Wall Street Journal July, 2014
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

Credible Punishments: In game theory as in parenting, you have to deliver on your
threats, like actually turning off the TV if you said you were going to, even if it
punishes you too. Joshua Gans, an economist at the University of Toronto and the
author of "Parentonomics," offers advice for gaining a credible reputation at home.
When his children were young and would disobey, he would say, "I'm thinking of a
punishment." It's much easier to pretend to think of a punishment than to come up
with a new one every time, he notes—or, worse, to issue a noncredible threat in the
heat of the moment. ("That's it, I'm canceling Christmas!") Once he earned his
credibility, he found that he had only to close his eyes and count to 10, and his
children would spring into action.
The Bedtime Ultimatum: For shortening the bedtime routine with several children to
tuck in, one parent advises using an ultimatum game of take-it-or-leave-it. Before
bed, just have the children play rocks, paper, scissors and allow the winning child to
choose the book. If the others don't agree with the choice, no one gets a story.
Sleep Training 101: Game theory can work from the earliest days of parenthood.
Prof. Nalebuff applies the concept of backward induction to help new mothers get
some sleep. If a mother repeatedly gets up in the middle of the night with the child, he
explains, eventually the child will only respond to the mother comforting him. Instead,
mothers should look forward and reason backward: If you ever want your husband to
get up in the middle of the night, then you have to get him involved at the very start.
Everyone, it seems, needs to be sleep trained.
10
Game Theory Terminology
Simultaneous Move Game – Game in
which each player makes decisions
without knowledge of the other players’
decisions (ex. Cournot or Bertrand
Oligopoly).
 Sequential Move Game – Game in which
one player makes a move after observing
the other player’s move (ex. Stackelberg
Oligopoly).

11
Game Theory Terminology
Strategy – In game theory, a decision rule
that describes the actions a player will
take at each decision point.
 Normal Form Game – A representation of
a game indicating the players, their
possible strategies, and the payoffs
resulting from alternative strategies.

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Example 1: Prisoner’s Dilemma
(Normal Form of Simultaneous Move Game)
Martha’s options
Don’t Confess
Peter’s
Don’t Confess
Options
Confess
Confess
M: 2 years
P: 2 years
M: 1 year
P: 10 years
M: 10 years
P: 1 year
M: 6 years
P: 6 years
What is Peter’s best option if Martha doesn’t confess? Confess (1<2)
What is Peter’s best option if Martha confess?
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Confess (6<10)
Example 1: Prisoner’s Dilemma
Martha’s options
Don’t Confess
Peter’s
Don’t Confess
Options
Confess
Confess
M: 2 years
P: 2 years
M: 1 year
P: 10 years
M: 10 years
P: 1 year
M: 6 years
P: 6 years
What is Martha’s best option if Peter doesn’t confess? Confess (1<2)
14
What is Martha’s best option if Peter Confesses? Confess (6<10)
Example 1: Prisoner’s Dilemma
Martha’s options
First Payoff in each
“Box” is Row Player’s
Payoff .
Don’t Confess
Confess
Peter’s
Don’t Confess 2 years , 2 years 10 years , 1 year
Options
Confess
1 year , 10 years 6 years , 6 years
Dominant Strategy – A strategy that results in the highest payoff to a
player regardless of the opponent’s action.
15
Example 2: Price Setting Game
Firm B’s options
Firm A’s
Options
Low Price
High Price
Low Price
0,0
50 , -10
High Price
-10 , 50
10 , 10
Is there a dominant strategy for Firm B?Low Price
Is there a dominant strategy for Firm A? Low Price
16
Nash Equilibrium

A condition describing a set of strategies
in which no player can improve her payoff
by unilaterally changing her own strategy,
given the other player’s strategy. (Every
player is doing the best they possibly can
given the other player’s strategy.)
17
Example 1: Nash?
Martha’s options
Don’t Confess
Confess
Peter’s
Don’t Confess 2 years , 2 years 10 years , 1 year
Options
Confess
1 year , 10 years 6 years , 6 years
Nash Equilibrium: (Confess, Confess)
18
Example 2: Nash?
Firm B’s options
Firm A’s
Options
Low Price
High Price
Low Price
0,0
50 , -10
High Price
-10 , 50
10 , 10
Nash Equilibrium: (Low Price, Low Price)
19
Chump, Chump, Chump
http://videosift.com/video/Game-Theory-in-BritishGame-Show-is-Tense?loadcomm=1
20
EXAMPLE 3: Entry into a fast food market:
Is there a Nash Equilibrium(ia)?
Yes, there are 2 – (Enter,
Burger King’s options
Don’t Enter) and (Don’t
Enter, Enter). Implies, no
Enter
Don’t Enter
need for a dominant
Skaneateles
Skaneateles
strategy to have NE.
McDonalds’ Enter Skaneateles
Options
Don’t Enter
Skaneateles
PBK = -40
PM = -30
PBK = 0
PM = 50
PBK = 40
PM = 0
PBK = 0
PM = 0
Is there a dominant strategy for BK? NO
Is there a dominant strategy for McD? NO
21
EXAMPLE 4: Monitoring Workers
Is there a Nash Equilibrium(ia)?
Not a pure strategy Nash Equilibrium–
Worker’s1 options
player chooses to take one action with probability
Randomize the actions yields a Nash = mixed strategy
John Nash proved an equilibrium
alwaysShirk
exists
Work
Manager’s Monitor
Options
Don’t Monitor
W: 1
M: -1
W: -1
M: 1
W: -1
M: 1
W: 1
M: -1
Is there a dominant strategy for the worker? NO
Is there a dominant strategy for the manager? NO
22
Mixed (randomized) Strategy

Definition:
A strategy whereby a player
randomizes over two or more
available actions in order to keep
rivals from being able to predict his
or her actions.
23
Calculating Mixed Strategy
EXAMPLE 4: Monitoring Workers
Manager randomizes (i.e. monitors with
probability PM) in such a way to make the
worker indifferent between working and
shirking.
 Worker randomizes (i.e. works with
probability Pw) in such a way as to make
the manager indifferent between
monitoring and not monitoring.

24
Example 4: Mixed Strategy
Worker’s options
Work
Shirk
PW
Manager’s Monitor
Options
PM
Don’t Monitor
1-PM
1-PW
W: 1
M: -1
W: -1
M: 1
W: -1
M: 1
W: 1
M: -1
25
Manager selects PM to make Worker
indifferent between working and
shirking (i.e., same expected payoff)
Worker’s expected payoff from working
PM*(1)+(1- PM)*(-1) = -1+2*PM
 Worker’s expected payoff from shirking
PM*(-1)+(1- PM)*(1) = 1-2*PM

Worker’s expected payoff the same from working and
shirking if PM=.5. This expected payoff is 0 (-1+2*.5=0
and 1-2*.5=0). Therefore, worker’s best response is to
either work or shirk or randomize between working
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and shirking.
Worker selects PW to make Manager indifferent
between monitoring and not monitoring.
Manager’s expected payoff from monitoring
PW*(-1)+(1- PW)*(1) = 1-2*PW
 Manager’s expected payoff from not
monitoring
PW*(1)+(1- PW)*(-1) = -1+2*PW

Manager’s expected payoff the same from monitoring
and not monitoring if PW=.5. Therefore, the manager’s
best response is to either monitor or not monitor or
randomize between monitoring or not monitoring .
27
Nash Equilibrium of Example 4
Worker works with probability .5 and
shirks with probability .5 (i.e., PW=.5)
 Manager monitors with probability .5 and
doesn’t monitor with probability .5 (i.e.,
PM=.5)

Neither the Worker nor the Manager can increase
their expected payoff by playing some other
strategy (expected payoff for both is zero). They
are both playing a best response to the other
player’s strategy.
28
Example 4A: What if costs of
Monitoring decreases and Changes
the Payoffs for Manager
Worker’s options
Manager’s Monitor
Options
Don’t Monitor
Work
Shirk
W: 1
M: -1
W: -1
M: 1 1.5
W: -1
M: 1
-.5
W: 1
M: -1
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Nash Equilibrium of Example 4A
where cost of monitoring decreased
Worker works with probability .625 and
shirks with probability .375 (i.e., PW=.625)
 Same as in Ex. 5, Manager monitors with
probability .5 and doesn’t monitor with
probability .5 (i.e., PM=.5)

The decrease in monitoring costs does not change
the probability that the manager monitors. However, it
increases the probability that the worker works.
30
Example 5: Mixed Strategy and Tennis
http://www.fuzzyyellowballs.com/introducing-the-fyb-strategy-quiz/
Game:
Server’s Possible Strategies:
(Serve Left , Serve Right)
Receiver’s Possible Strategies:
(Defend Left , Defend Right)
Receiver has a high probability of winning the
point if she defends the side the server serves
to.
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Example 5: Mixed Strategy and Tennis
(Payoffs are probability of winning point)
Receiver
Server
Serve Left
Defend Left
Defend Right
DL
1-DL
.6 , .4
.75 , .25
.7 , .3
.55 , .45
SL
Serve Right
1-SL
Mixed Strategy Equilibrium (SL =.5 , DL =.67)
This results in the probability of the server winning the
point to be .65 irrespective of whether he serves to the
left or right.
32
Example 5: Mixed Strategy and Tennis
What about the Real World?
Minimax Play at Wimbleton
Walker and Wooders (AER 2001)
http://www.finance.uts.edu.au/staff/johnwooders/WimbledonAER.pdf
“We use data from classic professional tennis
matches to provide an empirical test of the theory of
mixed strategy equilibrium. We find that the serveand-return play of John McEnroe, Bjorn Borg, Boris
Becker, Pete Sampras and others is consistent with
equilibrium play.”
Results: Probability Server wins is the same whether serve
right or left. Which side server serves is not “serially
independent”.
33
Example 6

A Beautiful Mind
http://www.youtube.com/watch?v=CemLiSI5ox8
34
Example 6: A Beautiful Mind
Other Student’s Options
Pursue
Blond
John
Nash’s
Pursue
Blond
Options
Pursue
Pursue
Brunnette 1 Brunnette 2
0,0
100 , 50
100 , 50
Pursue
Brunnette 1
50 , 100
0,0
50 , 50
Pursue
Brunnette 2
50 , 100
50 , 50
0,0
Nash Equilibria: (Pursue Blond, Pursue Brunnette 1)
(Pursue Blond, Pursue Brunnette 2)
(Pursue Brunnette 1, Pursue Blond)
(Pursue Brunnette 2, Pursue Blond)
35
Sequential/Multi-Stage Games
Extensive form game: A representation of
a game that summarizes the players, the
information available to them at each
stage, the strategies available to them, the
sequence of moves, and the payoffs
resulting from alternative strategies.
(Often used to depict games with sequential
play.)

36
Example 7
Potential Entrant
Don’t Enter
Enter
Incumbent Firm
Potential Entrant:
0
Incumbent:
+10
Price War
(Hard)
Potential Entrant:
Incumbent:
-1
+1
Share Market
(Soft)
+5
+5
37
Example 7: With “Downstream” Actions
Potential Entrant
Don’t Enter
Incumbent Firm
Enter
Potential Entrant
PIM1
PE1
Incumbent Firm
Incumbent Firm
PIM2
and so on….
Suppose each period the incumbent
sets the optimal price as a monopolist
and maximizes the present discounted
value of profits which is +10.
PID1
Potential Entrant
PE2
The present discounted
value of profits for the
incumbent and potential
entrant depends on their
strategies.
and so on….
38
Example 7
Potential Entrant
Don’t Enter
Enter
Incumbent Firm
Potential Entrant:
0
Incumbent:
+10
Price War
(Hard)
Potential Entrant:
Incumbent:
Share Market
(Soft)
-1
+1
What are the Nash Equilibria?
+5
+5
39
Nash Equilibria
1.
(Potential Entrant Enter,
Incumbent Firm Shares Market)
2.
(Potential Entrant Don’t Enter,
Incumbent Firm Price War)
Is one of the Nash Equilibrium more likely to
occur? Why?
Perhaps (Enter, Share Market)
because it doesn’t rely on a noncredible threat.
40
Subgame Perfect Equilibrium
A condition describing a set of strategies
that constitutes a Nash Equilibrium and
allows no player to improve his own payoff
at any stage of the game by changing
strategies.
(Basically eliminates all Nash Equilibria that
rely on a non-credible threat – like Don’t
Enter, Price War in Prior Game)

41
Example 7
Potential Entrant
Don’t Enter
Enter
Incumbent Firm
Potential Entrant:
0
Incumbent:
+10
Price War
(Hard)
Potential Entrant:
Incumbent:
Share Market
(Soft)
-1
+1
+5
+5
What is the Subgame Perfect Equilibrium?
(Enter, Share Market)
42
Big Ten Burrito
Example 8
Enter
Don’t Enter
Chipotle
Enter
BTB: -25
Chip: -50
Chipotle
Don’t
Enter
Enter
+40
0
0 +70
Don’t
Enter
0
0
43
Big Ten Burrito
Enter
Don’t Enter
Chipotle
Enter
BTB: -25
Chip: -50
Chipotle
Don’t
Enter
Enter
+40
0
0 +70
Don’t
Enter
0
0
Use Backward Induction to Determine
Subgame Perfect Equilibrium.
44
Subgame Perfect Equilibrium
Chipotle should choose Don’t Enter if BTB chooses
Enter and Chipotle should choose Enter if BTB chooses
Don’t Enter.
BTB should choose Enter given Chipotle’s strategy
above.
Subgame Perfect Equilibrium:
(BTB chooses Enter, Chipotle chooses Don’t Enter if
BTB chooses Enter and Enter if BTB chooses Don’t
Enter.)
45
Example 9: Limit Pricing
When a firm sets it price and
output so that there is not enough
demand left for another firm to
enter the market profitably.
46
Incumbent (suppose monopolist)
Example 9:
Lower Price, PL
Potential
Entrant
Monopoly Price, PM
Don’t
Enter
Enter
Potential
Entrant
Enter
Incumbent
Hard
Ball
PE:
Inc:
Soft
Ball
PL
Don’t
Enter
Incumbent
PM Hard
Ball
-1
+5
0
0
8+1
8+5
8+8
8+10
-1
10+1
Soft
Ball
+5
10+5
PL
0
10+8
PM
0
10+10
Note: Incumbent’s profits are $10 per period if set monopoly price and $8 per period
if set lower price. What price the incumbent sets initially does not influence second
period profits for incumbent or potential entrant. For simplicity, second period
47
payoffs are not discounted.
Incumbent (suppose monopolist)
Example 9:
Lower Price, PL
Potential
Entrant
Monopoly Price, PM
Don’t
Enter
Enter
Potential
Entrant
Enter
Incumbent
Hard
Ball
PE:
Inc:
Soft
Ball
PL
Don’t
Enter
Incumbent
PM Hard
Ball
-1
+5
0
0
8+1
8+5
8+8
8+10
-1
10+1
Soft
Ball
+5
10+5
PL
0
10+8
PM
0
10+10
Note: Incumbent’s profits are $10 per period if set monopoly price and $8 per period
if set lower price. What price the incumbent sets initially does not influence second
period profits for incumbent or potential entrant. For simplicity, second period
48
payoffs are not discounted.
Incumbent (suppose monopolist)
Example 9a:
Lower Price, PL
Potential
Entrant
Monopoly Price, PM
Don’t
Enter
Enter
Potential
Entrant
Enter
Incumbent
Hard
Ball
PE:
Inc:
Soft
Ball
PL
Don’t
Enter
Incumbent
PM Hard
Ball
-1
-.5
0
0
8+1
8+5
8+8
8+10
-1
10+1
Soft
Ball
-.5
10+5
PL
0
10+8
PM
0
10+10
Note: Incumbent’s profits are $10 per period if set monopoly price and $8 per period
if set lower price. What price the incumbent sets initially does not influence second
period profits for incumbent or potential entrant. For simplicity, second period
49
payoffs are not discounted.
Incumbent (suppose monopolist)
Example 9a:
Lower Price, PL
Potential
Entrant
Monopoly Price, PM
Don’t
Enter
Enter
Potential
Entrant
Enter
Incumbent
Hard
Ball
PE:
Inc:
Soft
Ball
PL
Don’t
Enter
Incumbent
PM Hard
Ball
-1
-.5
0
0
8+1
8+5
8+8
8+10
-1
10+1
Soft
Ball
-.5
10+5
PL
0
10+8
PM
0
10+10
Note: Incumbent’s profits are $10 per period if set monopoly price and $8 per period
if set lower price. What price the incumbent sets initially does not influence second
period profits for incumbent or potential entrant. For simplicity, second period
50
payoffs are not discounted.
Questions:
1.
2.
Can you think of examples where the price the
incumbent sets the first period could influence
second period profits of the incumbent and
perhaps the entrant?
Are there other actions the incumbent can take
prior to the potential entrant’s entry decision that
could influence this decision? (R&D, Capital
Investment, Lobbying, etc.)
51
Predatory Pricing
Definition: When a firm first lowers its price in order to
drive rivals out of business (and scare off potential
entrants), and then raises its price when its rivals exit
the market.
What insights does the analysis on limit
pricing provide for the logic of predatory
pricing?
52
Example 10: The Hold-Up Problem
Dan Conlin
Invest in Firm
Specific Knowledge
Don’t Invest
Dan Conlin
Dan Conlin
and M&M
and M&M
negotiate
negotiate
salary
salary
Dan Conlin:
wI-CI
wDI
Marsh&McClennan:
200-wI
150-wDI
Let wI and wDI denote Dan’s wage if he invests and doesn’t
invest in the firm specific knowledge, respectively. Let the
cost of investing for Dan be CI and let CI=30. Dan Conlin is
worth 200 to M&M if he invests and is worth 150 if he
53
doesn’t.
Example 10: The Hold-Up Problem
Dan Conlin
Invest in Firm
Specific Knowledge
Dan Conlin
and M&M
negotiate
salary
Dan Conlin:
wI-CI
Marsh&McClennan:
200-wI
Don’t Invest
Dan Conlin
and M&M
negotiate
salary
wDI
150-wDI
Assume that Dan’s best “outside option” is a wage of 100
whether or not he invests in the firm specific knowledge and
that the outcome of the negotiations are such that Dan and
54
M&M split the surplus. This means that wI=150 and wDI=125.
Example 10: The Hold-Up Problem
Dan Conlin
Invest in Firm
Specific Knowledge
Don’t Invest
Dan Conlin
Dan Conlin
and M&M
and M&M
negotiate
negotiate
salary
salary
Dan Conlin:
wI-CI=150-30
wDI=125
Marsh&McClennan:
200-wI =200-150
150-wDI=150-125
Subgame Perfect Equilibrium outcome has Dan Conlin not
investing in the firm specific knowledge and receiving a wage
of 125 even though the cost of the knowledge is 30 and it
55
increases his value to the firm by 50.
Example 10: The Hold-Up Problem
Dan Conlin
Invest in Firm
Specific Knowledge
Don’t Invest
Dan Conlin
Dan Conlin
and M&M
and M&M
negotiate
negotiate
salary
salary
Dan Conlin:
wI-CI=150-30
wDI=125
Marsh&McClennan:
200-wI =200-150
150-wDI=150-125
What would you expect to happen in this case?
Dan Conlin and M&M would divide cost of obtaining
the knowledge.
56
Example 11: General Knowledge Investment
Dan Conlin
Invest in
General Knowledge
Don’t Invest
Dan Conlin
Dan Conlin
and M&M
and M&M
negotiate
negotiate
salary
salary
Dan Conlin:
wI-CI=160-30
wDI =125
Marsh&McClennan:
200-wI =200-160
150-wDI=150-125
Assume the game is as in the “hold-up” problem but that
Dan’s best “outside option” is a wage of 120 if he invests in
general knowledge and 100 if he does not. This means that
57
wI=160 and wDI=125 (assuming split surplus when negotiate).
Example 11: General Knowledge Investment
Dan Conlin
Invest in
General Knowledge
Don’t Invest
Dan Conlin
Dan Conlin
and M&M
and M&M
negotiate
negotiate
salary
salary
Dan Conlin:
wI-CI=160-30
wDI =125
Marsh&McClennan:
200-wI =200-160
150-wDI=150-125
Subgame Perfect Equilibrium outcome has Dan Conlin
investing in the general knowledge and receiving a wage of
160.
58
Example 12: Hold-up Problem (same idea
as the Fisher Auto-body / GM situation)
Suppose there are two players: a computer chip maker (MIPS) and a
computer manufacturer (Silicon Graphics). Initially, MIPS decides
whether or not to customize its chip (the quantity of which is
normalized to one) for a specific manufacturing purpose of Silicon
Graphics. The customization costs $75 to MIPS, but adds value of
$100 to the chip only when it is used by Silicon Graphics . The value
of customization is partially lost when the chip is sold to an alternative
buyer, who is willing to pay $60. If MIPS decides not to customize
the chip, it can sell a standardized chip to Silicon Graphics at a price
of zero and Silicon Graphics earns a payoff of zero from using the
chip. If MIPS customizes the chip, the two players enter into a
bargaining game where Silicon Graphics makes a take-it-or-leave-it
price offer to MIPS. In response to this, MIPS can either accept the
offer (in which case the game ends) or reject it (in which case MIPS
approaches an alternative buyer who pays $60).
59
Example 12: Hold-Up Problem
MIPS
Don’t Customize
Customize
Silicone Graphics
0 : MIPS
0 : Silicon Graphics
Offer
Price p
MIPS
Accept
MIPS:
p-75
Silicon Graphics: 100-p
Reject
60-75= -15
0
Subgame Perfect Equilibrium – MIPS accepts price p if p>60.
Silicone Graphics offers a price p=60. MIPS does not
customize. The outcome of this game is that MIPS does not
60
customize even though there is a surplus of $25 to be gained.
Is the Hold-Up Problem Applicable
to other Situations? YES
1.
2.
3.
4.
5.
Upstream Firm Investing in Specific Capital to produce
input for Downstream Firm.
Coal Mines located next to Power Plants.
An academic buying a house before getting tenure or a
big promotion.
Taxing of Oil and Gas Lines by local jurisdictions.
Multinational firms operating in foreign countries
(Foreign Direct Investment)
East Lansing Public Schools allocating a certain
amount of money for capital expenditures and a
certain amount for operating expenditures
61
Applying Game Theory to
an Oligopoly Market
Definition of an OligopolyA market structure in which there
are only a few firms each of
which is large relative to the total
industry (results in strategic
interaction).
62
Warning

Due to the complexity involved in
analyzing oligopolies and the
differences across
industries/markets, there is no
single model that is relevant to
all oligopolies.
63
Cournot Oligopoly Example
1.
2.
3.
4.
Few firms in market serving many
customers.
Firms produce either differentiated
or homogeneous products.
Each firm believes rivals will hold
their output constant if it changes its
output.
Barriers to entry exist.
64
Numerical Example of Cournot Oligopoly





Two Firms: Firm 1 and Firm 2
Firms produce a homogenous
product
Market Demand is P=100-Q
Q=Q1+Q2 where Q1 is Firm 1’s
output and Q2 is Firm 2’s output
Each firm has constant marginal
cost of 20 and zero fixed costs.
65
What if the firms perfectly collude?
What total output should they produce?
Q=40. Can’t have more
profits than what a
monopolist would.
100
90
80
70
60
50
D
40
30
MC
Q
20
10
0
0
10
20
30
40
50
60
70
80
90
100
MR
66
Suppose firms collude where both firms
produce an output of 20 (i.e., Q1=Q2=20)
Firm 1’s Profits = 60*20-20*20=800
100
90
Firm 2’s Profits = 60*20-20*20=800
80
70
60
50
D
40
=AVC=ATC
30
MC
Q
20
10
0
0
10
20
30
40
50
60
70
80
90
100
67
Why might you expect that the firms will not be able to
collude in this manner?
If Firm 1 thinks Firm 2 will produce 20, then Firm 1 can
increase his profits to 900 if produce 30.
100
Firm 1’s Profits = 50*30-20*30=900
90
Firm 2’s Profits = 50*20-20*20=600
80
70
60
50
D
40
30
=AVC=ATC
MC
Q
20
10
0
0
10
20
30
40
50
60
70
80
90
100
68
Nash Equilibrium

A situation in which neither firm has
an incentive to change its output
given the other firm’s output. (Also
called Cournot Equilibrium.)
In this numerical example, it is for each firm to
produce an output of 26.67. If Firm 2 produces an
output of 26.67, Firm 1 maximizes profits by
producing an output of 26.67 (and vice versa).
69
Profits from Cournot Equilibrium:
Q1=26.67 and Q2=26.67 so Q=Q1+Q2=53.3
100
Firm 1 Profits=46.66*26.67-20*26.67=
713
Firm 2 Profits=46.66*26.67-20*26.67=
713
90
80
70
60
50
D
46.6640
30
MC =AVC=A
Q TC
20
10
0
0
10
20
30
40
50
60
70
80
90
100
53.33
70
Cournot Equilibrium compared
to Perfect Collusion

Cournot Equilibrium
Q1=26.67 , Firm 1 Profits = 713
Q2=26.67 , Firm 2 Profits = 713

Perfect Collusion
Q1=20 , Firm 1 Profits = 800
Q2=20 , Firm 2 Profits = 800
71
What if Firms Interact Repeatedly:
Infinitely Repeated Interaction
Suppose Firm 1 thinks Firm 2 won’t deviate from Q2=20 if
Firm 1 doesn’t deviate from collusive agreement of Q1=20
and Q2=20. In addition, Firm 1 thinks Firm 2 will produce at
an output of 80 in all future periods if Firm 1 deviates from
collusive agreement of Q1=20 and Q2=20.
Firm 1’s profits from not cheating
Today
In 1 Year
In 2 Years
In 3 Years
In 4 Years
800
800
800
800
800
…
Firm 1’s profits from cheating (by producing Q1=30 Today)
Today
In 1 Year
In 2 Years
In 3 Years
In 4 Years
900
0
0
0
0
…
72
Industry Characteristics that
Facilitate Collusion
2.
3.
4.
5.
6.
7.
Stable Industry
Few Number of Firms
If a firm cheats on a collusive agreement,
the probability the firm is “caught” is high.
Ability to Credibly Punish in a Severe
Manner.
Industry demand is growing.
Expectation of firms’ behavior is clear.
73
My All Time Favorite example of
how expectations are formed
Coca-Cola, PepsiCo Set To Call Off Bitter Soft-Drink Price War
Staff Reporter of The Wall Street Journal
ATLANTA -- A brief but bitter pricing war within the soft-drink
industry might be drawing to a close -- all because no one
wants to be blamed for having fired the first shot.
Coca-Cola Enterprises Inc., Coca-Cola Co.'s biggest bottler, said
in a recent memorandum to executives that it will "attempt to
increase prices" after July 4 amid concern that heavy price
discounting in most of the industry is squeezing profit margins.
The memo is a response to statements made to analysts last
week by top PepsiCo Inc. executives. Pepsi, of Purchase,
N.Y., said "irrational" pricing in much of the soft-drink industry
might temporarily squeeze domestic profits, and it laid the
blame for the price cuts at Coke's door.
74
My All Time Favorite example of
how expectations are formed
In the June 5 memo, Summerfield K. Johnston Jr. and Henry A.
Schimberg, the chief executive and the president of Coca-Cola
Enterprises, respectively, said the bottler's plan is to "succeed
based on superior marketing programs and execution rather
than the short-term approach of buying share through price
discounting."
"This is a first step to disengagement," said Andrew Conway, an
analyst in New York for Morgan Stanley & Co. "Coke and
Pepsi are out to improve profitability for the category, not
destroy it, so this would bode for a stabilization."
For all the signals of a truce, though, Coca-Cola Enterprises'
memo could just as easily be seen as throwing down the
gauntlet. Messrs. Johnston and Schimberg said in the memo
that should "the competition" view the attempt to raise prices
"as an opportunity to gain share through predatory pricing, we
will, as we have in the past, respond immediately."
75
Bertrand Oligopoly
1.
2.
3.
4.
5.
Few firms in market serving many
customers.
Firms produce a homogeneous product
at a constant marginal cost (need not
actually be the case).
Firms engage in price competition and
react optimally to prices charged by
competitors.
Consumers have perfect information and
there are no transaction costs.
Barriers to entry exist.
76
What if Firm 1 and Firm 2 choose price and react
optimally to price charged by other firm?
Will firms be able to collude on a price of $60?
Firms could not collude
on a price of $60
because each firm would
have incentive to
undercut other firm. In
D the end, you would
expect both firms to set
a price of $20 (equal to
MC) and haveMC
zero
Q
profits.
100
90
80
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100
77
Using Game Theory to Devise
Strategies in Oligopolies that
Increase Profits
Examples:
1.
Price Matching- advertise a price and promise to
match any lower price offered by a competitor.
100
Bertrand Oligopoly
90
80
In the end, you would
expect both firms to set a
price of $20 (equal to MC)
and have zero profits.
70
60
50
D
40
30
MC
Q
20
10
0
0
10
20
30
40
50
60
70
80
90
100
78
Using Game Theory to Devise
Strategies in Oligopolies that
Increase Profits
Examples:
1. Price Matching- advertise a price and promise
to match an lower price offered by a
competitor. In Bertrand example, perhaps each
firm would set a price of $60 and say will
match.
2. Induce Brand Loyalty – frequent flyer program
3. Randomized pricing – inhibits consumers
learning as to who offers lower price and
reduces ability of competitors to undercut
price.
79