Game Theory
• Greater attention in business is being given to tactics
and strategy to achieve competitive advantage.
• The development of strategic and tactical choices
can be analyzed using a “game theory” framework.
• This chapter allows the prediction of rival firm
behavior as if they were games.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 1
Oligopolistic Rivalry
and Game Theory
• Game Theory – a theory of interdependent
decision making by the participants in a conflict of
interest or opportunity-for- collaboration situation.
» Examples: Pricing of a few firms; Strategic Arms Race;
Advertising plans for a few firms; Output decisions of an
oligopoly
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 2
Oligopolistic Rivalry
and Game Theory
• Strategy--is a course of action (raise price, lower price,
expand output, contract output, and the like)
» The PAYOFF is the outcome of the strategy.
»
» Listing of PAYOFFS appear in a payoff matrix.
• A Strategy Game – a decision-making situation with
consciously interdependent behavior between two or
more participants.
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posted to a publicly accessible website, in whole or in part.
Slide 3
Simple Two Person, Zero Sum Game
•
•
•
•
•
ASSUMPTIONS
PLAYER 2
Each player knows both his
and his opponent’s alternatives
c
d
Preferences of all players are
known
3, -3
a 1, -1
Single period game
PLAYER 1
Sum of payoffs are zero
» Like a Poker Game
b -2, 2
0, 0
An Equilibrium (or Nash
Equilibrium) -- if none of the
Player 1 is the first number in
participants can improve their
each pair. We will get to {a,c}
payoff
which is an Equilibrium
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posted to a publicly accessible website, in whole or in part.
Slide 4
Dominant Strategies &
Dominated Strategies
• For Player 1, strategy (a) is a
PLAYER 2
dominant strategy - an action that
maximizes the decision maker’s
c
d
welfare independent of the actions of
the other players.
1, -1
3, -3
a
» Also, strategy (b) is a dominated
strategy, which is worst
PLAYER 1
regardless of what others do
0, 0
b -2, 2
• Player 2 also has a dominant
strategy of (c).
With dominant strategies of (a)
• Dominant strategies make games
easy to solve.
for Player 1 and ( c) for Player
2, the solution will be {a, c},
which is an Equilibrium.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 5
Two Person Game, Non-Zero Sum Game:
ASSUMPTIONS
TV Show Survivor
Table 13. 1
• Each player can invade the territory of
the other (Maraude) or Guard his own
territory
• Kahn’s payoff is given first.
• Randle always ranks Guard above
Maraude, so Randle has a Dominant
Strategy
• Knowing what Randle will do, Kahn
decides to Guard as well.
• An Equilibrium--none of the
participants can improve their payoff
Randle
Guard
Maraude
st Worst, 4th
Better,
1
Guard
Kahn
Maraude Worse, 2nd Best, 3rd
We will get to {Guard, Guard}
which is an Equilibrium
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 6
Unstable Games:
No Equilibrium Is Found
Lem
• Suppose Zelda thinks
c
d
that the solution is
going to be: {b, c}
a 3, - 3 1, - 1
• Then, Zelda has an Zelda
b 2, - 2 4, - 4
incentive to switch to
strategy-a
There is no, single stable equilibrium
• Then Lem has an
Each player may elect a random
incentive to switch to strategy
strategy-d, etc., etc.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 7
Iterated Dominant Strategy
• Sharp and Xerox compete in
copiers. Payoffs for Xerox are in
the lower triangle
• The payoffs depend on the
number of territories in which
they compete
• Sharp has a dominant strategy of
6 territories.
• What should Xerox do?
• We see we get to {6, 6} as the
iterated dominate strategy – an
action rule that maximizes selfinterest in light of the predictable
dominant-strategy behavior of the
other players.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 8
Other Types of Strategic Games
• These are viewed as single period, but businesses tend to
be on-going, or multi-period games
• These are two-person games, but oligopolies often
represent N-person games (N >2),
• Some games are zero-sum games in that what one player
wins, the other player loses, like a game of poker
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posted to a publicly accessible website, in whole or in part.
Slide 9
Other Types of Strategic Games
• Other games are non-zero sum games where the whole
payoffs depend on strategy choices by all players.
• Some games are cooperative that allow binding
coalitions.
• Some games are noncooperative that prohibit coalitions.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 10
The Prisoner’s Dilemma:
most famous non-zero sum game
• Often the payoffs vary
depending on the strategy
choices
• The Prisoner’s Dilemma
» Two suspects are caught
& held separately
• Their strategies are either to
Confess (C) or Not Confess
(NC)
» a one period game
» Suspect 1’s payoffs are
in the lower triangle
(underlined and in bold
)
• Noncooperative Solution
» both confess: {C, C}
• Cooperative Solution
» both do not confess {NC,NC}
• Off-diagonal represent a Double
Cross
suspect 2
NC
C
1 yr
NC
suspect 1 C
1 yr
15 yrs
0 yrs
0 yrs
15 yrs
6 yrs
6 yrs
Table 13.3
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 11
Solving the Prisoner’s Dilemma
• Suppose each suspect is pessimistic and follows
the Maximin Strategy
» This is the strategy that minimizes the absolute losses.
» Look at each strategy, find the worst thing that can
occur, and then selects the Best among the worst.
• For suspect 1, the worst case scenario for Not
Confessing is 15 years in prison. The worst case
scenario for Confessing is 6 years in prison.
Therefore, the Maximin Strategy would be to
CONFESS.
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posted to a publicly accessible website, in whole or in part.
Slide 12
Solving the Prisoner’s Dilemma
• The maximin strategy for suspect 2 is also
CONFESS
• It turns out that { Confess, Confess } is also an
equilibrium, since switching to Not Confess is
undesirable for each player separately.
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posted to a publicly accessible website, in whole or in part.
Slide 13
Why is it called a Paradox?
• The Prisoner’s Dilemma highlights the situation
where both parties would be best off if they
cooperated
• But the logic of their situation ends up with a noncooperative solution
• The solution to cooperate appears to be transforming
a one-period game into a multi-period game.
• The actions you take now will then have
consequences in future periods.
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posted to a publicly accessible website, in whole or in part.
Slide 14
Cruise Ships
$450
• When all players make their best
reply responses (so changing
Carnival
$450
$300
their choices cannot improve
their position) then the game is in
an Equilibrium.
$275
$375
• Royal Caribbean’s payouts are in
the bottom triangles.
$350
$50
Royal
• The cooperative solution is for
Caribbean
both to charge $450, but
$60
$185
Carnival has a dominant
strategy of charging $300
$320
$175
• Knowing this, Royal Caribbean
also charges $300. The outcome
Table 13.4
is the Prisoner’s Dilemma again.
• {$300, $300} is an
Equilibrium
$300
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 15
Business Strategy Games
• When an oligopolistic rival alters its product or
pricing, our firm must react or adapt.
• Best would be proactive behavior that could
anticipate actions.
• A simultaneous game occurs when all players must
chose their actions at the same time.
• A sequential game is one in which there is an
explicit order of play.
» A sequential example is when one firm has
announced a price cut, your decision to respond or
not is sequential.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 16
Coke & Pepsi and Price Discounting
Maintains Price Discounts Price
• Pepsi’s payouts are in the
Table 13.5
bottom triangles.
• The cooperative solution is for
both to maintain high prices.
COKE
• No dominant strategies exist.
Maintains Price Discounts Price
$13,000
$16,000
• Both Coke and Pepsi have an
incentive to switch to discount
price, making this similar to
$12,000
$9,000
the Prisoner’s Dilemma
PEPSI
$10,500
$8,000
• But {Discount Price, Discount
Price} is not an equilibrium,
since both are better off
$14,000
$6,300
switching to a high price.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 17
Renegade Discounting
Maintains Price Discounts Price
• If either player discounts, the other
player is better off maintaining high
Table 13.5
prices.
• Indeed, there are two equilibria at
{Maintain, Discount} and
{Discount, Maintain}.
COKE
• The best-reply response – is an
Maintains Price Discounts Price
action that maximizes self-interest
$13,000
$16,000
from among feasible choices.
• A Nash equilibrium game – is an
equilibrium concept for
$12,000
$9,000
nondominant strategy games.
PEPSI
$10,500
$8,000
• With two equilibria, Coke and Pepsi
may want to randomize their pricing
$14,000
$6,300
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 18
Randomized
Pricing
Maintains Price
• Suppose “p” is the probability that
Pepsi maintains price & (1-p) is
probability that Pepsi discounts price
• If Coke maintains price, Coke gets
13,000p + 10,500(1-p)
COKE
• If Coke discounts price, Coke gets
Maintains Price Discounts Price
16,000p + 8,000(1-p)
$13,000
$16,000
• The two strategies are identical for
Coke when they are equal
$12,000
$9,000
• 13,000p + 10,500(1-p) =
16,000p + 8,000(1-p)
PEPSI
$10,500
$8,000
• This occurs at p=.454
» Pepsi randomizes by this
probability and Coke is
$14,000
$6,300
indifferent.
• In the same manner, Coke can find a
way to randomize its discounting of
price to make Pepsi indifferent.
Discounts Price
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posted to a publicly accessible website, in whole or in part.
Slide 19
The Escape From Prisoner's Dilemma:
Repeated Games
• If the games are repeated, there is greater
expectation that firms will achieve the
cooperative solution.
• Each firm "shows" by its behavior each
period that it wants to cooperate.
• Firms that expand production "show" that
they do not want to cooperate.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 20
Repeated Prisoner’s Dilemma
Table 13.6 with new Payoffs
• Best is the cooperation solution, where
both players maintain price.
• This is the grim trigger strategy which
has an infinitely long punishment.
Maintains Price Discounts Price
$12,000
$17,000
$12,000
$6,000
PEPSI
Discounts Price
• Suppose Coke announces that it will
always Maintain Price unless it finds
Pepsi defects to discount pricing, in
which case it will always Discounts.
COKE
Maintains Price
• The Dominant Strategy is for both to
Discount. We fall into the
noncooperative solution, which is
8,000+8,000=16,000.
$6,000
$17,000
$8,000
$8,000
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 21
Repeated Prisoner’s Dilemma
Table 13.6 with new Payoffs
• With low enough interest rates, it is in
Pepsi’s interest to Maintain its Price too.
COKE
Maintains Price
• Pepsi must decide whether it wants to
keep $12,000 or end up with a perpetuity
of just $8,000 each period.
• If the rival acts noncooperatively once,
perhaps you can forgive. But fool me
twice, and then watch out!
Discounts Price
• Some game theorists have wondered if
the slight defections could go
unpunished, called a trembling hand PEPSI
trigger strategy.
Maintains Price Discounts Price
$12,000
$17,000
$12,000
$6,000
$17,000
$6,000
$8,000
$8,000
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 22
The Unraveling Problem
Finite Lived Games
Infinitely Lived Games
• In a two period game, the
incentive to double-cross is
huge in the second period.
• Knowing this, the other player
double-crosses in period one.
• The Unraveling Problem is
this failure of cooperation in
games of finite length.
• Games that last forever have usually has
a greater chance of cooperation.
• The Chain Store Paradox involves a
game tree of Accommodate or Fight
entry (Figure 13.2) of new stores.
• The prediction is that chain stores will
always accommodate, since in the last
period it pays to accommodate.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 23
Figure 13.2
The Chain Store Paradox
• Consider only the last
choice of Enter or Stay
Out decision
• With Incumbent payoff
first, potential entry
(PE) will expect that
incumbent (I) to
PE
accommodate.
• Backward induction
leads to prediction of
always accommodate.
Accommodate {80,10}
ENTER
I
Fight {-10,-10}
Accommodate {100,0}
I
STAY OUT
20th
Store
Fight {60, 0}
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 24
Mutual Forbearance and Cooperation
• Can even cooperate in a 2 period
game if uncertain ending to game.
• Payoff to firm 1 is given first in
each pair.
• p is the probability that the game
goes to period 2
• If keep small output both periods,
payoff is: 100 + p 100
• If produce a large output and
double-cross in first period, payoff
is: 150 + p (20)
• The larger is “p” the greater is the
chance of cooperation.
FIRM 2
S
S
L
100, 100
10, 150
150, 10
20, 20
FIRM 1
L
Expect to reach cooperative
solution if:
100 + p 100 > 150 + p (20)
or 80 p > 50 or p > 62.5%
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 25
Other Strategies in Multi-period Games
• When games involve 3 or more players, coalitions of
players can "win" the game. These n-person games have
complex solutions.
• A tit-for-tat strategy can lead to cooperation. If two
cruise ship firms were competing on the price of
staterooms, one ship line could match the price
announced by the other. Each time the other cut its
price, the other would too. Soon the first cruise line
‘learns’ to pick a price that is best for both lines.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 26
Other Strategies in Multi-period Games
• A conspicuous focal point is an outcome that
attracts mutual cooperation.
» Living Without and Vegetarian Times magazines both sell in
the specialty cooking category at the newsstand for $5.95. This
is a focal point, where higher prices kill sales and lower prices
do not help much.
» This reduces the chance of a price war.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 27
Cruise Ships
with Price Matching
•
•
Match
•
$300
•
$450
$450
•
Carnival is in the upper
triangle in each pair.
In the 2x2 figure 13.4,
Carnival has a $300
dominant strategy.
With a Tit-for-Tat (TFT)
strategy, Carnival can
Royal
announce a $450 stateroom
Caribbean
policy.
Royal Caribbean can match
whatever Carnival says and
both payers achieve {$350,
$275}
If Royal Caribbean
announces $450, Carnival
can also match.
Carnival
$300
$275
$350
$375
$50
$350
$185
$175
$275
$275
$350
$60
$320
Matching
$185
$175
$185
$175
$275
$350
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or Table
in part. 13.8
Slide 28
Analyzing Sequential Games
Table 13.9
Increase
Margins
• A Truck manufacturer and a
retail distributor (which
sometimes services & repair
Truck Manufacturer
trucks)
Price Increase No Price Increase
• Payoffs for the retail
distributor are in the lower
$280,000
$150,000
triangles
• Neither player has a dominant
strategy
$130,000
Retail $120,000
• If the truck manufacturer selects
Price Increase, the best decisionDistributor
is to continue service of trucks at
$300,000
$380,000
the retail distributor
• If the truck manufacture doesn’t
raise price, the best decision is to
$180,000
$60,000
discontinue the service
• This shows that sequential
decisions influence outcomes
Continue
Service
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 29
Game Tree
An Illustration of a Sequential Game
• A game tree is like a decision tree. It is a schematic
diagram of a sequential game.
• Solutions to games parallels board games like chess or
checkers.
• One way to solve a decision problem is to use end-game
reasoning, where we start with the final decision and use
backward induction to find the best starting decision on
the game tree.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 30
Two Accounting Firms Bid on Audit
Illustrated as a Sequential Game Tree
• Alpha & Daughters () is the incumbent auditor at $200
per hour.
• Omega & Sons () could bid the same or less (say $50
increment reductions) to unseat the incumbent in year 1.
Alpha Matches $150
$200
Alpha wins bid
$150

Omega wins bid
Alpha Cuts price to $100
If this pattern continues, the price
could be driven too low for
either firm
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posted to a publicly accessible website, in whole or in part.
Slide 31
Subgames in Game Trees
• Since game trees have several branches, we can examine
the concept of equilibrium in each part of the tree, called a
subgame
» example: If Alpha always matches any cut by Omega
(tit for tat style), this would be a “branch” or a subgame.
• When all players make their best reply responses then the
game is in a Nash equilibrium.
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posted to a publicly accessible website, in whole or in part.
Slide 32
Subgames in Game Trees
• Looking to the end-game, it may be that both offering $150/hour is
an equilibrium
• If keep cutting prices, this ends in losses.
» Optometrists, accountants, insurance, and other homogeneous
suppliers of services seem to recognize this.
» Avoid price wars through recognition of its outcome.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 33
Business Rivalry
as a Sequential Game
• The first to introduce a product, lower price,
etc., often achieves recognition and an
advantage, called a first-mover advantage..
• When games last several periods, the actions
by firms in one period can be punished or
rewarded in future period.
» If a new firm enters a market, the threat is that the
incumbent firm may drop prices down to levels that
are unprofitable.
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posted to a publicly accessible website, in whole or in part.
Slide 34
First Mover Games
• Andrew Carnegie:
B
civilian
military
The first person gets
30, 15
the oyster, the second civilian -10, -10
person gets the shell. A
military 15,
30
-10, - 10
• Assume markets are too
small for multiple firms.
• First number in each pair
is for firm A.
• Game with Military and
Civilian markets for
“water-land vehicles”
(DUCKS).
In a simultaneous game, both
would want the civilian market. But
in a sequential game, the first to get
the civilian market preempts it. The
other firm takes the military market.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 35
Figure 13.5
Second Best Advantages
• Two incumbents I1 and
I2 react to an entrant in
two different markets.
• Being first has strategic
advantages, but being
second lets you know
what the other firm did
with entrant.
PE
• With Incumbent's
payoff first, being
second leads the entry
to pick a low price
strategy.
• Incumbent 2, comes
back with high price.
High price {$0, $80}
ENTER
I1
Moderate price {35,50}
Low price { $50, $40}*
High price{$80,$30}
I 2 moderate price {70,60}
STAY OUT
Or License
Low price {$40, $60}
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 36
Credible Threats & Commitments
• A credible threat is a conditional strategy that is
perceived as a possible penalty in a noncooperative
game.
» Its existence sometimes induces cooperative
behavior
» Example: If you cut your price, I will cut my price
too! If believed, the parties tend to avoid price wars.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 37
Credible Threats & Commitments
• A credible commitment is a conditional strategy
for establishing trust by promising to make the
promise-giver worse off by violating that trust.
» Such as a reward for good behavior in a noncooperative
game.
» Example: If any of my products fail to work, I will pay
the buyer three-times their purchase price in
recompense! Clearly, this commitment makes the firm
worse off if they sell shoddy goods.
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posted to a publicly accessible website, in whole or in part.
Slide 38
The Tactical Advantage of
Licensing and Leasing
• There is a tactical advantage in leasing and renewal
licenses between sellers of major capital equipment and
their customers.
• The renter fears that the equipment will become quickly
obsolete.
• The seller is in a better position to know what changes
are occurring in technology.
• A lease or license works for both parties in the contract.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 39
Pricing Techniques
and Analysis
• Value-based more than cost-based pricing often helps build
profits.
• Firms charge different customers different prices, which is
known as differential pricing or price discrimination.
• This chapter explains pricing used by many multi-product
firms, such as full-cost pricing and target return pricing.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 40
Proactive Value-based Pricing
• If the price doesn’t fit what customers are willing to pay, then the
product may not be profitable.
• Customer value is the focus for pricing, not just the costs
associated with producing the good or service.
• For a time, Apple Computer lost market share by ignoring
customer value, but it has been gaining trend-setting customers
through style and functions of its products.
• The Ford Mustang was a success, as Ford found that people
wanted a sports car, but didn’t want it to be too expensive. They
started with a price and then designed the product.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 41
Prestone and Zerex
Radiator Fluid
• Zerex matches competitors price so long as price exceeds
its costs.
• Rather than use cost-based pricing, Zerex should consider
segmenting customers, and design products for these
segments.
• Value-in-use – the difference between the value the
customers place on something versus the cost of acquiring
it.
» Water has a high value in use, whereas diamonds are
relatively low in value-in-use.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 42
Pricing of Coated Coronary Stents: An
Example of Value-Based Pricing
• Clogged arteries can be repaired using an $800 stent, but 1530% of the time anther open-heart surgery is needed to repair
scaring caused by the stent some years later.
• Coated stents reduce the likelihood of scar tissue and thus
having to go through a second surgery that costs about $42,000
• What would you be willing to pay to reduce the need for a
second surgery to less than 3%?
• A reduction to a 27% chance of another surgery is
worth: .27($42,000) = $11,340. It is no wonder that
the price of coated stents is higher than then uncoated
by an extra $1,165 (or about $1,965 in all).
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posted to a publicly accessible website, in whole or in part.
Slide 43
EMR is the
equal marginal
revenue from
each class
equals MC
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posted to a publicly accessible website, in whole or in part.
Slide 44
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 45
Differential Pricing and the
Price Elasticity of Demand
•
•
•
Using elasticities MR  P( 1 + 1/ ED ) = MC
In two regions: MR1 = P1( 1 + 1/ E1 ) = MC
MR2 = P2( 1 + 1/ E2 ) = MC
Therefore: P1( 1 + 1/ E1 ) = P2( 1 + 1/ E2 )
or: P1/ P2 = ( 1 + 1/ E2 )/( 1 + 1/ E1 )
•
•
•
If the price elasticity in region 1 is -1.25 and if the price elasticity
in region 2 is -2.5, then P1/ P2 = (1+1/ -2.5)/(1+1/ -1.25 ) = 3.
Hence, P1 = 3P2.
The price is three times higher in region 1, which the less elastic
region.
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posted to a publicly accessible website, in whole or in part.
Slide 46
An Example: Differential Pricing at
Taiwan Instrument
• Japan: P1 = 12 – Q1 and US: P2 = 8 – Q2
• Total cost: C = 5 + 2(Q1 + Q2)
• In differential pricing, maximize profits:
p= P1Q1 + P2Q2 – C = (12 – Q1)Q1 + (8–Q2)Q2
- 5 - 2(Q1 + Q2) = 10Q1 - Q12 +6Q2 - Q22 -5.
Find ∂p/∂Q1 = 10 – 2Q1 = 0, or Q1= 5
Find ∂p/∂Q2 = 6 – 2Q2 = 0, or Q2= 3
• So, P1 = $7 and P2 = $5 and p = $29 (million)
• When prices uniform at $6, p = $27 (million)
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 47
Differential Pricing in Target
Market Segments
• If at peak rush hour, the toll is higher than at the offpeak, we are using different prices at different time
periods.
• The peak toll can encourage shifting travel patterns to
off-peak times or discourage some commuting
altogether.
• Differential pricing appears more frequently than one
thinks. Aside from earning greater tolls, it can relieve
congestion.
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posted to a publicly accessible website, in whole or in part.
Slide 48
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 49
Direct Segmenting with “Fences”
• Price differentiation is difficult if products are
easily arbitraged
• Ralph Lauren sells in upscale stores and sells
some goods in discount outlet malls
• Customers of the boutiques seldom frequent
outlet malls along highways. The two groups
of customers are separated or “fenced” away
from each other.
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posted to a publicly accessible website, in whole or in part.
Slide 50
Price Discrimination


Price Discrimination- Goods which are NOT
priced in proportion to their marginal cost, even
though technically similar
Some Necessary Conditions:
1. Have Some Monopoly Power
• Otherwise, in pure competition, P = MC
2. Be Able to Prevent Arbitrage
• Separate customers and prevent reselling
• Think of a “Fence” that prevents reselling to
others.
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posted to a publicly accessible website, in whole or in part.
Slide 51
Arbitrage •
Buy Low to Sell Higher
Arbitrage of Goods is fairly Easy
» Price Discrimination of goods is typically
ineffective. The price is the same for all customers
found in grocery items
• Arbitrage of Services is often Difficult
» Price Discrimination of services is often effective,
so it is found at restaurants by age, as restaurant
food is a service
» Lawyers charge different prices for wills, based on
ability to pay
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posted to a publicly accessible website, in whole or in part.
Slide 52
Why practice differential pricing
and price discrimination?
• In Simple Monopoly,
there is only one price
• Consumers receive a
CS
consumer surplus (CS) PSM
• In differential pricing,
the incentive is to
SCOOP OUT all
consumer surplus
• The object is to earn
greater profits.
MC
Simple
Monopoly
D
QSM
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posted to a publicly accessible website, in whole or in part.
Q
Slide 53
Perfect Price Discrimination
(or 1st Degree Price Discrimination)
• Charge the MOST
that a person is
willing to pay for
each good
• Zero consumer
surplus
• Produce MORE than
in Simple Monopoly
• Output the same as in
Competition
Price Discriminating
Monopoly
MC
D
Q1st
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posted to a publicly accessible website, in whole or in part.
Q
Slide 54
Notice: Incentives to Understate
One’s True Willingness to Pay
• The conditions for In Second Degree Price
perfect price
Discrimination:
discrimination are Units are Grouped
seldom met
• Hence, some close
• There are a variety of
approximations
ways to group units to
exist
attempt to scoop out
consumer surplus
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly accessible website, in whole or in part.
Slide 55
An Example of “Second Degree” Price
Discrimination
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posted to a publicly accessible website, in whole or in part.
Slide 56
Bundling: Another Example of Second
Degree Price Discrimination
Time Warner could offer the History Channel (H) and
Showtime (S) individually or as a bundle of both.
Suppose the reservation prices of customers 1& 2
are presented in the boxes below.
CASE A : Preferences are negatively correlated
S
H
1
9
2
11
2
3
8
11
9
8 = $17
Selling separately
$22
If the cost to Time Warner
is $1 per customer for
licensing fees, the profits
of bundling is 22 – 4 = $18,
In contrast, the profits of selling
Bundling
each separately is 17-2= $15.
generates
more revenue Bundling is more profitable!
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posted to a publicly accessible website, in whole or in part.
Slide 57
Changing the preferences:
Bundling
Suppose, however, that everyone likes Showtime
more than the History Channel, such that
preferences are positively correlated as given below.
CASE B: Preferences are positively correlated
If the cost to Time Warner
is $1 per customer for
licensing fees, the profits
of bundling is 20 – 4 = $16,
In contrast, the profits of selling
each separately is 22-3= $19.
Selling separately is more profitable!
S
H
1
9
1
10
2
8
6
14
20
16
6 = 22
Selling separately
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posted to a publicly accessible website, in whole or in part.
Slide 58
Mixed Bundling
• McDonalds sells Extra Value Meals, as a bundle of sandwich, fries,
and a soft drink for less than it sells them separately. But selling both
bundles and items separately is mixed bundling.
» Suppose that Bob would pay $3 for a burger and $1 for a soft
drink
» Mary would pay $2 for a burger and $2 for a soft drink
» Jim would pay $3.50 for burger and nothing for a soft drink
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posted to a publicly accessible website, in whole or in part.
Slide 59
Mixed Bundling
• If the individual price of a burger is $3 and the individual price of a
drink is $1.50, then Bob buys a burger, Mary buys a soft drink, and
Jim buys a burger. With only ala carte pricing, the revenue $3 (Bob)
+ $1.50(Mary) + $3(Jim) = $7.50.
• If the extra value meal bundle (of a burger and drink) costs $4, both
Bob and Mary buy the bundle, but Jim buys nothing. Hence, with
only bundling, the revenues is $4 (Bob) + $4 (Mary) = $8.
• Mixed Bundling yields revenue of $4 (Bob) + $4 (Mary) + $3(Jim)
= $11, which is the highest revenue.
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posted to a publicly accessible website, in whole or in part.
Slide 60
Nine Ways to Separate Customers
for Price Discrimination
1. Geography as when the price in the East-side and West-side
differ
2. Income as the American Economics Association charges
more to professors than students
3. Gender as when jeans for women are priced higher than
similar jeans for men
4. Age as when kids get in at lower prices for movies
5. Time of day or season
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posted to a publicly accessible website, in whole or in part.
Slide 61
Nine Ways to Separate Customers
for Price Discrimination
6. Versions as when software for home use is slightly different but
priced much differently than business use.
7. Language as when products printed in Spanish are priced
differently than those in English
8. Transient/Resident as when contractors pay less at hardware
stores than other customers
9. Ability to Haggle when those who ask for a lower price get it
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posted to a publicly accessible website, in whole or in part.
Slide 62
Couponing
• Some customers use
coupons. These
customers identify
themselves as being
highly price sensitive
• Other customers
seldom bother to use
coupons. They
demonstrate that they
are less price sensitive.
• The customers that use
coupons pay less.
• The customers don’t
bother pay more.
• Both are buying the
same items.
• This is an efficient
way to price
discriminate.
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posted to a publicly accessible website, in whole or in part.
Slide 63
Pricing in Practice
• In practice, pricing strategy involves the whole
life-cycle pricing of the product.
» A plan to start with a high price when it is
new, with the idea of lowering the price when
it is no longer as fashionable (e.g., demand
falls).
• An example of this life-cycle pricing is price
skimming.
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posted to a publicly accessible website, in whole or in part.
Slide 64
Price Skimming
• Price declines over time
• Those who wish to get it first
pays the highest price, others
are willing to wait
• Examples:
P
D
» Hardcover & Paperback Books
» New electrical, computer
products, PDAs, iPhone, etc.
• Sometimes, in the long run the
product fills a small niche, and
the producer can raise its price
in the long run to fill this niche
pricing.
TIME
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posted to a publicly accessible website, in whole or in part.
Slide 65
Cost-Based Pricing Methods
• Managers also report wide use of cost-plus
pricing methods because it:
» Streamlines pricing of multiple products
» Streamlines pricing of retail prices
• P = ACn + Markup or P = ACn(1 + m)
» where ACn is average cost at a normal output
and m is a percentage markup
» Notice: This procedure does not use MC pricing or use
elasticities, as in: P( 1 + 1/Ep ) = MC.
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posted to a publicly accessible website, in whole or in part.
Slide 66
Cost-Plus Pricing:
Advantages & Disadvantages
• Cost-plus is simple
• It is easy to delegate to
others
• Easy to apply to
thousands of items
» Can use categories
of markups for
different classes of
products
• But cost-plus ignores
demand changes
• Pricing may be based on
poor cost data
• Output varies in business
cycle
Hybrid Method: Variable
Cost-Plus Pricing -- the
markup can vary over the
season, or business cycle
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posted to a publicly accessible website, in whole or in part.
Slide 67
Full Cost & Target Rate of Return on
Investment Pricing
• Full Cost Pricing:
» Covers all Costs at the standard or normal output
» Plus a return on the investment which is the markup
• Target Rate of Return: P = ACN + p K / QN
» Where ACN is the AC at a normal amount of output (which is
average variable cost plus average fixed cost).
» where p K is the target amount of profit, and pis the desired
profit rate and K is gross operating assets and QN is the
number of units expected to be produced over this time
horizon.
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posted to a publicly accessible website, in whole or in part.
Slide 68