bài giảng kinh tế vi mô tiếng anh ch14 strategy multistage game

1
Chapter 14
Strategy: Multistage Games
Key issues
1. preventing entry: simultaneous decisions
2. preventing entry: sequential decisions
3. creating and using cost advantages
4. advertising
Nonprice strategies: Satanism
• Procter & Gamble (P&G) sued Amway and 11 of
its distributors
• P&G accused them of disparaging P&G products
and spreading stories about Satanism at P&G in an
effort to attract customers from P&G
• Amway responded, claiming P&G was engaged in
a false public relations campaign of its own
Nonprice strategies: Hiring
• Volkswagen (VW) settled with General
Motors (GM) after GM accused VW of
hiring one of its executives who brought
with him confidential information
• H J Heinz and Campbell Soup Company
agreed to mediation over Heinz's attempt to
hire away a Campbell executive
Preventing entry: Simultaneous
decisions
• consider a market with either 1 or 2 firms
• simultaneous entry decision: neither firm
has an advantage that helps it prevent other
firm from entering
• sequential decision: incumbent (firm

already in market) may have an advantage
over firm deciding whether to enter
Simultaneous decisions
• initially no gas stations
• physical space for at most 2 gas stations
• 2 firms consider opening a gas station at a
highway rest stop
2
Room for 2 firms
• firms have pure (dominant) strategies: both
enter
• unique, pure strategy equilibrium
Room for only one firm
• game is similar to game of chicken
• neither firm has a dominant strategy
Problem with pure strategies
• game has two Nash equilibria in pure strategies:
• Firm 1 enters and Firm 2 does not
• Firm 2 enters and Firm 1 does not
• players don’t know which Nash equilibrium will
result
• could collude: firm that enters could pay other
firm to stay out of market
• these pure Nash equilibria are unappealing
because identical firms use different strategies
Mixed strategies
• firms may use same strategies if their
strategies are mixed: firm chooses between
its possible actions with given probabilities
• each firm enters with 50% probability

• result: Nash equilibrium in mixed strategies
3
Mixed strategy equilibria
• if both firms use this mixed strategy, each of four
outcomes in payoff matrix equally likely
• Firm 1 has
• ¼ chance of earning $1 (upper-right cell)
• ¼ chance of losing $1 (lower-right cell)
• ½ chance of earning $0 (left cells)
• thus, Firm 1's expected profit is
($1 × ¼) + (-1 × ¼) + (0 × ½) = $0
Firm 2’s response
• if Firm 1 uses this mixed strategy, Firm 2
cannot do better using a pure strategy
• if Firm 2 enters with certainty, it earns
• $1 half time
• loses $1 other half
• so its expected profit is $0
• if Firm 2 stays out with certainty, Firm 2
earns $0
Nash equilibria
• firms play mixed strategy
• one firm plays pure strategy of entering and
other firm plays pure strategy of not
entering
Games without pure-strategy
equilibria
• some games have no pure-strategy Nash
equilibrium, so mixed strategies must be
used

• Theorem (Nash, 1950): every game with a
finite number of firms and a finite number
of actions has at least one Nash equilibrium,
which may involve mixed strategies
Preventing entry: Sequential
decisions
• incumbent (monopoly) firm knows potential
entrant is considering entering
• stage 1: incumbent decides whether to take an
action to prevent entry
• stage 2: potential entrant decides whether to enter,
and firms choose output levels
• no entry: incumbent earns monopoly profit
• entry: each firm earns duopoly profit
• assume potential entrant does not enter if it breaks
even or loses money
To act or not to act?
• incumbent can act strategically to prevent
other firm from entering
• does it pay to take action?
4
Three possibilities
1. blockaded entry: market conditions make
profitable entry impossible so no action
necessary
2. deterred entry: incumbent acts to prevent an
additional firm from entering because it pays
3. accommodated entry: doesn't pay for incumbent
to prevent entry
• incumbent does nothing to prevent entry

• reduces its output (or price) from monopoly to
duopoly level
Two-stage game
• stage 1: incumbent decides whether to pay
rest stop landlord b for exclusive right to be
only gas station
• stage 2: if incumbent doesn't take this
strategic action, potential entrant decides
whether or not to enter in second stage
Coke vs. Dr Pepper
• Coca-Cola wanted McDonald's restaurant
owners to carry its drinks exclusively
• offered each franchise a payment of enough
soda syrup to make from 30,000 to 90,000
drinks
• Dr Pepper made a comparable counteroffer
Phone companies
• regional telephone companies (Baby Bells)
lobbied FCC and state regulatory bodies to block
potential entrants from providing local phone
service
• when Teleport Communications announced plans
to build fiber-optic network to offer phone
services in Houston, Southwestern Bell
Corporation (SBC) claimed that Teleport was
violating state law and demanded that Texas
regulators issue a "cease and desist" order
Phone (cont.)
• then, when state adopted rules to promote
more competition, SBC challenged in court

• although federal telecommunication laws
were changed to permit entry in 1996, Baby
Bells were able to delay entry for years by
lobbying and suing
Incumbent’s decision
• blockaded entry: duopoly profit is negative,
Q
d
< 0 (entry doesn't pay)
• deterred or accommodated entry: Q
d
> 0
(entry occurs unless incumbent acts)
• incumbent can prevent entry by paying b,
but it may not pay for incumbent to do so
5
Figure 14.1 Whether an Incumbent Pays to Prevent Entry
Incumbent
Enter
Do not enter
(
π
m
, $0)
(
π
m
– b, $0)
(
π

d
,
π
d
= R – F )
Do not pay
Second stageFirst stage
Pay for exclusive rights (entry is impossible)
Entrant
(
π
i
,
π
e
)
Does incumbent pay?
• incumbent pays b if monopoly profit minus
payment is greater than duopoly profit
tQ
m
– b > Q
d
• incumbent accommodates entry if
Q
d
> Q
m
- b
Fixed costs and demand

• entry is profitable only if Q
d
> 0
• duopoly profit Q
d
= R – F
• assume firms have no variable costs
• fixed cost of entering, F
• firm’s revenue is R (depends on demand)
Blockaded entry
•if R < F, 3
d
< 0, and second firm doesn't enter
• not enough demand given fixed cost
• still possible that 3
m
> 0
• entry is blockaded only if a firm must incur a fixed
cost to enter
• if F = 0, then R > F, then 3
d
> 0
• with F > 0 and demand so low there's room for only
one firm in market: a natural monopoly
Incumbent’s advantage
• Because incumbent is already in market,
• its fixed entry cost is sunk
• so it ignores its sunk cost in deciding whether
to operate
• potential entrant

• views fixed cost of entry as avoidable cost
• incurs cost only if entry takes place
Commitment and entry
prevention
• credible threat: rivals must believe that
firm's threatened strategy is rational: it is in
firm's best interest to use it to prevent entry
• commitment makes a threat credible:
burning bridges
6
Figure 14.2 Noncredible Threat
Incumbent
($300, $300)
(–$100, –$100)
Cournot output
Large output
(
π
i
,
π
e
)
Cournot vs. Stackelberg
• these models illustrate role of commitment
• Stackelberg model
• leader chooses its output level before follower so has
first-mover advantage
• moving first allows leader to commit to producing a
relatively large quantity, q

s
• Cournot model
• firms choose output levels simultaneously
• so no firm has an advantage over its rival
• no firm can commit credibly to produce large quantity
Output commitment
• incumbent can commit to large quantity of output
before potential entrant decides whether to enter
• 3 possibilities
1. no commitment: entry occurs, Cournot equilibrium
2. commit to Stackelberg-leader quantity: entry occurs,
Stackelberg equilibrium
3. commit to larger quantity: deters entry, monopoly
equilibrium
Commitment and fixed cost
• incumbent's decision depends on potential
entrant's fixed cost of entry, F
• illustrate role that F plays in incumbent's
decision by looking at demand and cost
structure that underlie game tree:
Figure 14.3 Game Trees for the Deterred Entry and Stackelberg
Equilibria
Incumbent
Enter
Do not enter
(b) Entrant ’s Fixed Cost Is $16.
($900, $0)
($450, $209)
Accommodate (q
i

= 30)
Accommodate (
q
i
= 30)
Enter
Do not enter
($416, $0)
($208, $0)
Deter (q
i
= 52)
Entrant
Entrant
Incumbent
Enter
Do not enter
(a) Entrant
’
s Fixed Cost Is $100.
($900, $0)
($450, $125)
Enter
Do not enter
($800, $0)
($400, $0)
Deter (
q
i
= 40)

Entrant
Entrant
(π
i
, π
e
)
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Figure 14.4 Cournot and
Stackelberg Equilibria
q
e
, Units
per period
q
i
, Units per per iod
Entrant’s
best-response curve
Incumbent’s best-response curve
e
s
e
c
(a) Best-Response Curves
03020 60
15
20
30
60

π
i
, $ per period
q
i
, Units per per iod
π
i
(b) Incumbent
’s Profit
03020 60
450
400
F = $0; Stackelberg equilibrium
Figure 14.6 Incumbent
Loss If It Deters Entry
q
e
, Units per period
q
i
, Units per period
Entrant’s best-response curve
e
s
(a) Entrant’s Best-Response Curve
0305260
15
30
π

i
, $ per period
q
i
, Units per period
π
i
π
m
π
s
(b) Incumbent’s Profit
0305260
416
900
450
F = $16
Creating/using cost advantages
• incumbent invests to lower its MC (relative to its
rivals’) in later periods to deter entry
• firm with a lower MC has a larger market share
and a higher profit than its higher-cost rival
• incumbent with relatively low costs can price low
enough to prevent rivals from entering
• incumbent may benefit if it lowers its cost relative
to that of its rivals (or raises its rivals' costs)
Lowering MC but raising C
• should monopoly buy new piece of
equipment that lowers its MC but raises its
total cost, C?

• answer depends on whether buying
equipment will prevent potential rivals from
entering
Monopoly manufacturing plant
• currently uses many workers to pack boxes
with its product
• can replace workers with robotic arms that
• raise the monopoly's F substantially
• lowers MC cost (no longer has to hire as many
workers)
Should firm buy robots?
• monopoly definitely buys robotic arms if labor
savings large so that total cost (C) falls
• even if C rises (monopoly can't sell enough units
that robot arms pay for themselves), might still
buy
• purchasing robotic equipment is a credible commitment
• increases potential entrant's expectations about
incumbent's output
• thus, could deter entry
8
Figure 14.7 Investment Game Tree
Incumbent
Enter
Do not enter
($900, $0)
($400, $300)
Do not invest
Enter
Do not enter

($500, $0)
($132,
–
$36)
Invest
Entrant
Entrant
(
π
i
,
π
e
)
Raising rivals' costs
• by raising its rivals’ variable costs relative
to its own, firm may increase its own profit
• firm can raise rivals’ variable costs either
directly or indirectly
Direct method: Interfere
• interfere with production or sales of rival to
raise its cost
• British Airways vs. Virgin Atlantic Airways
• buy up all of a rival's product during periods
of heavy advertising and return it later,
depriving rival of extra advertising-induced
sales
Direct method: Signal jamming
• firm conducts marketing experiment:
introduces new brand at a single location

• rival firm disrupts experiment by
• offering large discounts
• engaging in a massive advertising campaign
• or otherwise “jamming the signal”
Indirect methods
• incumbent lobbies for government regulation that
disproportionately affects new firms
• many such regulations (e.g., environmental
regulations) grandfather (exempt) older firms
• incumbent buys up market supplies of scarce
resources to prevent rivals from using them
Example
alleged [in U.S vs. Aluminum Co. of America,
148 F.2d 416 (1945)] that, by certain provisions
in its contracts with power companies, Alcoa
prevented those companies from supplying
power to any other firm for the purpose of
making aluminum
9
Essential facility
• resource may be an essential facility: scarce
resource that rival must use to survive
• railroad bridges in St. Louis
• owned by group of railroads
• railroads could have prevented entry by refusing rivals
access to their essential facilities (bridges)
• U.S. v. Terminal Railroad Association of St. Louis, 224
U.S. 383 (1912): owning group had to provide access to
rival railroads on reasonable terms
Preventing customers from

switching
• incumbent makes it difficult for customers
to switch to entrant in future to discourage
entry
• industrial customers of Pacific Gas and
Electric (PG&E) were told that they'd have
to pay a fee to stop buying from PG&E
Raising all firms' costs
• incumbent may raise costs of all firms,
including its own
• incumbent wants to raise costs if its cost is
sunk and potential rivals' entry costs are
avoidable
Strategic advantage
• incumbent derives strategic advantage from
its sunk-cost commitment
• incumbent is willing to spend more money
to keep other firms out of market than they
are willing to spend to enter
Figure 14.8 Raising-Costs Game Tree
Incumbent
Enter
Do not enter
($10, $0)
($3, $3)
Do not raise costs
Enter
Do not enter
($6, $0)
(

–
$1, –$1)
Raise costs $4
Entrant
Entrant
(
π
i
,
π
e
)
cost to all firm rises by $4
Advertising
• advertising/promotional activities
• ads in newspapers & magazines mailings
• free samples
• branding
• placing cereals on lower shelves
• one of many strategic actions firms use to
boost their profits
10
Monopoly advertising
• successful advertising campaign shifts market
demand curve by
• changing consumers' tastes
• informing them about new products
• if advertising convinces some consumers they
can't live without product, demand curve may
• shift out

• become less elastic at new equilibrium
• firm charges a higher price for its product
Decision whether to advertise
• even if advertising shifts demand, it may
not pay to advertise
• if demand curve shifts out or becomes less
elastic, firm's gross profit (ignores cost of
advertising) must rise
• firm undertakes advertising campaign only
if it expects net profit (= gross profit - cost
of advertising) to increase
Figure 14.9 Advertising
Price of Coke,
p
c
, $ per unit
B
Q
c
, Units of Coke per year
0
19
17
5
Q
2
=28 68 76Q
1
=24
MR

1
MR
2
D
2
D
1
p
2
= 12
p
1
= 11
e
2
e
1
π
1
MC = AC
(unit = 10 cases)
Coke example
• advertising º Coke's gross profit rises over
36%
• if cost of advertising is < B, its net profit
rises
How much to advertise
• How much should a monopoly advertise in
order to maximize its net profit?
• level of advertising maximizes firm’s net

profit if last $1 of advertising increases its
gross profit by $1
O J trial effect
• O J Simpson's 1995 trial for murder was broadcast
by many television and radio stations
• O J factor cut take from infomercials on other
television stations
• marginal benefit (MB) curve for infomercials
shifted
• estimates of average infomercial sales declines
due to the Simpson trial ranged from 10% to 60%
across cities
11
$1,000 of advertising produces
sales of
$790
(fall of 54.6%)
$1,740San Francisco 9:30 AM
$1,530
(fall of 30.5%)
$2,200Philadelphia, Southern NJ
5 PM
$1,790
(down 18.3%)
$2,190Charlotte, NC 12:30 PM
during trialbefore
Effect of trial
• for a given quantity ($1,000 worth of
advertising time)
• marginal benefit for San Francisco shifted

down by 54.6% from MB
1
to MB
2
Figure 14.10 Shifts in the Marginal Benefit of Advertising
Marginal benefit,
marginal cost, $ per unit
A
1
A
2
Minutes of advertising time purchased per day
MB
2
MB
1
MC
Advertising that helps rivals
• firm informs consumers about a new use for
its product increasing demand for its own
and rival brands (pink toothbrush)
• some industry groups advertise collectively
to increase demand for their product:
• raisin growers (dancing raisins)
• milk producers (milk mustache)
Generic milk promotions
• Japanese generic advertising paid for by voluntary
assessments of retailer, wholesalers, and farmers
and by government subsidies
• marginal rate of return to promotion

• 6.04% in 1981
• 4.33% in 1989 (it falls because market power falls)
• so they should advertise more to maximize profits
Advertising that hurts rivals
• firm's advertising may increase demand for
its product by taking customers from rivals
• firm may use advertising to differentiate its
products from those of rivals (possibly
spuriously)
12
Empirical evidence
• cigarette advertising is cooperative
• increases size of market
• doesn't change market shares substantially
• cola advertising cannibalize
• each firm's gain from advertising comes at expense of
its rival
• cola advertising has almost no effect on total market
demand
• saltine crackers lie between these extremes
Strategic advertising equilibria
whether advertising hurts or helps rivals
affects advertising strategies firms use
Brand switching advertising
• R J Reynolds opened first American cigarette
manufacturing factory in Eastern Europe in 1994
• RJR picked Poland because Polish smokers are
probably heaviest smokers in the world
• 38.5 million Poles buy an estimated 90 billion
cigarettes a year

• 1990-92, average adult smoked 3,620 cigarettes a year
(U S average was 2,670), up from 3,400 a decade
earlier
Advertising in Poland
• with no antismoking pressures, RJR heavily
advertise to persuade Poles to switch to its brands
• market researcher for RJR in Poland observes:
“We are able to replace something that is very harmful
[the unfiltered cigarettes with coarse tobacco and a
strong aroma, which Poles currently smoke] with
something that is of better quality. It's obvious that
Camel is much less harmful than traditional Polish
cigarettes.”
• it's nice to know that RJR’s primary concern is the
well-being of its customers
1 Preventing entry: Simultaneous
decisions
• firm's strategies depend on size of market
and possibly on chance
• if market is large enough that 2 firms can
make a profit, both enter
• if only one firm can profitably produce,
there are many possible Nash equilibria
13
2 Preventing entry: Sequential
decisions
• incumbent firm that can commit to producing
large quantities before another firm decides
whether to enter market
• may deter entry: first-mover advantage

• incumbent acts to prevent entry only if it pays to
do so (depends on entry costs):
• blockaded market: no action needed
• incumbent deters entry if it is profitable to do so
• incumbent accommodates entrant
Sequential decisions (cont.)
• incumbent with first-mover advantage prevents
entry by making a credible threat
• incumbent commits to producing so much output
that it will not be profitable for a rival to enter
market if fixed costs of entering are relatively high
• incumbent produces a smaller amount that makes
it a Stackelberg leader after entry occurs if fixed
entry cost low
3 Creating and using cost
advantages
• firm with a lower MC
• has a larger market share and a higher profit than a
higher-cost rival
• may prevent entry by a higher-cost rival
• thus, firms benefit from lowering their marginal costs
relative to those of rivals
• firm invests in technology that raises its total cost
of production if it lowers its MC substantially
• by lowering its MC, firm credibly commits to
producing relatively large levels of output, and
thereby discourages entry
4 Advertising
• firms advertise to
• shift out their demand curve, and/or

• reduce equilibrium elasticity of demand
• advertising may
• differentiate a firm's product, or
• inform consumers about new products or new
uses for a product
Strategic advertising
strategies firms use in deciding how much to
advertise depend on effect of advertising on
rivals’ customers
• if firm's advertising increases total market
demand, all firms may benefit
• if firm's advertising takes customers from
rival, one firm's gain comes at expense of
other firm