SØK/ECON 535 Imperfect Competition and Strategic Interaction
ENTRY AND EXIT
Lecture notes 09.10.02
Introduction
In the absence of entry barriers firms cannot make supernormal profits.
Barriers to entry
government regulations
technological barriers
economies of scale
access to (efficient) production technologies, inputs etc.
product differentiation, consumer switching costs, patents
strategic barriers
Bain (1956)
blockaded entry
deterred entry
accommodated entry
Contestable markets
Potential (as opposed to real) competition (Baumol et al, 1986)
sunk costs
hit and run strategies
Market characterisation
Consider an example in which firms produce one homogenous products
may be generalised to multi-product firms and differentiated products
All firms have access to the same technology
0 when q = 0
C (q ) = 
 > 0otherwise
E
Demand function: Q = Q ( p ) .
Market configuration: {q1, q2 ,..., qn , p}
A market configuration is feasible if
Q ( p ) = ∑ i =1 qi
n
pqi − C ( qi ) ≥ 0, i = 1,2,..., n
A market configuration is sustainable if
( )
e
e
e
there does not exist p ≤ p and q ≤ Q p
e
( )
e e
e
such that p q − C q ≥ 0 ,
e
where p and q are the entrants price and quantity.
A perfectly contestable market is market for which all market configurations
are feasible and sustainable.
Example: natural monopoly
C ( q ) = f + cq, q > 0
figure (sustainable market configuration where the demand curve cuts the
average-cost curve)
The sustainable market configuration is cost efficient and second-best (in the
Ramsey sense).
Generalisation to multi-product markets
total costs are minimised
no firm earns positive profit
no cross-subsidisation
Ramsey conditions are fulfilled
if the number of firms exceeds one
price equals marginal cost
Pareto optimality
Note:
distinguish between fixed and sunk costs
barriers to entry are associated with sunk costs
Hit and run
Consider an example with a single firm in the market (natural monopoly).
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A potential entrant can offer the market a contract at time 0 that specifies
quantity q
price p, and
duration τ .
The duration of contract should be thought of as the time it takes the
established firm to react (i.e. change its price offer).
Let
β be the unit price of capital at time 0
α be the unit price of capital at time τ
e
The user cost of capital µ may be defined implicitly by
β − αe
− rτ
τ
= ∫ µ ee − rt dt ⇒ µ e = β r +
r [β − α ]
e rτ − 1
0
The established firm may consequently hold a price that exceeds its own user
cost of capital ( β r ).
Figure
(
e
( C q, µ
(
)
q
)
and
C ( q, β r ) q .
pL
implicitly
defined
by
pLQ ( pL ) − C Q ( pL ) , µ e = 0 ; that is, where the demand curve cuts the
average-cost curve of the potential firm).
Conclusion: the market is perfectly contestable if
entry is free
firms face the same price of capital ( β )
firms have access to the same technology ( C , Q )
exit is costless
[β −α ]
e rτ − 1 = 0
Strategic entry barriers
Credible entry deterrence
An entry game between a (potential) entrant (e) and an incumbent firm (i):
Stage 1: entrant decides whether or not to enter the market;
Stage 2: incumbent (having observed the entrant’s choice) decides
whether or not to ‘fight’ the entrant;
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(
0
0
payoffs: ( Π i , Π e ) if entry is met by ‘fight’; Π i , Π e
‘fight’; and ( Π m ,0 ) if there is no entry.
)
if entry is not met by
Results
0
the strategy ‘fight’ is credible only if Π i ≥ Π i ;
‘fight’ leads to deterrence only if Π e ≤ 0 ;
0
if Π e ≤ 0 and Π i < Π i , then the strategy combination {fight, stay out} is a
Nash equilibrium but not a Subgame Perfect Equilibrium.
Note: it is the ex post market situation that is relevant.
‘Limit-pricing’
‘classic theory’: Bain, Sylos-Labini, Modigliani
game-theoretic critique: Spence, Dixit
asymmetric information and signalling: Milgrom and Roberts
A strategic entry game
We consider a new game in which the incumbent may take actions ex ante in
order to deter entry; subsequently a game similar to the one above is played
(this is summarised in the reduced-form profit functions):
Stage 1: incumbent decides on level of entry barrier b ( b = 0 corresponds
to no barrier);
Stage 2: entrant decides whether or not to enter;
payoffs: ( Π i ( b ) , Π e ( b ) ) if entry takes place and ( Π m ( b ) ,0 ) otherwise.
Definitions
entry is ‘blockaded’ if Π e ( 0 ) < 0 ;
deterrence possible if there exists b such that Π e ( b ) < 0
( )
( )
*
*
deterrence profitable if Π m b ≥ Π i ( 0 ) , where Π e b = 0 ;
( )
*
accommodation if Π m b < Π i ( 0 ) .
Issues
b must be irreversible (cannot be changed upon entry)
what forms can b take?;
how does different forms of
position;
b affect potential entrants’ competitive
asymmetric information;
oligopoly.
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The Spence-Dixit model
b = k is capacity.
Homogenous product, linear demand: p = 1 − Q .
Costs
ex ante (before investment): C ( q, k ) = ck + f , q ≤ k
ex post (after investment): C ( q, k ) = 0, q ≤ k .
After entry has taken place, firm i choose quantity simultaneously with firm e
choosing both quantity and capacity.
The ex post duopoly game (given entry and k i ):
clearly not profitable for firm e to hold excess capacity, hence qe = ke ;
{
}
*
*
*
*
reaction functions: qi = min ki , 1 − ke  2 and ke = 1 − qi − c  2
*
firm e’s profit: 1 − qi − c 
2
4−f .
Note that deterrence
*
requires qi ≥ 1 − c − 2 f
credible if ki ≥ 1 − c − 2 f and [1 + c ] 3 ≥ 1 − c − 2 f , i.e. c ≥ 21 1 − 3 f  .
The ex post subgame if firm i remains a monopolist:
{
}
max qi [1 − qi ] qi qi ≤ ki ;
*
at equilibrium we must have qi = ki since marginal revenue is greater for
a monopolist than for a duopolist and excess capacity cannot be optimal.
Consider then the first-stage choice of firm i and suppose first that the choice
involves deterrence:
{
max [1 − ki − c ] k i − f k i ≥ 1 − c − 2 f
} ⇒k
i
{
}
= max [1 − c ] 2,1 − c − 2 f ;
blockaded entry if [1 − c ] 2 ≥ 1 − c − 2 f ,or c ≥ 1 − 4 f ;
deterrence if [1 − c ] 2 < 1 − c − 2 f , yielding profits 2 f 1 − c − 2 f  − f .
Consider next the first-stage choice in the case of accommodation:
excess capacity clearly unprofitable;
{
max 1 − ki − k3 ( ki ) − c  ki − f
} where k
e
( ki ) = [1 − ki − c ]
2
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result is k i = [1 − c ] 2 and profits [1 − c ] 8 − f
2
It follows that firm i chooses deterrence rather than accommodation if
2
2 f 1 − c − 2 f  > [1 − c ] 8 , or c ≤ 1 − 4 f 2 − 2  , and vice versa.
Numerical example: f = 0.01:
entry blockaded if c ≥ 0.6 ;
deterrence credible if c ≥ 0.35 ;
deterrence blockaded if c ≤ 0.77 .
Conclusion
entry deterrence by over-investment in capacity;
no excess capacity;
strategic incentive for over-investment also in the case of accommodation
(cf Stackelberg);
price is low due to large capacity, but no ‘limit pricing’.
Variations
Price competition at the post-entry stage.
Multiple incumbents
deterrence is a ‘public good’;
price > marginal costs;
Gilbert and Vives (1986) show that second effect dominates and hence
deterrence is even more likely with many incumbents.
Strategic types and types of strategies
Consider the case in which the incumbent accommodates entry
Profit functions
incumbent: Π i ( qi , qe , k i )
entrant: Π e ( qi , qe , ke )
First-order condition for incumbent’s ex ante decision
0=
d Π i ∂Π i dqe dqi ∂π i
=
+
∂qe dqi dk i ∂k i
dki
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The first element on the right-hand side constitutes the ‘strategic effect’, and
so (assuming sign ( ∂Π i ∂qe ) = sign ( ∂Π e ∂qi ) )
 ∂Π e dqi 
 dqe 
sign ( strat .eff .) = sign 
 sign 

 ∂qi dk i 
 dqi 
2
2
Around the ‘open loop’ point ( ∂Π i ∂k i = 0 ) we have ∂ Π i ∂ki < 0 .
Consequently, a negative (resp. positive) strategic effect will lead to overinvestment (resp. under-investment).
Definitions
 ∂Π e dqi 
Firm i is tough (resp. soft) if sign 
 < 0 (resp. > 0 );
 ∂qi dk i 
Strategies are strategic substitutes (resp. complements) if reaction
 dq 
functions are increasing (resp. decreasing), or sign  e  > 0 (resp. < 0 ).
 dqi 
Ex ante investment makes the incumbent firm
Strategic complements
Strategic substitutes
Though
Soft
Puppy Dog
Fat Cat
Top Dog
Lean and Hungry Lool
Entry deterrence: only toughness/softness determines strategy (effect on
competitor’s profits).
Entry accommodation: type of strategies matters also (effect on own profit).
Quantity competition: Top Dog in both cases.
Price competition: Top Dog if deterrence, Puppy Dog if accommodation.
Examples:
generic advertising and price competition: excessive advertising when
accommodating entry (Fat Cat);
brand advertising and quantity competition: excessive to deter entry (Top
Dog);
location (product differentiation): The Principle of Differentiation (Puppy
Dog);
learning-by-doing: excessive production to deter entry (Top Dog);
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most-favoured-customer-clause with price competition (Puppy Dog)
Exit
Industries in decline
fight to survive.
War of attrition
Two symmetric firms supplying a homogenous good.
Production cost per unit of time: C ( q ) = f + cq
Bertrand competition: p1 = p2 = c
m
m
Monopoly gross profits (not including fixed costs): Π , Π > f
At any point in time, each firm may choose to leave the market (receives 0
profits afterwards – cannot re-enter).
We are looking for a symmetric equilibrium (in mixed strategies).
Let x ( t ) be the probability that a firm leaves the market at time t. Then the
other firm will be indifferent between staying in an leaving over the next period
of time dt if
−f d t + x d t
Πm − f
fr
=0 ⇒ x = m
.
r
Π −f
Conclusion
before exist happens, both firms run deficits (over a period with stochastic
length);
expected profits are zero (ex post the remaining firm earns positive
profits);
welfare loss both before (due to duplication of fixed costs) and after exit
(because of monopoly pricing);
in the a case of price collusion (maybe tacit) the exit rate would be lower,
and hence welfare would be lower also (due to both higher price and more
duplication ex ante)
Will small firms exist before large firms?
If contraction is not an option, large firms will leave first (Ghemawat and
Nalebuff, 1985).
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If contraction is possible, large firms will contract before exit takes place
(Whinston, 1986, and Ghemawat and Nalebuff, 1987).
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