Chapter 3 Strategic Behaviour
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Transcript of Chapter 3 Strategic Behaviour
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1Chapter 3Strategic Behavior
Industrial Organization and PricesMaster in Economics and Finance
Universidad de Navarra
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2Outline of the chaptero The Stackelberg modelo Endogenous number of firmso Entry deterrenceo Asymmetric information
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3Strategic behavioro Think of a situation where firms make their
choices sequentially. This may provide one of the firms with some sort of advantage
o Strategic behavior refers to the fact that the firm that moves first might modify its strategy choice to influence the other firms decision
o Simplest example is sequential choice of capacities in a duopoly: The Stackelberg model
unavSticky NoteDepends on first or second mover advantage
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4Strategic behavioro In the Stackelberg model, there are two
firms that choose capacities. Firm 1 chooses first, and then firm 2 chooses after observing firm 1s choice
o Analyze the game by backward induction:n Analyze firm 2s problem firstn Analyze firm 1s problem taking into account
that its choice of q1 affects firm 2s choice of q2o Capacity has a commitment value
unavSticky NoteStatic game, no dynamic. Only one period
unavSticky NoteNot the same as quantities
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5Strategic behavioro Firm 2s problem is:
giving rise to firm 2s reaction function:
2221qcqq))qq(ba(max
2
+
b2bqca)q(q 112
=
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6Strategic behavioro Firm 1 incorporates firm 2s reaction
function into its problem:
and hence, the equilibrium is:
111
1qcqq
b2bqcaqbamax
1
+
b16)ca(
b8)ca(
b4caq
b2caq
2
2
2
121
=
=
=
=
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7Strategic behavioro Firm 1 chooses the optimal point on firm
2s reaction function
q1
q2
qpc
qm
Firm 2s reaction function
qpc
qm
Firm 1s reaction function
qC
Firm 1s isoprofit curve
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8Strategic behavioro The closer the isoprofit to the horizontal
axis, the greater firm 1s profit
q1
q2
qpc
qm
Firm 2s reaction function
qpc
qS =qm
Firm 1s reaction function
qC
Firm 1s isoprofit curves
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9Strategic behavioro Notice that firm 1s choice is off its reaction
functiono This requires irreversibility in its capacity
choiceo Commitment value is related with
irreversibility: sunk costs have the greatest commitment value
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10
Outline of the chaptero The Stackelberg modelo Endogenous number of firmso Entry deterrenceo Asymmetric information
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11
Endogenous number of firmso So far, limited number of firms
n Implicit assumption: entry prohibitively costlyo If this assumption is abandoned
n No entry and exit barriers other than entrycosts.
n Firms enter as long as profits can be reaped.o Two-stage game
1. Decision to enter the industry or not2. Price or quantity competition
unavSticky NoteThe firms in order to enter a market pays entry costs in this model.Entry costs instead of being exogenous, are endogenous depending in the number of firms. Decreasing in the number of firms
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12
Endogenous number of firmso Properties of free entry equilibriao Settingo Industry with symmetric firms and equal entry coste > 0
o If n active firms, profit is (n), with (n) > (n+1)
o Number of firms under free entry, ne such that (ne ) - e >0 and (ne +1) - e < 0
o e ne
unavSticky NoteHomogeneous goods
unavSticky NoteStealing business effect of entry
unavSticky Notene is the number of firms in entry
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13
Endogenous number of firmso Linear Cournot model with free entry
o P(q) = a bq, Ci(q) = cq + e, c < a o Equilibrium: q(n) = (a c)/[b(n+1)]o Business-stealing effect: q(n+1) < q(n)
n Free-entry equilibrium
(ne ) = 1ba cne +1#$%
&'(
2
e = 0 ne +1( )2 = (a c)2
be
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14
Endogenous number of firmsn Social optimum (second best)
W (n) = n (n)+CS(n) = n(n+ 2)2ba cn+1"
#$
%
&'2 ne
W '(n) = 0 n +1( )3=(a c)2be
unavSticky NoteCompare with the previous slide
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15
Endogenous number of firms
Result: Socially excessive entry
n +1( )3
(a c)2be
n +1( )2
n* nen
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16
Outline of the chaptero The Stackelberg modelo Endogenous number of firmso Entry deterrenceo Asymmetric information
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17
Entry deterrenceo Analyze now strategic capacity choice by an
incumbent firm that faces potential entryo Let demand be p = a - bq. The cost of one
unit of capacity is c.o There is an entry cost Fo Timing:
n Firm 1 chooses productionn Firm 2 decides wheter to enter and production if
it entersn Price is determined, and profits are realized
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18
o Consider three possibilitiesn Blockaded entry: F is high enough so that firm 1
may ignore the threat of entryn Deterred entry: intermediate values of F. Firm 1
expands its capacity to prevent firm 2 from entering
n Accomodated entry: low values of F. Firm 1 lets firm 2 in and behaves as a duopolist
Entry deterrence
unavSticky NoteMonopoly satisties of the entry if he ends producing more
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o If entry is blockaded, firm 1 chooses a capacity level equal to the monopoly output, and produces up to capacity
o F is so high that firm 2 does not find it profitable to enter, even though firm 1 acts as a monopolist
o In order for this to be the case:
b16)ca(F2
Entry deterrence
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o For lower realizations of F, if the incumbent behaved as a monopolist, it would induce profitable entry
o Firm 1 might want to expand capacity to deter firm 2 from entering
o From firm 2s problem, firm 2 will enter as long as:
Fb4
)bkca()k(2
112 >
=
Entry deterrence
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o Hence, the minimum value of k1 thatprevents firm 2 from entering is:
which yields profits
bbF2cakd1
=
bF2bbF2cad
1
=
Entry deterrence
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22
o Thus, firm 1 will deter entry as long as:
and for lower values of F, firm 1 will accomodate, earning Stackelberg profits
( )8
22)ca(bFb8)ca(bF2
bbF2ca 2
Entry deterrence
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o Here is an example of deterred entry
q1
q2
qm
Firm 2s reaction function
qpc
qd
Entry deterrence
unavSticky NoteTangent: Entry accomodation (q stackelberg)
unavSticky NoteNo tangent, entry deterrance
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Outline of the chaptero The Stackelberg modelo Endogenous number of firmso Entry deterrenceo Asymmetric information
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25
Asymmetric informationo We consider asymmetric information on firms
costso The unobserved cost is revealed by firms
actionso Under price competition, firms might have
incentives to signal a high costo However, signalling a low cost (charging a low
price) may deter entryo Analyze Milgrom and Roberts model:
asymmetric information may be exploited by an incumbent firm to set a limit price that will preclude entry
unavSticky NoteEntrant does not know the marginal cost
unavSticky NoteHigh cost vs Low cost monopolist
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Asymmetric informationo Now an incumbent chooses its price prior to
entry by a potential entranto The incumbent knows its cost of
production. The entrant knows theprobability p of the cost being low
o Timing:n Period 1: incumbent chooses price p1 and the
entrant chooses whether to entern Period 2: active firm or firms choose second
period prices
unavSticky NoteMOnopolist select a price- High cost monopoly- Low cost monopoly
unavSticky NoteIf is monopoly, select a price, if not both or the number of firms select the prie.Clearing the market.
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o In period one, the incumbent earns monopoly profits which are a function of price and cost type.
o Denote it by , which result from setting pH and pL
o The first-period price may be informative about the incumbents cost
Asymmetric information
IL
IH and
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o That is, pricing pH when the incumbentis a high cost type fully reveals its typeto the entrant
o If, as seems likely, the entrant doesbetter against a high cost firm, then theincumbent increases probability of entryby setting pH
Asymmetric information
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o The incumbent may wish to set pL even when it is a high cost firm to fool the entrant and prevent entry.
o If entry occurs there is a duopoly. Denote profits by
o It happens that and assume that entry is profitable only if the incumbents cost is high: DHE > 0 > DLE
Asymmetric information
. and , , ELEH
IL
IH DDDD
0>> IHIL DD
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o Given the previous discussion, considerthese two possibilities:
n Separating equilibrium: types choosedifferent strategies, pH and pL accordingly.
n Pooling equilibrium: both types choose thesame strategy, always pL
.
Asymmetric information
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o Each of these possible equilibria are examples of a Perfect Bayesian Equilibrium
The entrant has prior expectations in a stochastic setting. It observes the first-periodprice and updates expectations with the logicof Bayes rule.
To be part of a NE, no firm must have anincentive to deviate from its particular strategygiven the strategy of the rival.
Asymmetric information
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o Prior beliefs are p of facing a low cost incumbent. Denote updated beliefs by p
o Suppose that the entrant adopts the following strategy to update its beliefs:
n If first period price is less than or equal to pL then p=1
n If first period price is greater than pL then p=0
Asymmetric information
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o Suppose that it enters when its expected profit based on those beliefs exceeds zero.
o That is, entrant believes that first-period price fully reveals its type.
Asymmetric information
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34
o Knowing this, the incumbent considers how to price in period one. Note that it could price following his type or not, but certainly it won't set a price above pL if it is a low-cost firm!
o It would not maximize profits and would invite entry, given the entrant's beliefs.
Asymmetric information
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o Suppose the incumbent prices according to type.
o If so, the entrants beliefs in previous slides are consistent.
o For this to be a NE no firm must deviate from this strategy
Asymmetric information
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o Suppose instead that the incumbent always sets pL . Then, according to entrants beliefs this strategy will prevent entry.
o By setting pL in period one (not optimal) the incumbent suffers a loss of
o However, because it prevents entry, second period profit increases by
o Therefore, a necessary condition to price according to type is that
Asymmetric information
)( LIH
IH p
IH
IH D
[C1] )( IHIHL
IH
IH Dp
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o It is indeed a sufficient condition to have a separating equilibrium.
o Incumbent prices high(low) when its costs are high(low) and the entrants updating scheme is consistent with what is observed and leads to a profit maximizing decision.
Asymmetric information
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o What happens if [C1] is not met?
o The incumbent has an incentive to alwayspricing pL.
o But now entrant always observes pL and updating beliefs as above no longer makes sense.
Asymmetric information
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o Observing the price does not yield anyinformation about incumbent's type. So itsticks to its priors. The entrant will enter aslong as expected profit is positive:
o However, if [C2] is satisfied the incumbent will set pH even though [C1] is met: entry would certainly occur. Therefore, not [C2] is a necessary condition for a pooling equilibrium
Asymmetric information
[C2] 0)1( >+ EHEL DppD
unavSticky NoteI have something to gain if in the end I affect the decision of entry of the other. If not I am losing money using the sufficient condition for separte equilibrium
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o Summing up, n A necessary condition for a separating
equilibrium is, for the incumbent, that the loss be greater than the gains (of pretending), which is an IC condition for the high-cost type.
n A necessary condition for a poolingequilibrium is that the entrant's expected profit be negative.
Asymmetric information
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o An example. o Demand is q=v p under monopoly;
o Denmands in case of duopoly are,
Asymmetric information
) 2
)2
1((21
jii ppvq ++=
unavSticky Notei=E or Ij= E or I (opposite)
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q Take v= 5, =1, cH =1, cL =0, cE =0. o Then,
o And
Asymmetric information
pH = 3, HI = 4, pL = 2.5, LI = 6.25
DHI =1.82, DLI = 3.13, DHE F = 0.15, DLE F = 0.08
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o It can be checked that [C1] does not hold, since
q So incumbent wouldnt price according to typebut if priors are p=1/2 then
q With priors p=2/3 a pooling equilibrium can be characterized
Asymmetric information
.070)(21) (
21
=+ FDFD ELEH
1.82 - 4 3.75 - 4 )(