Chapter 3 Strategic Behaviour

1Chapter 3Strategic Behavior

Industrial Organization and PricesMaster in Economics and Finance

Universidad de Navarra

2Outline of the chaptero The Stackelberg modelo Endogenous number of firmso Entry deterrenceo Asymmetric information

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

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

5Strategic behavioro Firm 2s problem is:

giving rise to firm 2s reaction function:

2221qcqq))qq(ba(max

2

+

b2bqca)q(q 112

=

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

=

=

=

=

7Strategic behavioro Firm 1 chooses the optimal point on firm

2s reaction function

q1

q2

qpc

qm

Firm 2s reaction function

qpc

qm


qC

Firm 1s isoprofit curve

8Strategic behavioro The closer the isoprofit to the horizontal

axis, the greater firm 1s profit

q1

q2

qpc

qm


qpc

qS =qm


qC

Firm 1s isoprofit curves

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

10

Outline of the chaptero The Stackelberg modelo Endogenous number of firmso Entry deterrenceo Asymmetric information

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

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

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

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

15

Endogenous number of firms

Result: Socially excessive entry

n +1( )3

(a c)2be

n +1( )2

n* nen

16


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

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

19

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

20

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

21

o Hence, the minimum value of k1 thatprevents firm 2 from entering is:

which yields profits

bbF2cakd1

=

bF2bbF2cad

1

=

Entry deterrence

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

23

o Here is an example of deterred entry

q1

q2

qm


qpc

qd

Entry deterrence

unavSticky NoteTangent: Entry accomodation (q stackelberg)

unavSticky NoteNo tangent, entry deterrance

24


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

26

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.

27

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

28

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


29

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


. and , , ELEH

IL

IH DDDD

0>> IHIL DD

30

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

.


31

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.


32

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


33

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.


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.


35

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


36

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


)( LIH

IH p

IH

IH D

[C1] )( IHIHL

IH

IH Dp

37

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.


38

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.


39

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


[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

40

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.


41

o An example. o Demand is q=v p under monopoly;

o Denmands in case of duopoly are,


) 2

)2

1((21

jii ppvq ++=

unavSticky Notei=E or Ij= E or I (opposite)

42

q Take v= 5, =1, cH =1, cL =0, cE =0. o Then,

o And


pH = 3, HI = 4, pL = 2.5, LI = 6.25

DHI =1.82, DLI = 3.13, DHE F = 0.15, DLE F = 0.08

43

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


.070)(21) (

21

=+ FDFD ELEH

1.82 - 4 3.75 - 4 )(

Chapter 3 Strategic Behaviour

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