1. ECON 4100: Industrial Organization
Lecture 13
Dynamic strategic interaction and credible commitment

2. Introduction
The question as to how the incumbent credibly commits to produce QD a quantity that will create problems for the other company
The Chain-Store Paradox

3. Credibility and Predation
Take a simple example
two companies Microhard (incumbent) and Newvel (entrant)
Newvel makes its decision first
enter or stay out of Microhard’s market
Microhard then chooses
accommodate or fight
pay-off matrix is as follows:

4. An Example of Predation
What is the
equilibrium for this
game?
An Example of Predation
There appear to be
two equilibria to
this game
The Pay-Off Matrix
But is
(Enter, Fight)
credible?
Microhard
(Enter, Fight)
is not an
equilibrium
Fight
Accommodate
(Stay Out,
Accommodate)
is not an
equilibrium
(0, 0)
Enter
(0, 0)
(2, 2)
Newvel
(1, 5)
Stay Out
(1, 5)
(1, 5)

5. Credibility and Predation
Note that options listed are strategies not actions
Thus, Microhard’s option to Fight is not an action of predatory nature but a strategy that says Microhard will fight if Newvel enters but will otherwise remain placid
Similarly, Accommodate defines what actions to take depending, again, on Newvel’s strategic choice

6. Credibility and Predation
The question is: Are the actions called for by a particular strategy credible?
In particular, is the promise to Fight if Newvel enters believable
If not, then the associated equilibrium is suspect
To put it differently, the matrix-form ignores timing. We can see this by representing the game in its extensive form to highlight sequence of moves

7. The Example Again What if Newvel decides to Enter?
Fight is
eliminated
Microhard had
better
Accommodate
(0,0)
(0,0)
Fight
Fight
(2,2)
Enter, Accommodate is the unique equilibrium for this game
Accommodate
Enter
Enter M2
(2,2)
Newvel
Newvel will choose
to Enter since Microhard
will Accommodate N1
Stay Out
(1,5)

8. Sequential games
A sequential game is one in which players make decisions following a certain predefined temporal order, and in which at least some players can observe the moves of players who preceded them
If no players observe the moves of previous players, then the game is simultaneous (like Cournot or Bertrand)

9. Sequential games
If every player observes the moves of every other player who has gone before her, the game is one of perfect information
If some (but not all) players observe prior moves, while others move simultaneously, the game is one of imperfect information
Sequential games are represented by game trees (the extensive form) and solved using the concept of subgame- perfect equilibrium

10. Some extra notions within sequential games
Sequential rationality: A player’s strategy, which is part of a proposed strategy profile for playing the game, is sequentially-rational if starting at any decision point (information set) for a player in the game (including ones that may not be reached if the game is conducted according to the strategy profile), his or her strategy from that point on represents a best response to the choices of the other players

11. Some extra notions within sequential games
A subgame: A subgame is any part of a game tree (extensive form) that begins with an information set that has a single node (a singleton) and includes all successor nodes of that branch of the game
Note that the game as a whole is also considered a subgame

12. Some extra notions within sequential games
Subgame perfect: A strategy that is a Nash equilibrium is also subgame perfect if the choices of actions specified for each node in a subgame represent a strategy profile that is a Nash equilibrium for the subgame
Some Nash equilibria are not subgame perfect. The concept allows the players in the game to reason that they can ignore Nash equilibria that are not subgame perfect.
Reinhard Selten (in 1975) introduced this notion of subgame perfection

13. Some extra notions within sequential games
Illegitimate threats or empty threats
Subgame perfection rules out threats of illegitimate threats. These are a claim that the player will make choices at certain points in the game that change the responses of other players so that they avoid sending the game to those decision nodes (ie: do not enter my soup market or I will dump prices to fight you off)
If these decisions are against the interest of the player who makes the threat, others will reason that he or she will not carry through with them if the decision nodes are actually reached

14. Some extra notions within sequential games
Backward induction
With common knowledge each player can start at the end of the game and solve backwards through the different subgames to identify equilibria that are both Nash and subgame perfect
Basically backward induction is an iterative process for solving finite extensive-form or sequential games.

15. Some extra notions within sequential games
Backward induction
First, one determines the optimal strategy of the player who makes the last move of the game.
Then, the optimal action of the next-to-last moving player is determined taking the last player's action as given.
The process continues in this way backwards in time until all players' actions have been determined.
Note that it is important that we know when the game finishes (it must have a finite number of rounds)

16. The Chain-Store Paradox
What if Microhard competes in more than one market or with more than one rival?
threatening one may affect the others
But: Selten’s Chain-Store Paradox arises
20 markets established sequentially
will Microhard “fight” in the first few as a means to prevent entry in later ones?

17. The Chain-Store Paradox
Trivia: Reinhard Selten first refined the Nash equilibrium concept for analyzing dynamic strategic interaction. He also applied these refined concepts to analyses of oligopolistic competition. In 1994, he shared the Nobel Prize with John F. Nash and John C. Harsanyi (proving that if your first name is John you are more likely to get a Nobel Prize )

18. The Chain-Store Paradox
20 markets established sequentially
will Microhard “fight” in the first few as a means to prevent entry in later ones?
No: this is the paradox
Suppose Microhard “fights” in the first 19 markets, will it “fight” in the 20th?
With just one market left, we are in the same situation as before
“Enter, Accommodate” becomes the only equilibrium
Fighting in the 20th market won’t help in subsequent markets . . There are no subsequent markets
So, “fight” strategy will not be adapted in the 20th market

19. The Chain-Store Paradox
Now consider the 19th market
Taken by itself, we know that the equilibrium for this market would be “Enter, Accommodate”
The only reason to adopt “Fight” in the 19th market is to convince a potential entrant in the 20th market that Microhard is a “fighter”
But as we have just seen, Microhard will not “Fight” in the 20th market regardless as to what has happened in earlier markets
“Fighting” in the 19th market will therefore not convince anyone that Microhard will “fight” in the 20th.
With the only possible reason to “Fight” in the 19th now removed, “Enter, Accommodate” becomes the unique equilibrium for this market, too

20. The Chain-Store Paradox
What about the 18th market? etc
Microhard’s threat to “Fight” in these markets is simply not credible. “Enter, Accommodate” is again the equilibrium
By repetition, we see that Microhard will not “Fight” in any market

21. The Chain-Store Paradox
Using backward induction, we see that the strategy is always to
LIVE AND LET LIVE!

22. Capacity Expansion and Entry Deterrence
Central point of previous discussion
For predation to be successful—and therefore rational—the incumbent must somehow convince the entrant that the market environment after the entrant comes in will not be a profitable one
How can the incumbent credibly make this threat?

23. Capacity Expansion and Entry Deterrence
One possible mechanism is to install capacity in advance of production
Installed capacity is a commitment to a minimum level of output
The lead firm can manipulate entrants through capacity choice
the lead firm may be able to deter entry through its capacity choice
We need, however, to make sure that the investment in capacity is not reversible, it must be sunk. After installing the capacity you need to burn the bridges (or burn the ships, if you are a Spanish conqueror ) allowing a way back (incumbent invest in highly specialized equipment, enter into contracts to take the decision on output off our hands)

24. Capacity Expansion and Entry Deterrence
The incumbent needs to make sure that the entrant is aware of the commitment to fight

25. Capacity Expansion and Entry Deterrence
An example Practice problem 12.2:
P = Q = (q1 + q2)
marginal cost of production $60 for incumbent and entrant
cost of each unit of capacity is $30 (so $30 is the per unit cost of capacity)
firms also have fixed costs of F
incumbent chooses capacity K1 in stage 1
NOTE: incumbent will always produce at least K1 in stage 1 otherwise it throws away revenue that could help cover the cost of installed capacity
entrant chooses capacity and output in stage 2
firms compete in quantities in stage 2.

26. best response function
The Example (cont.)
Consider the best response function of the entrant
Equate marginal
cost and marginal
revenue
This is the entrant’s
best response function
Residual demand is P = (120 - q1) - q2
Marginal revenue is:
MR2 = (120 - q1) - 2q2
Marginal cost is:
MC2 = 60
(120 - q1) - 2q2 = 60
so q2 =
30 - q1/2
What about the incumbent?
If we ignore any installed capacity it has a similar best response function
q1 = 30 - q2/2
What if the incumbent had a monopoly? (q2 = 0)
Then with marginal costs of $60 it would produce 30 units.

27. The Example (cont.)
The incumbent’s best
response function ignoring any installed capacity q2
Suppose that the incumbent can act as a Stackelberg
leader 60 R1
Here P=$120-$30-$15=$75. Therefore, the entrant earns a profit of ($75-$60)15=$225 less its fixed cost F in the Stackelberg equilibrium.
The entrant will then
choose output and
capacity of 15 units
A Stackelberg leader
always chooses the monopoly output, in this case, 30 units 30
The entrant’s best
response function S 15 R2 q1 30 60

28. The Example (cont.)
If the incumbent has installed capacity of K1 , its marginal cost up to K1 is 30, not 60. So, its best response function up to K1 is shifted out to q1 = 45 – q2/2. q2 90 60
There is a kink in the incumbent’s best response function at output Q=K1. NOTE: The incumbent will never let installed capacity stay idle, it can credibly commit to produce at least K1 in the production stage R1 30 R2 q1 30 45 60 K1

29. The incumbent can credibly commit to an output equal to the level of capacity installed in Stage 1. This permits it to act as a Stackelberg leader. So, it will never choose an initial capacity K1 < 30, i.e., less than that chosen by the Stackelberg leader.
The Example (cont.) q2 90
The choice of K1 = 30 would lead to the Stackelberg outcome. Is this predation? Does the incumbent have any incentive to choose K1 > 30? 60 R1 30 15 R2 q1 30 45 60

30. The Example (cont.) What if fixed costs are F > $225?
The entrant’s profit at S is ($ )15 - F = $225 – F. Then profit is null if F=$225 and if F > $225, Then the entrant cannot
Enter when the incumbent installs capacity K1 = 30
But this is not predation.
The incumbent is simply acting as a monopolist (q1 = 30) . It is not producing an output that is profitable only because it prevents entry .
The Example (cont.) q2 60 R1
If F $225, then there is a break in the entrant’s best response function. The entrant’s response function for q1 30, is q2 = 0.
What if fixed costs
are F > $225?
The entrant needs
to produce more than
15 units is order to be
able to enter 30 S 15 R2
R’2 q1 30 60

31. The Example (cont.) Does the incumbent Can the incumbent deterq2
Profit of the entrant at S is ($ ).15 - F = $225 - F
If F < $225, say $200, then the entrant can still enter if its
output is 15 units. The kink in its reaction function occurs at an output q2 < 15. 60 R1
Does the incumbent
want to deter
entry by installing
additional capacity?
Can the incumbent deter
entry by installing
additional capacity?
What if fixed costs
are F = $200?
The break in the
entrant’s best response
function now lies to
the right of S 30 S 15 R2
R’2 q1 30 60

32. If the incumbent installs 32 units of capacity it will
The Example (cont.)
Up until the break-even point, the entrant’s best response function is described by: q2 = 30 - q1/2
If the incumbent installs
32 units of capacity it will
deter entry
So if the incumbent has capacity q1 total output is Q = q1 + q2 = 30 + q1/2
Does the incumbent
want to do this?
What does q1 have to be
for this to be negative?
Price is then P = Q = q1/2 = 90 - q1/2
Profit of the entrant is (P - 60)q2 - F
= (90 - q1/2-60)(30 - q1/2) - 200
= q1 + q12/4
Suppose q1 = 32. Then the entrant’s profit would be = $-4

33. profitable in this case.
Entry deterrence by
adding capacity is
profitable in this case.
The Example (cont.)
Suppose that F = $200 and that the incumbent accommodates entry.
Acting as a Stackelberg leader, the incumbent installs 30 units of capacity in the first period.
Profit to the incumbent in the production stage will then be:
($75 - $60)x30 = $450 less F = $250. NOTE: the incumbent’s cost per unit is also $60 but $30 of that is the per unit cost of installed capacity
If the incumbent deters entry by installing 32 units, profit in the production stage is then:
($88 - $60)x32 = $896 less F = $696

34. q2
The Example (cont.) 90
By installing capacity of 32, the incumbent shifts out its best response function to pass through this output level. Effectively this commits the incumbent to q1 = 32. The entrant’s best response to q1 = 32 is q2 = 14. This would lead to P = $74 and operating profit of $196 to the entrant. Yet that operating profit does not cover its $200 overhead. If the entrant’s best response is not profitable, it will not enter. R1 60 30 S 15 R2
R’2 q1 30 60 32

35. The Example (cont.)
Note that entry deterrence by adding capacity is not always profitable.
Suppose that the entrant has no fixed costs.
Then the incumbent would need to install 60 units of capacity to deter entry.
Incumbent profit in the operating stage would be ($60 - $60)x60 – F = -$200
Now entry deterrence is not an attractive option.
However, at a minimum, the incumbent can always act as a Stackelberg leader (q1 = 30)

36. Next
Further issues on predation
Read Ch. 13 and 14