Deter Entry
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Here we see a model of deterring entry by an existing monopoly
firm.
We will also introduce the notion of a sequential, or dynamic,
game.
Here is the basic economics behind the game. A new firm can
enter a market or stay out of the market. The response of the
existing firm could be to either fight the entry of the new firm by
slashing prices, or accommodate the new firm by doing nothing
different.
The summary of profits under the various scenarios is on the
next screen.
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old firm
fight
accommodate
New
enter (0, 0) (2, 2)
Firm
stay out (1,5) (1,5)
The payouts are such that if the new firm enters and the old
firm fights, then profits will be zero for both firms (remember
that the ‘row’ player has their payout listed first.) But, if the
new firm enters and the old firm accommodates, then they
both earn 2.
If the new firm stays out, it will earn 1 in another market that
it operates in, while the old firm makes 5.
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The sequence of plays in this game is that the new firm moves
first and then the old firm plays. Note that the old firm really
won’t fight if the new firm stays out, but the terms fight and
accommodate are strategies, not necessarily actions.
When you study the table, the new firm does not have a
dominant strategy. To a certain extent, the old firm has a
dominant strategy of accommodation. Certainly if the new firm
enters, the old firm finds it more profitable to accommodate. If
the new firm stays out, then the old firm does not have to do
anything differently.
So, in this example, the existing firm does not have an interest
in deterring entry into the market. The ‘cost’ of deterrence is so
high that profits are lower than accommodation.
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Are there any Nash equilibria in the game? Let’s look at each
combination.
Enter, fight. If new enters, old would not stay at fight, it would
rather accommodate. Not a Nash Equilibrium.
Enter, accommodate. If new enters, old stays at accommodate.
If old accommodates, new stays at enter. Nash equilibrium
Stay out, accommodate. If new stays out, old firm
accommodates. If accommodate, new firm would enter. Not a
Nash equilibrium.
Stay out, fight. If new stays out, old firm fights. If old fights,
new stays out. The qualifies as a Nash equilibrium.
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There is something peculiar about the stay out, fight combination.
If the new firm stays out the old firm does not have to fight. But,
the fight response may be seen as a threat by the old firm against
the new firm.
We have to ask, is the threat credible? In this case it is not
because we have seen if the new firm enters, the old firm will not
fight. It will accommodate. So, Nash equilibra based on noncredible threats are not very satisfactory.
New concept: subgame perfect Nash equilibrium – any threats
(or promises) made in one period are carried out as part of a Nash
Equilibrium later should the occasion arise.
Let’s re-examine the two Nash equilibria.
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Enter, accommodate -> If new enters, old accommodates -> so
accommodation is carried out. If old accommodates, new enters>so entry is carried out
This above combo is subgame perfect.
Stay out, fight -> if old fights, new might say, yeah right, you
won’t fight if I come in because it is not in your interest – you
won’t carry it out.
Let’s turn to another way game theory developed, called the
extensive, or tree, form of the game.
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Fight
(0, 0)
Enter
old
new
Stay
out
(2, 2)
accommodate
(1, 5)
In this form of the game, the player to move first is
listed at the far left ‘node’ and the pay outs list this
players amount first.
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In the extensive form of the game the first player will want to
look out into the future and look at all the possible outcomes
and then reason back to make its first move. In essence, this
means that the first player will look at what the second player
would do under each scenario of moves for the first player.
In our simple game the second player only has to act when the
first player chooses enter. The old firm will choose
accommodate. So the new firm sees this game
Enter
(2, 2)
Stay
out
(1, 5)
In this form of the
game we see that the
new firm will enter and
then the old firm will
accommodate.
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So, in this form of the game, the solution to enter,
accommodate is subgame perfect.
The Chain Store Paradox
Say we have a monopoly like we just encountered and there
are 20 separate markets where it has potential competitors.
Could the monopoly act as a fighter early on (and make 0
profit) to gain a reputation and thus keep others from entering
later. In other words, can the fight strategy be made credible?
The answer is probably not. Let’s look at the logic next.
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Let’s say in the first 19 markets firms enter and the monopoly
fights and makes nothing. The 20th entrant says I do not believe
the monopoly will fight because there is no one else to deter
from entering so they will accommodate and make some money.
The 19th firm will see this logic and say to herself, if the
monopoly will not fight the 20th then it will not fight me either.
The logic is carried all the way back to the first firm. They all
enter!
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