Deter Entry. 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 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.
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.
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.
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.
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 non-credible 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.
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.
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.
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
In this form of the game we see that the new firm will enter and then the old firm will accommodate.
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.
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!