Topic: Is Collusion Possible?
Student: Matyukhin Anton,
2 group.
Teacher: Alla Friedman.
Международный Институт Экономики и Финансов, 3 курс.
Высшая Школа Экономики
Essay in Microeconomics.
Topic:
Is Collusion Possible?
18.12.2000
Contents:
1. Introduction.
2. Two types of behaviour (Collusive and non-collusive).
3. Game theory.
a. Concept.
b. The problem of collusion.
c. Predatory pricing.
4. Repeated games approach.
a. Concept.
b. Finite game case.
c. Infinite game case.
i. “Trigger” strategy
ii. Tit-for-Tat.
d.) Finite game case, Kreps approach.
5. The motives for retaliation.
6. Conclusion.
7. Bibliography.
1. Introduction.
In this essay I would discuss the price and output determination under
the one essential type of imperfect competition markets- oligopoly. Inter-
firm interactions in imperfect markets take many forms. Oligopoly theory,
those name refers to “competition among the few”, lack unambiguous results
of these interactions unlike monopoly and perfect competition. There is a
variety of results derived from many different behavioural assumptions,
with each specific model potentially relevant to certain real-world
situations, but not to others.
Here we are interested in the strategic nature of competition between
firms. “Strategic” means the dependence of each person’s proper choice of
action on what he expects the other to do. A strategic move of a person
influences the other person’s choice, the other person’s expectation of how
would this particular person behave, in order to produce the favourable
outcome for him.
2. Two types of behaviour (Collusive and non-collusive).
Models of enterprise decision making in oligopoly derive their special
features from the fact that firms in an oligopolistic industry are
interdependent and this is realised by these firms. When there are only a
few producers, the reaction of rivals should be taken into account. There
are two broad approaches to this problem.
First, oligopolists may be thought of as agreeing to co-operate in
setting price and quantity. This would be the Collusive model. According to
this model, firms agree to act together in their price and quantity
decisions and this would to exactly the same outcome as would have been
under monopoly. Thus the explicit or co-operative collusion or Cartel would
take place.
Second approach of the oligopoly analysis is based on the assumption
that firms do not co-operate, but make their decisions on the basis of
guesses, expectations, about the variables to which their competitors are
reaching and about the form and the nature of the reactions in question.
The Non-collusive behaviour deals with this model. Here, though in
equilibrium the expectations of each firm about the reactions of rivals are
realised, the parties never actually communicate directly with each other
about their likely reactions. The extreme case of this can even imply
competitive behaviour. Such a situation is much less profitable for firms
than the one in which they share the monopolistic profit. The purpose of
this paper is to analyse the case of the possibility of collusion between
firms in order to reach the monopolistic profits for the industry, assuming
that they do not co-operate with each other. This would be the most
interesting and ambiguous case to look at.
3. Game theory.
a.) Concept.
The notion of game theory would a good starting point in the study of
strategic competition and would be very helpful in realising the model and
the problems facing oligopolistic firms associated with it.
Game theory provides a framework for analysing situations on which there
is interdependence between agents in the sense that the decisions of one
agent affect the other agents. This theory was developed by von Neumann and
Morgenstern and describes the situation, which is rather like that found in
the children’s game “Scissors&Stones”. Each firm is trying to second-guess
the others, i.e. the behaviour of one firm depends on what it expects the
others to do, and the in turn are making their decisions based upon their
expectations of what the rivals (including the first firm) will do. In our
case, the players of the game are the firms in the industry and each of
them wants to maximise its pay-off. The pay-off that a player receives
measures how well he achieves his objective. Let’s assume in our model the
pay-off to be a profit. Their profits depend upon the decisions they make
(the strategies chosen by the various players including themselves). A
strategy in this model is a plan of action, or a complete contingency plan,
which specifies what the player will do in any of the circumstances in
which he might find himself. The game also depends on the move order and
the information conditions.
Games can be categorised according to the degree of harmony or
disharmony between the players’ interests. The pure coordination game is
the one extreme, in which players have the same objectives. The other
extreme is the pure conflict of the opposite interests of players. And
usually there is a mixture of coordination and conflict of interests- mixed
motive games.
Although the importance of the other players’ choices takes place,
sometimes a player has a strategy that is the best irrespective of what
others do. This strategy is called dominant, and the other inferior ones
are called dominated. A situation in which each player is choosing the best
strategy available to him, given the strategies chosen by others, is called
a Nash equilibrium. This equilibrium corresponds to the idea of self-
fulfilled expectations, tacit, self-supporting agreement. If the players
have somehow reached Nash equilibrium, then none would have an incentive to
depart from this agreement. Any agreement that is not a Nash equilibrium
would require some enforcement.
b.) The problem of collusion.
Now I would like to use an example of a game in which the Cournot output
deciding duopoly is involved. This game is illustrated by the table below:
| | |Firm B’s output level |
| | |HIGH |LOW |
|Firm |HIGH |(1;1) |(3;0) |
|A’s | | | |
|output | | | |
|level | | | |
| |LOW |(0;3) |(2;2) |
Here a firm chooses between two alternatives: high and low output
strategies. The corresponding pay-offs (profits) are given in the boxes. In
this game, the best thing that can happen for a firm is to produce a high
level of output while its rival produces low. Low output of the rival
provides that price is not driven down too much, thus a firm could earn a
good profit margin. The worst thing for a firm is to change places with its
rival assuming the same situation takes place. If both firms produce high
levels of output, then the price would be low, allowing each of them to
earn still positive but very small profits. Nevertheless, (HIGH;HIGH) would
be the dominant strategy of this game (we would observe a Nash equilibrium
in strictly dominant strategies here). It is the best response of firm A
whenever B produces a high or low output and this is also true for firm B.
The non-co-operative outcome for each firm would be to get the pay-off of
1. But as we can see, it would be better for both to lower their output and
thereby to raise price, as their profits would increase to 2 for each firm
instead of 1 in NE. Strategy (LOW;LOW) would be the collusive outcome. The
problem of collusion is for the firms to achieve this superior outcome
notwithstanding the seemingly compelling argument that high output levels
will be chosen.
This was an example of a “one-shot” game and we saw that the collusive
outcome was not available for that case. But in reality these games are
being played over and over (on a long-term basis) and we will see later in
this essay how the collusion can be sustained by threats of retaliation
against non-co-operative behaviour.
c.) Predatory pricing.
Here we need to introduce the explicit order of moves in the model.
There are again two players-firms on the market- an incumbent firm and a
potential entrant in the market. The game is illustrated below:
The potential entrant chooses between entering and staying out of the
industry. In the case of his entering, the incumbent firm can either fight
this entry (which as we see would be costly to both), or acquiesce and
arrive at some peaceful co-existence (which is obviously more profitable).
The best thing for incumbent is for entry not to take place at all. There
are in fact two Nash equilibria: (IN;ACQUIESCE) and (OUT;FIGHT). But the
last mentioned (OUT;FIGHT) is implausible, as if the incumbent were faced
with the fact of entry, it would more profitable for him to acquiesce
rather than to fight the entry. Due to this fact the potential entrant
would choose to enter the industry and the only equilibrium would be
(IN;ACQUIESCE). Thus we can conclude, that in this case the incumbent’s
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