FREE ESSAY ON IS COLLUSION POSSIBLE?

IS COLLUSION POSSIBLE?

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 A's output level HIGH (1;1) (3;0)
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 threat to fight was empty threat that wouldn't be believed, i.e. that threat
was not a credible one. The concept of perfect equilibrium, developed by Selten
(1965;1975), requires that the strategies chosen by the players be a Nash equilibrium,
not only in the game as a whole, but also in every subgame of the game. (In our model on
the picture, the subgame starts with the word incumbent). We have got the perfect
equilibrium to rule out the undesirable one.
4. Repeated games approach. 
a.) Concept.
As I have already mentioned, in practice firms are likely to interact repeatedly. Such
factors as technological know-how, durable investments and entry barriers promote
long-run interactions among a relatively stable set of firms, and this is especially true
for the industries with only a few firms. With repeated interaction every firm must take
into account not only the possible increase in current profits, but also the possibility
of a price war and long-run losses when deciding whether to undercut a given price
directly or by increasing its output level. Once the instability of collusion has been
formulated in the one-shot prisoners dilemma game, it raises the question of whether
there is any way to play the game in order to ensure a different, and perhaps more
realistic, outcome. Firms do in practice sometimes solve the co-ordination problem either
via formal or informal agreements. I would focus on the more interesting and complicated
case of how collusive outcomes can be sustained by non-co-operative behaviour (informal),
i.e. in the absence of explicit, enforceable agreements between firms. We have seen that
collusion is not possible in the one-shot version of the game and we will now stress upon
a question of whether it is possible in a repeated version. The answer depends on at
least four factors:
1. Whether the game is repeated infinitely or there is some finite number of times;
2. Whether there is a full information available to each firm about the objectives of,
and opportunities available to, other firms;
3. How much weight the firms attach to the future in their calculations;
4. Whether the cheating can/can not be detected due to the knowledge/lack of knowledge
about the prior moves of the firm's rivals. 
The fact of repetition broadens the strategies available to the players, 
because they can make their strategy in any currant round contingent on the others' play
in previous rounds. This introduction of time dimension permits strategies, which are
damaging to be punished in future rounds of the game. This also permits players to choose
particular strategies with the explicit purpose of establishing a reputation, e.g. by
continuing to co- operate with the other player even when short-term self-interest
indicates that an agreement to do so should be breached. 
b.) Finite game case.
But repetition itself does not necessarily resolve the prisoner's dilemma. Suppose that
the game is repeated a finite number of times, and that there is complete and perfect
information. Again, we assume firms to maximise the (possibly discounted) sum of their
profits in the game as a whole. The collusive low output for the firms again,
unfortunately for the firms, could not be sustained. Suppose, they play a game for a
total of five times. The repetition for a predetermined finite number of plays does
nothing to help them in achieving a collusive outcome. This happens because, though each
player actually plays forward in sequence from the first to the last round of the game,
that player needs to consider the implications of each round up to and including the
last, before making its first move. While choosing its strategy it's sensible for every
firm to start by taking the final round into consideration and then work backwards. As we
realise the backward induction, it becomes evident that the fifth and the final round of
the game would be absolutely identical to a one-shot game and, thus, would lead to
exactly the same outcome. Both firms would cheat on the agreement at the final round. But
at the start of the fourth round, each firm would find it profitable to cheat in this
round as well. It would gain nothing from establishing a reputation for not cheating if
it knew that both it and its rival were bound to cheat next time. And this crucial fact
of inevitable cheating in the final round undermines any alternative strategy, e.g.
building a reputation for not cheating as the basis for establishing the collusion. Thus
cheating remains the dominant strategy. 
* NOTE: the is however one assumption about slightly incomplete information, which allows
collusive outcome to occur in the finitely repeated game, but I will left it for the
discussion some paragraphs later.
c.)_ Infinite game case.
Now lets consider the infinitely repeated version of the game. In this kind of game there
is always a next time in which a rival's behaviour can be influenced by what happens this
time. In such a game, solutions to the problems represented by the prisoners dilemma are
feasible. 
i.) Trigger strategy
Suppose that firms discount the future at some rate w, where w is a number between O and
1. That is, players attach weight w to what happens next period. Provided that w is not
too small, it is now possible for non-co-operative collusion to occur. Suppose that firm
B plays trigger strategy, which is to choose low output in period 1 and in any subsequent
period provided that firm A has never produced high output, but to produce high output
forever more once firm A ever produces high output. That is B co-operates with A unless A
defects, in which case B is triggered into perpetual non-co-operation. If A were also to
adopt the trigger strategy, then there would always be collusion and each firm would
produce low output. Thus the discounted value of this profit flow is:
2+2w+2w^2+2w^3+...=2/(1-w)
If fact A gets this pay-off with any strategy in which he is not the first to defect. If
A chooses a strategy in which he defects at any stage, then he gets a pay-off of 3 in the
first period of defection (as B still produces low output), and a pay-off of no more than
1 in every subsequent period, due to B being triggered into perpetual non-co-operation.
Thus, A's pay-off is at most
3+w+w^2+w^3+...=3+w/(1-w)
If we will compare these two results, we will get that it is better not to defect so long
as 
W * (or =) ?
We can conclude that is the firms give enough weight to the future, then non-co-operative
collusion can be sustained, for example, by trigger strategies. The trigger strategies
constitute a Nash equilibrium = self-sufficient agreement. However it is not enough for a
firm to announce a punishment strategy in order to influence the behaviour of rivals. The
strategy that is announced must also be credible in the sense that it must be understood
to be in the firm's self-interest to carry out its threat at the time when it becomes
necessary. It must also be severe in a sense that the gain from defection should be less
than the losses from punishment. But because it is possible that mistakes will be made in
detecting cheating (if, for example, the effects of unexpected shifts in output demand
are misinterpreted as the result of cheating), the severity of punishment should be kept
to the minimum required to deter the act of cheating. 
ii.) Tit-for-Tat.
Trigger strategies are not the only way to reach the non-co-operative collusion. Another
famous strategy is Tit-for-Tat, according to which a player chooses in the current period
what the other player chose in the previous period. Cheating by either firm in the
previous round is therefore immediately punished by cheating, by the other, in this
round. Cheating is never allowed to go unpunished. Tit-for-Tat satisfies a number of
criteria for successful punishment strategies. It carries a clear threat to both parties,
because it is one of the simplest conceivable punishment strategies and is therefore easy
to understand. It also has the characteristics that the mode of punishment it implies
does not itself threaten to undermine the cartel agreement. This is because firms only
cheat in reaction to cheating be others; they never initiate a cycle of cheating
themselves. Although it is a tough strategy, it also offers speedy forgiveness for
cheating, because once punishment has been administered the punishing firm is willing
once again to restore co-operation. Its weakness is in the fact that information is
imperfect in reality, so it is hard to detect whether a particular outcome is the
consequence of unexpected external events such as a lower demand than forecast, or
cheating, Tit-for-Tat has a capacity to set up a chain reaction in a response to an
initial mistake.
d.) Finite game case, Kreps approach.
Lets now return to the question of how collusion might occur non-co-operatively even in
the finitely repeated game case. Intuition said that collusion could happen- at least at
the earlier rounds- but the game theory apparently said that it could not. Kreps et al.
(1982) offered the elegant solution to this paradox. They relax the assumption of
complete information and instead suppose that one player has a small amount of doubt in
his mind as to the motivation of the other player. Suppose A attaches some tiny
probability p to B referring- or being committed- to playing the trigger strategy. In
fact it turns out that even if p is very small, the players will effectively collude
until some point towards the end of the game. This occurs because its not worth A
detecting in view of the risk that the no-collusive outcome will obtain for the rest of
the game, and because B wishes to maintain his reputation for possibly preferring, or
being committed to, the trigger strategy. Thus even the small degree of doubt about the
motivation of one of the players can yield much effective collusion.
5. The motives for retaliation.
The motives for retaliation differ in three approaches. In the first approach, the price
war is a purely self-fulfilling phenomenon. A firm charges a lower price because of its
expectations about the similar action from the other one. The signal that triggers such a
non-co-operative phase is previous undercutting by one of the firms. The second approach
presumes short-run price rigidities; the reaction by one firm to a price cut by another
one is motivated by its desire to regain a market share. The third approach (reputation)
focuses on intertemporal links that arise from the firm's learning about each other. A
firm reacts to a price cut by charging a low price itself because the previous price cut
has conveyed the information that its opponent either has a low cost or cannot be trusted
to sustain collusion and is therefore likely to charge relatively low prices in the
future. 
6. Conclusion.
So far I have discussed the collusion using some simple example with a choice of output
levels made by the two firms. But there may be several firms in the industry, and in fact
firms have a much broader choice. It may be that their decision variable is price,
investment, R&D and advertising. Nevertheless the more or less the same analysis could be
applied in each of the case. 
I have examined different assumptions and predictions, which allow or do not allow the
possibility of collusion. In reality such thing as collusion definitely takes place, if
it had not, there would not have been any strong an ambiguous discussion of this topic.
But I think it would be appropriate to end this essay with an explicit reminder that once
we leave the world of perfect competition, we lose the identity of interests between
consumers and producers. So, the discussion of benefits to firms in oligopoly that arise
from finding strategies to enforce collusive behaviour might well have been the
discussion of the expenses of consumers.
Bibliography
7. Bibliography. 
1. J.Vickers, Strategic competition among the few- Some recent developments in the
economics of industry.
2. J.Tirole, The theory of industrial organisation. Ch 6.
3. Estrin & Laidler. Introduction to microeconomics. Ch 17.
4. W.Nicholson, Microeconomic theory. Ch 20.