Реферат: Topic: Is Collusion Possible?

Student: MatyukhinAnton,

2 group.

Teacher: Alla Friedman.

МеждународныйИнститут 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 andnon-collusive).

3.

Game theory.

a.)

Concept.

b.)

The problem ofcollusion.

c.)

Predatorypricing.

4.

Repeated games approach.

a.)

Concept.

b.)

Finite game case.

c.)

Infinite gamecase.

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 andoutput determination under the one essential type of imperfect competitionmarkets- oligopoly. Inter-firm interactions in imperfect markets take manyforms. Oligopoly theory, those name refers to “competition among the few”, lackunambiguous results of these interactions unlike monopoly and perfectcompetition. There is a variety of results derived from many different behaviouralassumptions, with each specific model potentially relevant to certainreal-world situations, but not to others.

Here we are interested in the strategicnature of competition between firms. “Strategic” means the dependence of eachperson’s proper choice of action on what he expects the other to do. Astrategic move of a person influences the other person’s choice, the otherperson’s expectation of how would this particular person behave, in order toproduce the favourable outcome for him.

2.

Two types of behaviour(Collusive and non-collusive). Models of enterprise decision making inoligopoly derive their special features from the fact that firms in anoligopolistic industry are interdependent and this is realised by these firms.When there are only a few producers, the reaction of rivals should be takeninto account. There are two broad approaches to this problem.

First, oligopolists may be thought of asagreeing to co-operate in setting price and quantity. This would be theCollusive model. According to this model, firms agree to act together in theirprice and quantity decisions and this would to exactly the same outcome aswould have been under monopoly. Thus the explicit or co-operative collusion orCartel would take place.

Second approach of the oligopoly analysis isbased on the assumption that firms do not co-operate, but make their decisionson the basis of guesses, expectations, about the variables to which theircompetitors are reaching and about the form and the nature of the reactions inquestion. The Non-collusive behaviour deals with this model. Here, though inequilibrium the expectations of each firm about the reactions of rivals arerealised, the parties never actually communicate directly with each other abouttheir likely reactions. The extreme case of this can even imply competitivebehaviour. Such a situation is much less profitable for firms than the one inwhich they share the monopolistic profit. The purpose of this paper is toanalyse the case of the possibility of collusion between firms in order toreach the monopolistic profits for the industry, assuming that they do notco-operate with each other. This would be the most interesting and ambiguouscase to look at.

3.

Game theory.

a.) Concept.

The notion of game theory would a goodstarting point in the study of strategic competition and would be very helpfulin realising the model and the problems facing oligopolistic firms associatedwith it.

Game theory provides a framework foranalysing situations on which there is interdependence between agents in thesense that the decisions of one agent affect the other agents. This theory wasdeveloped by von Neumann and Morgenstern and describes the situation, which israther like that found in the children’s game “Scissors&Stones”. Each firmis trying to second-guess the others, i.e. the behaviour of one firm depends onwhat it expects the others to do, and the in turn are making their decisionsbased 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 andeach of them wants to maximise its pay-off. The pay-off that a player receivesmeasures how well he achieves his objective. Let’s assume in our model thepay-off to be a profit. Their profits depend upon the decisions they make (the strategies chosen by the various playersincluding themselves). A strategy in this model is a plan of action, or acomplete contingency plan, which specifies what the player will do in any ofthe circumstances in which he might find himself. The game also depends on themove order and the information conditions.

Games can be categorised according to thedegree of harmony or disharmony between the players’ interests. The purecoordination game is the one extreme, in which players have the sameobjectives. The other extreme is the pure conflict of the opposite interests ofplayers. And usually there is a mixture of coordination and conflict ofinterests- mixed motive games.

Although the importance of the otherplayers’ choices takes place, sometimes a player has a strategy that is thebest irrespective of what others do. This strategy is called dominant, and theother inferior ones are called dominated. A situation in which each player ischoosing the best strategy available to him, given the strategies chosen byothers, is called a Nash equilibrium. This equilibrium corresponds to the ideaof self-fulfilled expectations, tacit, self-supporting agreement. If theplayers have somehow reached Nash equilibrium, then none would have anincentive to depart from this agreement. Any agreement that is not a Nashequilibrium would require some enforcement.

b.) The problem of collusion.

Now I would like to use an example of a gamein which the Cournot output deciding duopoly is involved. This game isillustrated 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 twoalternatives: high and low output strategies. The corresponding pay-offs(profits) are given in the boxes. In this game, the best thing that can happenfor 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 afirm could earn a good profit margin. The worst thing for a firm is to changeplaces with its rival assuming the same situation takes place. If both firmsproduce high levels of output, then the price would be low, allowing each ofthem to earn still positive but very small profits. Nevertheless, (HIGH;HIGH)would be the dominant strategy of this game (we would observe a Nashequilibrium in strictly dominant strategies here). It is the best response offirm A whenever B produces a high or low output and this is also true for firmB. 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 andthereby to raise price, as their profits would increase to 2 for each firminstead of 1 in NE. Strategy (LOW;LOW) would be the collusive outcome. Theproblem of collusion is for the firms to achieve this superior outcomenotwithstanding the seemingly compelling argument that high output levels willbe chosen.

This was an example of a “one-shot” game andwe saw that the collusive outcome was not available for that case. But inreality these games are being played over and over (on a long-term basis) andwe will see later in this essay how the collusion can be sustained by threatsof retaliation against non-co-operative behaviour.

c.) Predatory pricing.

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Here we need tointroduce the explicit order of moves in the model. There are again twoplayers-firms on the market- an incumbent firm and a potential entrant in themarket. The game is illustrated below:

The potential entrant chooses betweenentering and staying out of the industry. In the case of his entering, theincumbent firm can either fight this entry (which as we see would be costly toboth), or acquiesce and arrive at some peaceful co-existence (which isobviously more profitable). The best thing for incumbent is for entry not totake 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 theincumbent were faced with the fact of entry, it would more profitable for himto acquiesce rather than to fight the entry. Due to this fact the potentialentrant 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 threatto fight was empty threat that wouldn’t be believed, i.e. that threat was not acredible one. The concept of perfect equilibrium, developed by Selten(1965;1975), requires that the “strategies chosen by the players be a Nashequilibrium, not only in the game as a whole, but also in every subgame of thegame”. (In our model on the picture, the subgame starts with the word“incumbent”). We have got the perfect equilibrium to rule out the undesirableone.

4.

Repeated games approach.

a.)

Concept.

As I have already mentioned, in practicefirms are likely to interact repeatedly. Such factors as technologicalknow-how, durable investments and entry barriers promote long-run interactionsamong a relatively stable set of firms, and this is especially true for theindustries with only a few firms. With repeated interaction every firm musttake into account not only the possible increase in current profits, but alsothe possibility of a price war and long-run losses when deciding whether toundercut a given price directly or by increasing its output level. Once theinstability of collusion has been formulated in the “one-shot” prisonersdilemma game, it raises the question of whether there is any way to play thegame in order to ensure a different, and perhaps more realistic, outcome. Firmsdo in practice sometimes solve the co-ordination problem either via formal orinformal agreements. I would focus on the more interesting and complicated caseof how collusive outcomes can be sustained by non-co-operative behaviour(informal), i.e. in the absence of explicit, enforceable agreements betweenfirms. We have seen that collusion is not possible in the “one-shot” version ofthe game and we will now stress upon a question of whether it is possible in arepeated version. The answer depends on at least four factors:

1.

Whether the game is repeatedinfinitely or there is some finite number of times;

2.

Whether there is a fullinformation available to each firm about the objectives of, and opportunitiesavailable to, other firms;

3.

How much weight the firmsattach to the future in their calculations;

4.

Whether the “cheating” can/can not be detected dueto the knowledge/lack of knowledge about the prior moves of the firm’s rivals.

The fact of repetition broadens thestrategies available to the players,

because theycan make their strategy in any currant round contingent on the others’ play inprevious rounds. This introduction of time dimension permits strategies, whichare damaging to be punished in future rounds of the game. This also permitsplayers to choose particular strategies with the explicit purpose ofestablishing a reputation, e.g. by continuing to co- operate with the otherplayer even when short-term self-interest indicates that an agreement to do soshould be breached.

b.) Finite game case.

But repetition itself does not necessarilyresolve the prisoner’s dilemma. Suppose that the game is repeated a finitenumber of times, and that there is complete and perfect information. Again, weassume firms to maximise the (possibly discounted) sum of their profits in thegame as a whole. The collusive low output for the firms again, unfortunatelyfor the firms, could not be sustained. Suppose, they play a game for a total offive times. The repetition for a predetermined finite number of plays doesnothing to help them in achieving a collusive outcome. This happens because,though each player actually plays forward in sequence from the first to thelast round of the game, that player needs to consider the implications of eachround up to and including the last, before making its first move. Whilechoosing its strategy it’s sensible for every firm to start by taking the finalround into consideration and then work backwards. As we realise the backwardinduction, it becomes evident that the fifth and the final round of the gamewould be absolutely identical to a “one-shot” game and, thus, would lead toexactly the same outcome. Both firms would cheat on the agreement at the finalround. But at the start of the fourth round, each firm would find it profitableto cheat in this round as well. It would gain nothing from establishing areputation for not cheating if it knew that both it and its rival were bound tocheat next time. And this crucial fact of inevitable cheating in the finalround undermines any alternative strategy, e.g. building a reputation for notcheating as the basis for establishing the collusion. Thus cheating remains thedominant strategy.

* NOTE:the ishowever one assumption about slightly incomplete information, which allowscollusive outcome to occurin thefinitely repeated game, but I will left it for the discussion some paragraphslater.

c.)_ Infinite game case.

Now lets consider the infinitely repeatedversion of the game. In this kind of game there is always a next time in whicha rival’s behaviour can be influenced by what happens this time. In such agame, solutions to the problems represented by the prisoners dilemma arefeasible.

i.) “Trigger” strategy

Suppose that firms discount the future atsome rate “w”, where “w” is a number between O and 1. That is, players attachweight “w” to what happens next period. Provided that “w” is not too small, itis now possible for non-co-operative collusion to occur. Suppose that firm Bplays “trigger” strategy, which is to choose low output in period 1 and in anysubsequent period provided that firm A has never produced high output, but toproduce high output forever more once firm A ever produces high output. That isB co-operates with A unless A “defects”, in which case B is triggered intoperpetual 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 anystrategy in which he is not the first to defect. If A chooses a strategy inwhich he defects at any stage, then he gets a pay-off of 3 in the first periodof defection (as B still produces low output), and a pay-off of no more than 1in every subsequent period, due to B being triggered into perpetualnon-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, wewill get that it is better not to defect so long as

W > (or =)½

We can conclude that is the firms giveenough weight to the future, then non-co-operative collusion can be sustained,for example, by “trigger” strategies. The “trigger” strategies constitute aNash equilibrium = self-sufficient agreement. However it is not enough for afirm to announce a punishment strategy in order to influence the behaviour ofrivals. The strategy that is announced must also be credible in the sense thatit must be understood to be in the firm’s self-interest to carry out its threatat the time when it becomes necessary. It must also be severe in a sense thatthe gain from defection should be less than the losses from punishment. Butbecause it is possible that mistakes will be made in detecting cheating (if,for example, the effects of unexpected shifts in output demand aremisinterpreted as the result of cheating), the severity of punishment should bekept to the minimum required to deter the act of cheating.

ii.) Tit-for-Tat.

Trigger strategies are not the only way toreach 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 playerchose in the previous period. Cheating by either firm in the previous round istherefore immediately punished by cheating, by the other, in this round.Cheating is never allowed to go unpunished. Tit-for-Tat satisfies a number ofcriteria for successful punishment strategies. It carries a clear threat toboth parties, because it is one of the simplest conceivable punishmentstrategies and is therefore easy to understand. It also has the characteristicsthat the mode of punishment it implies does not itself threaten to underminethe cartel agreement. This is because firms only cheat in reaction to cheatingbe others; they never initiate a cycle of cheating themselves. Although it is atough strategy, it also offers speedy forgiveness for cheating, because oncepunishment has been administered the punishing firm is willing once again torestore co-operation. Its weakness is in the fact that information is imperfectin reality, so it is hard to detect whether a particular outcome is theconsequence 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 aresponse to an initial mistake.

d.) Finite game case,Kreps approach.

Lets now return to the question of howcollusion might occur non-co-operatively even in the finitely repeated gamecase. Intuition said that collusion could happen- at least at the earlierrounds- but the game theory apparently said that it could not. Kreps et al.(1982) offered the elegant solution to this paradox. They relax the assumptionof complete information and instead suppose that one player has a small amountof doubt in his mind as to the motivation of the other player. Suppose Aattaches some tiny probability p to B referring- or being committed- to playingthe “trigger” strategy. In fact it turns out that even if p is very small, theplayers 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 theno-collusive outcome will obtain for the rest of the game, and because B wishesto maintain his reputation for possibly preferring, or being committed to, the“trigger” strategy. Thus even the small degree of doubt about the motivation ofone of the players can yield much effective collusion.

5.

The motivesfor retaliation.

The motives for retaliation differ in threeapproaches. In the first approach, the price war is a purely self-fulfillingphenomenon. A firm charges a lower price because of its expectations about thesimilar action from the other one. The signal that triggers such anon-co-operative phase is previous undercutting by one of the firms. The secondapproach presumes short-run price rigidities; the reaction by one firm to aprice cut by another one is motivated by its desire to regain a market share.The third approach (reputation) focuses on intertemporal links that arise fromthe firm’s learning about each other. A firm reacts to a price cut by charginga low price itself because the previous price cut has conveyed the informationthat its opponent either has a low cost or cannot be trusted to sustaincollusion and is therefore likely to charge relatively low prices in thefuture.

6. Conclusion.

So far I have discussed the collusion usingsome simple example with a choice of output levels made by the two firms. Butthere may be several firms in the industry, and in fact firms have a muchbroader choice. It may be that their decision variable is price, investment,R&D and advertising. Nevertheless the more or less the same analysis couldbe applied in each of the case.

I have examined different assumptions andpredictions, which allow or do not allow the possibility of collusion. Inreality such thing as collusion definitely takes place, if it had not, therewould not have been any strong an ambiguous discussion of this topic. But Ithink it would be appropriate to end this essay with an explicit reminder thatonce we leave the world of perfect competition, we lose the identity ofinterests between consumers and producers. So, the discussion of benefits tofirms in oligopoly that arise from finding strategies to enforce collusivebehaviour might well have been the discussion of the expenses of consumers.

7. Bibliography.

1.

J.Vickers, “Strategiccompetition among the few- Some recent developments in the economics ofindustry”.

2.

J.Tirole, “The theory ofindustrial organisation”. Ch 6.

3.

Estrin & Laidler.“Introduction to microeconomics”. Ch 17.

4.

W.Nicholson, “Microeconomic theory”. Ch 20.

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