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The new microeconomics and the oligopoly strategic behaviour.

I. Introduction

Preoccupied by the problem of economic quantification and by the rigorous express of the relations between them, the marginality school of the economic thinking contributed to the enrichment of the analytical instrument from this field and enriched a lot the problematic of the economic science, emphasising the modernity.

The importance of knowing the market mechanisms, the ratio between costs and the others economic variables is in general recognised at microeconomic and macroeconomic level. The economic agent (named player in the game theory), seller or producer must define its behaviour and formulate strategies for future actions. The companies interest for the elaboration of favourable strategies, which many times go low to the price game.

The economic models and the practice of economical--mathematics constituted an excellent instrument for studying the economic games, stimulating the research in this field. In the last decade, a series of methods regarding the representation of the economic theory were used in order to study the evolution of state parameters of the social-economic field. The category of systems highly studied in the economic dynamism are those who pattern the business circle, patterns of economic increase and patterns which study the costs game in a dynamic perspective. In the last decade, from time to time, evolution and chaotic behaviour were noticed in the economic patterns. The main conception of the economic science was demonetized, which says that the economic balances are constant even with the lack of external shocks, the economy leaning towards a stationary state.

From this point of view, conducting a study in a dynamic environment, about costs mechanism seems to be a very important problem. Taking into account the cost which is an economic phenomenon, this work trying to approach it, using a modern instrument of work, belonging exclusively to mathematics, which is the game theory.

We are interested in the theoretical results which are revealed in literature regarding the theory of games starting with the key concepts of this one: games, strategies, balance, game value, etc. the research is focused on the main oligopoly market structures from the microeconomics point of view.

The new microeconomics is based on the imperfection of the real markets, affected by risk and uncertainty. The study regarding the behaviour of the economic agents is conducted in a business environment where the intelligence is not completely and constantly available. Sticking to the hypothesis of rationality the new microeconomics has two important instruments of analyse: the theory of games and the intelligence economy.

II. Literature Review

The theory of games studies the human behaviour in situations of conflict, where the reason is contrary to the reason, each of the parties involved being able to analyse and to decide in order to reach their own targets. It emphasises the meaning of the rationality hypothesis when the contentment of a person is directly affected by the other agents' decisions and defines solutions for various situations of conflict. The theory of games is a method of research for strategic interaction situations, where the economic agents are aware of the interdependence which exists between them and each of them will make their own decisions taking into account the others' behaviour.

The theory of games was first mentioned and historically related to the year 1944 when the mathematician John von Neumann and the economist Oskar Morgenstern publish the famous work: Theory of Games and Economic Behaviour. This work represented the first mathematic pattern which included people as rational human beings. After a period of growing up, influenced by works of J.F. Nash (1951), R.D. Luce and H. Raiffa (1957), L. Shapley (1953), the theory of games becomes by the end of the '80 a strong instrument for analysing the situations of strategic interaction, introduced in the works of J.W. Friedmann (1986), D.M. Kreps (1990), D. Fundenberg and J. Tirole (1991), A. Mass-Colell (1995) and P. Cahuc (1998). Even if the theory of games is quite recent, the economic theory specifies other studies which explain this kind of problematic in a more restricted manner.

Augustin Cournot studied in 1838 the operation of the oligopoly markets where each company takes action knowing that its volume of production affects the market cost. In 1833 /. Bertrand studied the operation of the oligopoly markets where the companies with constant efficiencies produce the same product settling the selling price. The result mentioned by Bertrand is known as Bertrand paradox. In 1934 Stackelberg shows that some companies can be leader and that are able to impose the price to the others. The leader company, as a barometer company, knows best the market situation and has the means necessary in order to control the counter party. This doesn't mean that the company is the most powerful but well informed and organised.

The following question comes up: Which of the behaviours mentioned above should be followed? In order to answer this question, a theory was needed which could explain the interactions between companies. This is the great contribution of the game theory. It allows the elaboration of an analytical framework regarding the situations when an agent's decisions can affect the earnings of the other agents.

The theory of games studies the manner in which the rational decision are made by people in interactive situations when the results of their action depend directly on the others; actions. In this case, where the coordination of the individual actions is adjusted by competition, each economic agent (named player in the game theory) must forecast the future actions of the other agents and then optimise their own behaviour depending on the results.

In the last two decades the rent-seeking type of dynamic games were analysed (to share the fortune). A systematic study of the balance point for this kind of games was made by Okuguchi K. and Szidarovsky F. who revealed that these games are equal to the Cournot type of oligopoly with price hyperbolic function.

Summarising the phrases mentioned above, three stages of evolution were identified regarding the theory of games:

1) beginning with the '20 until the end of the II nd World War. In all this time the strategic games and their extensions were elaborated, military tactics games, special those with zero-sum. The strategic researches are emphasised serving the at maximum the purpose of settling the possible solutions of these games;

2) the period which starts with the work John von Neumann and Oskar Morgenstern ,,Theory of Games and Economic Behaviour" (1944) and ends with the '70. The interest is focused on the cooperative theory of games which finds important the coalitions formed between the rational persons in order to maximise their earnings;

3) nowadays, the main place is given to the non-cooperative games with Nash equilibrium considered to be a privileged solution as well as the dynamic games..

The theory of games hyphens the meaning of the rationality hypothesis when the contentment of the person is directly affected by the decisions of the other agents and defines solutions for different situations of conflict. Out of this reason knowing the analysis instruments of this theory is essential nowadays, the theory of games constituting a real matrix of the contemporary financial theory. Its postulates are based on the analysis of the people's interdependent relations. The economic description and analysis must be oriented towards solving the conflicts caused by the problems of redistribution. The approach moves from solving problems related to assignment towards the analysis of the availability restrictions which influences the resources assignment and distribution. In conclusion, the economic reality can't be properly presented by a static approach, as the traditional microeconomics theory does it, but it must be seen as a process, with the help of a dynamic approach, from the new microeconomics perspective.

3. Competitive strategies on the oligopoly market

Some of the economic agents have a different behaviour on the market affecting the other economic agents' behaviour. This type of reality resides in the "market structure" concept. The meaning of market structure represents the features of a market by the number and the relative power of the companies which operate on the market having the purpose of settling their behaviour and its consequences on the economic efficiency of the economic system. The contributions of the game theory to the study of the market structures and to the competition can solve some problems related to the costs system and to the intelligence exchange. Competition was and is related to the behaviour hypothesis of the economic agents and to the relative hypothesis of the market operation.

The market structures vary depending on: the influence on the costs settlement; the companies' production of standardized or non--standardized products; the companies' possibility to enter on the market; the publicity, the products' features, etc.

The oligopoly means a market structure controlled by a restricted number of producers, the actions of each producer affecting the others competitors' actions. If a producer cuts the price in order to increase the sales, then its competitors will react by cutting their price too, thing which will determine a profit decrease for the first company. Before making the decision regarding the price cut, the oligopoly company would have to analyse first the future reaction of its competitors and the consequences upon it. In the first works on oligopoly, Cournot (1838) and Bertrand (1883), write about the elements used by the theory of games for analyse of the imperfect competition. The theory of games uses a general method of analysing the strategic interaction situations. This theory applies on analysing the companies' strategic behaviour, starting with the general framework of a game situation.

The game situations are based on few important elements: game rules; strategies to follow; earnings and in oligopoly situations we have: rules of the oligopoly game; strategies of the oligopoly game; earnings of the oligopoly game. The rules of an oligopoly game are made starting with the features of the economic, social and politic environment of the oligopoly market, with the laws of the trade practices. One of these rules regards the number of players meaning the number of companies operating on the market. The rules of an oligopoly game represent all the possible actions of each player. This one makes a complete list of game strategies. The possible strategies in an oligopoly game can be: prices increase, cutting prices or keeping them at the same level; increase, decrease or keeping the production at the same level; more, less or the same advertising; improving, lowering or maintaining the quality, etc. The earnings of an oligopoly game may be represented by the economic profits or losses of each company. The earnings of the companies depend on their strategies and on their constraints which they deal with.

Studying the situations of imperfect competition, especially the one of oligopoly where the buyers' decisions are interdependent, can be achieved with the help of non--cooperative games. Important applications of the game theory reside in different aspects of the oligopoly competition, for example: secret agreements or price forming study in a closed economic system. The situation of oligopoly competition, the companies can't deal with an unreceptive environment. The interdependent situations between different centres of decision and their contribution to obtaining a credible solution can be done with the help of non-cooperative games which developed a lot over the last years.

The theory of games can shape strategic behaviours of economic actors and allows a description of the competition highlighting the intelligence problems. M. Shubik (1959) used the term ,,contingent request" in order to describe the request a company has to deal with, the other competitors' actions being already decided. He showed that the contingent request structure depends on the aggregate method of the individual request and a clear difference between market's structure, the companies' intentions and their behaviour.

For the duopoly games, the possible strategies the two companies can follow are: agreement for profit division; or breaking the first agreement, thing that would allow the cheating company to obtain greater profits than its partner. This kind of structure is similar to the one of the game named prisoner's dilemma. In case of a balance situation the two companies break or follow the duopoly agreement, they will sell at the same price, producing the same volume and obtaining the profit of a monopolist.

The theoreticians of the game with practice in economy showed that price war can be considered to be the result of a repeated duopoly game. The producers follow the concluded agreements until the request variation determine the price cut under a certain limit. The companies' reaction to the price cut is like it would be the result of a problem the competitors deal with. They have to operate in order to make the competitors believe in the penalty in case of agreement breakage. Updating the credibility of the menaces is important in order to respect the agreement as longer as possible. On this kind of markets, from time to time, price war can occur, which can end with the exclusion from the market of the weaker competitors.

3.1. Cournot competition on the amount model

In the Cournot model the two players (two companies, in this case) produce the same product, without any cost and with an infinite production capacity (two mineral--water springs). Each company chooses the amount they offer to the market for selling; the market's answer will consist in settling the price in order to sell the entire amount. This price is a decreasing straight line function of the total offer. An "auctioneer" announces the price in order to balance the total offer of the two companies with the consumers' request. The only difference from the situation of perfect competition is that if the request decreases proportionally to the price, then any increase of the products' amount must lead to price cutting. Each company is interested in other lesser production in order to increase the price.

Cournot duopoly model seems to be one of dynamic and progressive, each action answers to a production period. He solves two problems: one regarding the difference between the static and dynamic features; and the other one regarding the financial conditions. In this model the strategic interactions are not taken into account assuming that each seller thinks about the other seller's amount to be given at the moment he chose his strategy. In general, each seller takes into account that his choice of the amount affects the choice made by his competitor. A situation of conjectural equilibrium is obtained. The role of game theory in this case is to allow the exact description of the hypothesis needed in order to obtain the wanted result. In a static non-cooperative game, where the players chose simultaneously and without communication their strategies, the Cournot equilibrium is obtained by settling the function of each player's best answer. If we suppose the two companies agree upon a lesser production than in the Cournot equilibrium situation, then none of the companies is interested in keeping this kind of agreement because in a static framework is impossible to build credible cartels based on agreements upon the amounts. The situation mentioned above can be formalised following the next game: X =Y = [0, [infinity]); [u.sub.1](x, y) = (p-(x + y)) x; [u.sub.2](x, y) = (p-(x + y)) y; x [member of] X and y[member of] Y.

The non-cooperative behaviour of the companies is showed by the best answer's curve to any strategy chosen by the other player at time "t". A player can give the best answer at time "t+1". For [for all]y [member of] Y : x = 1/2 (p-y) being the best answer of player [X.sup.*] to strategy y of player [Y.sup.*] and for [for all] x [member of] X : y = 1/2 (p-x) being the best answer of player [Y.sup.*] to strategy x of player [X.sup.*].

The dynamic adjustment which Cournot proposes is the following: starting with an initial situation (x0, y0) which the two players observe, they react alternatively, adjusting with the help of best answer to the strategy used by the others player. If we suppose that player "X" is the first who reacts we will obtain the following strategy introduced in fig.1:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

From a graphic point of view the equilibrium situation corresponds to the best answer's functions intersections (the reactions functions of the two companies). In this case the price is not affected by the individual decisions of production. (see fig. 1):

[FIGURE 1 OMITTED]

From fig. 1 we observe that ([x.sub.t] [y.sub.t]) converge fast to the unique Nash equilibrium of the game meaning the result (p/3, p/3). If this feature is valid independent of the initial result ([x.sub.0] [y.sub.0]) then the Nash equilibrium is globally stable. The global stability of the equilibrium implies the uniqueness of this one for any kind of Cournot adjustment sequence [x.sub.t] constant in [x.sub.0]. Each player reacts in a "myopic" way to the successive strategies chosen by other players, if player "i" would take into account at each of its interventions the currents strategy of the partners as final strategy and would use the best associate answer.

The two companies coordinate their actions very well, being interested in settling a lower production level. With Cournot equilibrium a lower production level can be settled than the one obtained in a situation of perfect competition and higher than the monopoly one. Cournot equilibrium leans towards a perfect competition when the companies umber leans toward infinite. The game theory practice leads to the research of these situations as Nash equilibrium. Being critical we should notice that Cournot used 1838, without knowing, the Nash concept (elaborated in 1950) in order to explain the oligopoly competition. This kind of equilibrium where the players strategies regarding the amounts, represents also a Cournot, was called the Cournot--Nash equilibrium. Describing exactly the strategies and the decision sequences and using the instrument offered by the game theory, the Cournot equilibrium can be explained as non-cooperative game equilibrium. The Cournot model shows that the competition system is not necessarily a procedure of effective resources assignment because in case of imperfect competition the production level is inferior to the one of perfect competition. Mean time this model is a special one, because it answers to the operation of the centralised market when an auctioneer is the one who recommends the prices.

Augustin Cournot makes the first definition regarding the noncooperative equilibrium, which is later analysed and developed by J. Nash (1951). The analysis of the duopoly is emphasised being understood as a peculiarity of the oligopoly market. Starting with Cournot's theory, which was entirely reconsidered, and with Nash's research programme, Martin Shubik developed his research regarding the function of the game theory in economy. The first problem studied was about the relations between the formal instrument used and the economic content of the phenomenon. The analytical wording chose by Cournot for introducing the relations between the amounts and the prices in case of duopoly, is the foundation of the wrong economic explanation given by Bertrand to Cournot.

The informal definitions given by theoreticians regarding the noncooperative games are not relevant in order to represent only the situations described by Cournot without using the concept of mixed strategy, with the terms used in the game theory. The transposition in algebraic terms of the mathematic model set off by Cournot in the model of cooperative games proved to be necessary in order to disclose the original economic content of the duopoly theory developed by Cournot. A re-examination of the equations system given by Cournot in the game theory logic leaded to the identification of a strategic theory of the competition between producers. The solution for the duopoly model given by Cournot is without doubt the one of the unique and stable Nash equilibrium. In the Cournot duopoly the competition between two producers of the same product sets a significant economic solution, used for the strategic knowledge of the market.

In the Cournot model the competition resides in the non-cooperative feature of the two independent producers' conflict. It is opposite to the possibility of an agreement between the two producers offered by the cooperative game with economic consequences which would be equal to a monopoly situation. The borderline between competition and monopoly regroups the classic dissimilarity of the game theory in non-cooperative games and cooperative games. The two producers, the exclusive sellers of the same product, in the Cournot model, can choose between two possible situations: they don't agree or they agree and in this case their cooperation is supposed to be a monopoly. This kind of interpretation allows the duopoly analysis with strategic variable of production, which can be seen as a prisoner's dilemma game, the instability of the cooperative strategies pair game according to an optimal Pareto situation. The two producers are in a competition situation where they produce the same product according to the same terms without any executorial agreement. What Cournot defined as ,,formal binding" is used in the game theory as ,,binding agreements" in order to describe the non--cooperative games. The Cournot model of duopoly provided not only an economic interpretation of cooperative and non--cooperative games dissimilarity but also the executive signification of the contractual agreements.

3.2. Bertrand price competition model

Bertrand (1883) criticised the Cournot model showing that the oligopoly companies can use the same assignments as in case of perfect competition, if the prices are simultaneously settled. He suggested a solution which depended on price variation; he started with a rather simple case where two companies produce the same product, settling their selling price. The production costs for each product are constant (marked with letter ,,c") and identical for both companies. In this case the consumers will buy from the company which has lower prices. We suppose that the two companies share the total request in two, if the prices are the same.

Bertrand's paradoxical result is that at an equilibrium level the price is equal to the marginal cost and the profits are null. None of the companies can improve the profits because it would obtain a negative one cutting the price. If a company settles a price higher than the marginal cost, the other company will be interested in settling a lower price in order to cover the entire request. The question is if Nash equilibrium is present where the price is equal to the marginal cost. The Nash equilibrium, if present, is it unique?

In the Bertrand model, Nash equilibrium is a combination of strategies weakly controlled: some players are not interested in settling an equal or higher price than ,,c" (the cost), others set an price equal to ,,c". An irrational player who sets a price (P) higher than the cost (c) he obtains the same profit as the player who will obtain Nash equilibrium if the competitor always sets a price (P) equal to the cost (c). The player's irrationally occurs when a competitor must explore such behaviour, choosing a price (P1) higher to the cost but lower to P. This kind of argument shows that players can be interested in manipulating their competitors making them believe that they are irrational. If player 1 is an agent with "irrational" reputation, choosing a monopoly price, then player 2 sets a price P2 lower to the monopoly one. But he is not sure that player 1, declared irrational but being rational benefits by his reputation, then he will chose a price lower to P2.

Such reputation problems can be studied in a dynamic framework. We will consider the reputation game for two companies, marking with 8 the discount factor and trying to settle the perfect Bayesian equilibrium. The game can run by converse induction taking into account the beliefs. If the cooperation was supported in the first period, then in the final period the players will have the same reputation. If the players broke the agreement then they would lose the initial reputation. But choosing a cooperative strategy the player maintains the reputation, without bringing any new information regarding his behaviour, meaning the cooperative one. If we assume that the players cooperated in the first period then in the last one, a player obtained [alpha][delta][pi] this one being a price lower than the monopoly one. The question which rises is: are the players interested in cooperating at the beginning? The company has an updated hope for earning equal to [alpha] ([pi]/2 + [delta][pi]) in case of cooperation. In case of non cooperation for the entire monopoly profit the company will obtain [alpha][pi], losing its reputation. The company is interested in cooperation when [delta] [greater than or equal to] 1/2. This model shows that the companies can be interested in cooperating at the beginning when their option for the present is low enough. In this case, we can talk about cooperation at the beginning of the game which degenerates in a price war. The reputation phenomena can be very important if there is the slightest incertitude regarding the perfect rationality of the players. Such a feature can explain many behaviours assuming that the players believe there are other "irrational" players but with a lower probability.

The examples mentioned above express the result of the strategic interaction which is very sensitive to the companies', products' and markets' features. There are many different situations by which the consequences of these features can be studied (for example: the problems related to noticing the products' quality, the advertising, the strategies of research and development, the network of distribution, the possibilities of market input and output). If we start with a normal game ([x.sub.1], ..., [x.sub.n]; [u.sub.1], ..., [u.sub.n]) we will assume that the players behaviour is decentralized, each of them having to chose alone a strategy, ignoring any decision of other players. The communication possibility between players is excluded. There is no initial result or a game history which could emphasize the strategies used more frequently than the one of the others. We can take into account all the strategies as being a priori equally possible and also the choice of the best strategy.

In order to determine a non-cooperative behaviour the controlling strategies can be removed. Strategy [Y.sub.i] of player "i" is controlled by strategy [x.sub.i] (where the results ([x.sub.1], ..., [x.sub.i-1]; [y.sub.i], [x.sub.i+1] ..., [x.sub.n]) represent a non-controlling assembly of strategies of player "i") when whatever would be the strategic choice of other players, the use of [x.sub.i] is at least as profitable for "i" than the use of "[y.sub.i]", meaning strategy "[x.sub.i]" better than [y.sub.i]. The games which have an equilibrium regarding the controlling strategies will be the decentralized solution of the non-cooperative game. The strategy used by the company depends on the forecasts made on the reactions of the competitor companies, its analysis can be achieved with the help of the "game theory". A game that can show such an oligopoly analysis introduced by W. Tucker and called the prisoner's dilemma it is well--known. This kind of game is one of the most famous games in the game theory. In this game each player must choose between a pacifist strategy and an aggressive strategy.

The results of this game are described in picture 2.

In picture 2 we can notice that the strategies of player [X.sup.*] are shown by lines in the matrix of results and the strategies of player [Y.sup.*] are shown by columns in the matrix of results. Each of the four boxes in the game matrix represent a result of the game with use of [X.sup.*] in upper left and use of [Y.sup.*] in lower right. We can verify if the pacifist strategy of a player is controlled by his aggressive strategy. In our situation the game has only an equilibrium in controlling strategies (aggressive, aggressive) which corresponds to an open price war. Such a result is not acceptable because the result "peace" meaning (pacifist, pacifist) is proffered by the two players in other words the war is not an optimal Pareto. The dilemma of the game shows that for a player which is not entirely sure on the pacifist intentions of its partner the use of the aggressive strategies is needed to follow the individual interests but the mutual interest recommends that everything has to be done in order to obtain a pacifist result.

The dynamic approach of the economic reality goes to the change of parameters of the variables which compete with the span of economic and social life. The key to survive in case of economic games is the capability of the companies to adjust their strategies to the environment which is in continuous change. A correct forecast of the future events it is necessary. The cross - impact analysis, the request--hazard forecast as well as other numerous scenarios are just a few of the methodologies used in economic forecasts. Over the last years these forecasts are made with the help of programmes implemented on the computer and decision modules. The economic processes are studied in time (year, month, trimester, semester, decade, week, day, hour) or by introducing a simulating unit, the dynamic of these processes being described through discrete models like finite differences equations, finite differences systems of equations or recurrent equations. The microeconomic models are nuclei which compose the macroeconomic models, because the estimation of the parameters depends on microeconomic features. If the models forecast a cyclic evolution, then their assessment is ok only if the system did not suffer from any structural mutations, like a governmental demarche which can modify the entire reaction mechanism of the system.

Conclusions

In economy, structural changes and oscillations are the rule and not the exception and the stationary states become instable when certain parameters vary. The microeconomic models constitute nuclei of which macroeconomic models are conceived, because the parameters estimation for the last one depends on microeconomic model.

The economic actors have different behaviours on the market which have different consequences depending on the number, relative size and strategies approached by the other economic actors. Starting with the rationality hypothesis when the agent's contentment is affected by the others decisions the game theory defines solutions for solving the situations of conflict.

The economic level of the competition can be considered as a mechanism of resources allocation which allows, in many cases, the promotion of the economical efficiency. The game theory contribution to the development of the competition politics can solve some problems related to the price system and to the intelligence exchange. For this reason the notion of competition was and is related first to the behaviour hypothesis of the economical agents and second to the relative hypothesis of the market operation. When the coordination of the individual actions is adjusted by competition, each economic agent must forecast the other agents' actions and then maximise depending on the results their own behaviour.

Conducting a study in a dynamic environment regarding the market structures represents a very important problem of the contemporary economy. We are interested in the theoretical results which are revealed in literature regarding the theory of games starting with the key concepts of this one: games, strategies, balance, game value, etc. The research is focused on the main oligopoly market structures from the microeconomics point of view. For this reason it is an opportunity to study the structure of oligopoly type of markets with the aid of non-cooperative games.

The use of the game theory as reference framework regarding the representation of the economic agents' on different market structure opens the way for an expansive field of investigation. The problem of the economic agents is no longer. The problem of the economic agents is no longer conducting studies for the operation of the perfect competition markets but to analyse the means in which they can coordinate the decisions, in dynamic configurations in a competitive environment affected by risk and uncertainty.

References

(1.) Binmore K., Jeux et theorie des jeux (Bruxelles : Ed. De Boeck Universite, 2001), 46.

(2.) Cahuc P., La nouvelle microeconomie (Paris : Ed. La Decouverte, 2004), 14.

(3.) Kreps D. M., Theorie des jeux et modelisation economique ( Paris : Ed. Dunod, 2002), 67.

(4.) Parkin M., Fluet C. D., Bade R., Introduction a la Microeconomie (Paris : Ed. du Renouveau Pedagogie, 1997), 51.

SIRGHI NICOLETA Faculty of Economics and Business Administration, West University of Timisoara.
Fig. 2--Game matrix
                              Y *

                   Pacifist   Aggressive

      Pacifist     2          0
X *                    2          3
      Aggressive   3          1
                       0          1
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Date:Jan 1, 2009
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