THE GAMES THEORY AND THE MARKET WITH IMPERFECT COMPETITION

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THE GAMES THEORY AND THE MARKET WITH IMPERFECT COMPETITION Powered By Docstoc
					      GAMES THEORY AND THE MARKET WITH IMPERFECT
                     COMPETITION

                        Associate Professor Ph.D. SÎRGHI Nicoleta
                              West University of Timisoara
                   Faculty of Economics and Business Administration
                                   Timisoara/Romania
                               nicoleta.sirghi@yahoo.com


                                                     Abstract
           Studying the conflict situations, using the game theory, where more rational agents take
action leads to the conclusion that each of them has a particular purpose and being independent
regarding selection of the decisions but dependent of the results. The author proposes a study in this
work regarding the patterning process of the market structures with imperfect competition by using
the games theory. This particular theory suggests solutions for actions taking place among rational
individuals by using adequate mathematical patterns with possible applicability in the economic field.
            In perfectly competitive markets, buyers and sellers are sufficiently large in number to
ensure that no single one of them, alone, has the power to determine market price. Equilibrium in a
competitive market thus requires the simultaneous compatibility of disparate and often conflicting self-
interested plans of a large number of different agents. Perfect competitive occupies one polar extreme
on a spectrum of possible market structures from the ,,more,, on the ,,less,, competitive. Many markets
display a blend of monopoly and competition simultaneously. Firms become more interdependent the
smaller the number of firms in the industry, the easier entry, and the closer the substitute goods
available to consumers. When firms perceive their interdependence, they have an incentive to take
account of their rivals’ actions and formulate their own plans strategically. When firms are behaving
strategically, one of the first things we need to do is ask ourselves how we should characterize
equilibrium in situations like this. On the face of it, one might be tempted to reason as follows:
Because firms are aware of their interdependence, and because the actions of one firm may reduce the
profits of others. Putting the legality of such collusion aside, there is something tempting in the idea of
a collusive equilibrium such as this. From this reason the analysis instrument of games theory making
up the new syntax of the market efficiency. The final conclusions of this paper refer to optimal
strategies chosen by players, strategies with applicability in patterning different market structures and
the equilibrium.

          Keywords
Market structures, imperfect competition, equilibrium, games theory, strategies, players.




1. INTRODUCTION

          The games theory studies the modality in which rational individuals act during
conflicts. This theory emphasizes the significance of the rationality hypothesis within which
the individual satisfaction is directly determined by the other agent’s decisions and it defines
solutions for different conflictive situations. The economic actors have distinctive behaviors
on the market which generate distinctive consequences depending on the number, relative
size and strategies adopted by the other economic actors.
          Therefore, the economic level of the competition can be considered as a
mechanism of resource allocation, mechanism which sometimes can promote economic
effectiveness. The main problem of economists is to decide whether, depending on
circumstances, competition can favor or not cost cutting, most performing companies
selecting, increasing consumer’s welfare, creating new products, new companies coming out
on the market, developing the technical and innovational progress. The contribution of the
games theory to developing the competition policy can solve some difficulties regarding the
price system and information exchange.
         Thus, the competition notion was and continues to be strongly related on the one
hand, to hypotheses of economic agent’s behaviors, and to relative hypotheses of market
functioning, on the other hand. The market with pure and perfect competition represents the
theoretical pattern, an ideal situation which emphasizes the intrinsic virtues of the „ invisible
hand” as being the best natural mechanism of economy functioning and adjusting. Although
considered as theoretical pattern, the market with perfect competition stresses upon the
market strengths which naturally lead to the most rational and the best possible fulfilling of
both producers and consumers interests.
         Real markets are generally characterized by imperfect competition. It’s been
concluded that there is imperfect competition in a specific field (industry) if salesmen
themselves decide or influence the price levels to their offer individually. The capacity of
putting pressure on price depends on the power of each supplier, on the market
characteristics within opposition rapports. In parallel with price deciding or influencing,
every supplier is preoccupied with increasing the market share (the percentage from the
accomplished offer of industry) as a premise in maximizing the total profit.
         Market forces are not impersonal and the reduced number of economic actors leads
to adopting a strategic behavior by anticipating competitor’s reactions. There are some rules
that need to be followed, rules given by the free game of economic actors. The
interdependence principle of different actor’s behaviors represents one of the minimal rules
of imperfect competition policy.
         The specificity of this competition type can be realized with the help of the games
theory. Markets with imperfect competition are of huge diversity, but they are never in pure
pattern. Therefore, on imperfect markets, consumers are confronted with particular product
brands, with a finite range of substitution products, etc. Thus, the modality in which
competitive companies choose quality, quantity, price, etc should be studied first. Unlike
free entering and exiting the market postulated by the perfect competition, this hypothesis is
not verified for the imperfect competition. There already are companies on this market
which impose entering barriers for other new companies.
         Considering the information imperfect to which economic agents relate, it contrasts
with the hypothesis of transparency characteristic to the perfect market. The behavior of
rational agents on the imperfect market when being confronted with imperfect information
can be greatly solved with the games theory, conclusions being used for patterning different
market structures. Theoreticians approach the aspects of incomplete information beginning
with the principles of the games theory. They proved that some situations in which
economic agents confront with incomplete information can be simulated and for this type of
demonstration they use both the static and dynamic games principles as incomplete
information.
         Concerned about the economic quantification and about the strict expression of
relations between them, the marginal school of economic thinking contributed to the
enriching of the analytical instrument in this field and greatly enriched the economic science
issue giving it a strong touch of modernity [ 1].
         The game theory studies the human behaviour in situations of conflict, where the
reason is opposed to reason, each of the parties involved having analytical authority and the
capability to make decisions in order to achieve its objective. It marks the meaning of the
rationality hypothesis when the individual satisfaction is altered by the decisions of other
agents and describes solutions for different situations of conflict. The game theory is a
research method of strategic interaction situations where the economic agents are aware of
the interdependence between them; each making a decision according to others behaviour.
          The game theory issue is historically linked to the year 1944 when the
mathematician John von Neumann and the economist Oskar Morgenstern published the
famous work: Theory of Games and Economic Behaviour. The work was the first
mathematical pattern that included the man as rational human being [3].
          A player, according to the game theory, is an independent decision unit consciously
aiming to a particular purpose. Moreover, these players are given the rationality feature.
This is the reason why the game theory studies the making of rational decision by
individuals in interactive situations where the results of their action depend directly on the
actions of others.
          Although game theory is rather new, the economic theory reveals other studies that
explained this issue in an isolated manner. In 1838, Augustin Cournot studied the operation
of oligopolistic markets where each company acts knowing that its production volume
affects the market price. He described equilibrium as a situation where each company
chooses the output which would maximize the profit but taking into account the production
declared by other companies, showing that such a balance leads to a price above the
marginal productivity. [1]
          In 1833 J. Bertrand studied the operation of oligopolistic markets where companies
whose returns are constant producing the same product establishing the selling price. The
result stated by Bertrand is known as the Bertrand paradox: if in case of equilibrium
situation each company chooses the price that would maximize its profit taking into account
the prices given by the other companies then the equilibrium price is equal to the marginal
cost.
          In 1934 Stackelberg shows that certain companies may have a leading role and are
able to impose the price to the other companies. The leading company, as Barometer
Company, knows best the market situation and has the means necessary in order to control
the opponents. It is not necessarily the powerful one but well informed and organized.
      After having passed the maturation period, marked by the works of J.F. Nash, R.D.
Luce and H. Raiffa, L. Shapley, the game theory became in the late '80s a powerful
instrument for analyzing strategic interaction situations, presented in the work of J.W.
Friedmann D.M. Kreps, D. and J. Fundenberg and J. Tirole, A. Mass-Colella and P. Cahuc
[2] [3]. Although game theory is rather new, the economic theory reveals other studies that
explained this issue in an isolated manner.
      In conclusion, starting with the early twentieth century we have identified three stages
of evolution in the game theory. This period began in the '20s and ended with World War II.
In this period strategic games were developed and their extensions, military tactic games,
particularly those with zero-sum. The focus is put on strategic researches which serve the
purpose of selecting the possible solutions for these games.
      Another period is the one starting with the work of John von Neumann and Oskar
Morgenstern, "Theory of Games and Economic Behaviour" (1944) and ending with late
'70s. The concern is determined by cooperative games theory focused on coalitions which
can occur between rational individuals in order to maximize their earnings.
          Nowadays, the central place goes to the non-cooperative games with Nash
equilibrium considered to be a privileged solution as well as to the dynamic games.
Knowledge of analytical instruments of the game theory and its application scope is
essential today; it constitutes a real matrix of contemporary economic theory.
2. IMPERFECT COMPETITION AND GAMES THEORY

          In the neoclassical theory of consumer and firm behavior, consumers have perfect
information about important features of them commodities they buy, such as their quality
and durability. Firms have perfect information about the productivity of the inputs they
demand. A situation in which different agents possess different information is said to be one
of asymmetric information. As we shall see, the strategic opportunities that arise in the
presence of asymmetric information typically lead to inefficient market outcomes, a form of
market failure Is important the effect of asymmetric information on the efficiency properties
of market outcomes. Many real-life situations involve substantial doses of incomplete
information about the opponents’ payoffs.
          Games theory is the systematic study of how rational agents behave in strategic
situations, or in game, where each agent must first know the decision of the other before
knowing which decision is best for her. The solution concepts include Nash equilibrium and
strategic decision making. For example the Bertrand models of duopoly capture strategic
decision making on the part of the two firms. Each firm understands well its optical action
depends on the action taken by other firm.
          In general, when it is possible to make someone better off and no one worse off, we
say that a Pareto improvement can be made. If there is no way at all to make a Pareto
improvement then we say that situation Pareto efficient. That is, a situation a Pareto
efficient if there is no way to make someone better off without making someone else worse
off.
          The idea of Pareto efficiency is pervasive in economics and it is often used as one
means to evaluate the performance of an economic system. The basic idea is that if an
economic system is to be considered as functioning well, and then given the distribution
resources it determines, it should not be possible to redistribute them in a way that results in
a Pareto improvement. Which, if any, of the three types of market competition- perfect
competition, monopoly or oligopoly- function well in the sense that they yield Pareto-
efficient outcome?
          Note that difference between the three forms of competition is simply the prices
and quantities they determine. For example, were a perfectly competitive industry taken
over by a monopolist, the price would rise from the perfectly competitive equilibrium price
to the monopolist’s profit-maximizing price ant the quantity of the good produced and
consumed would fall. Our conclusion is that the only price-quantity pair yielding a Pareto-
efficient outcome it’s the perfectly competitive one. In particular, neither the monopoly
outcome nor the oligopoly outcome is Pareto efficient [4].
           Note well that we cannot conclude from this analysis that forcing a monopoly to
behave differently than it would choose to must necessarily result in a Pareto improvement.
It may well lower the price and increase the quantity supplied, but unless the consumers
who are made better off by this change compensate the monopolist who is made worse off,
this move will not be Pareto improving.
          In the games theory the information is incomplete when some players don’t know
the earnings associated with distinctive strategic combinations. Incomplete information
creates strategic problems when some players possess some private information which is
inaccessible to other players. Therefore, the games theory studies this sort of situation in
which the information is not only incomplete, but also asymmetric.
          Pure monopoly, the last competitive market structure imaginable, is at the opposite
extreme. In pure monopoly, there is a single seller of a product for which there are no close
substitutes in consumption, and entry into the market is completely blocked by
technological, financial, or legal impediments [3].
          The monopolist takes the market demand function as given and chooses price and
quantity to maximize profit. Because the highest price the monopolist can charge for any
given quantity (q), is inverse demand p(q), the firm’s choice can be reduced tot that of
choosing q alone. The firm would then set price equal to p(q). As a function of q, profit is
the difference between revenue, r(q)= p(q)q, and cost, c(q). That is Π (q)= r(q)- c(q).
          When market demand is less than infinitely elastic, will be finite and the
monopolist’s price will exceed marginal cost in equilibrium. Moreover, price will exceed
marginal cost by a greater amount the more market demand is inelastic, other things being
equal. As we’ve remarked, pure competition and pure monopoly are opposing extreme
forms of market structure. Nonetheless, they share one important feature: Neither the pure
competitor nor the pure monopolist needs to pay any attention to the actions of other firms
in formulating its own profit-maximizing plans. The perfect competitor individually cannot
affect market price, or therefore the actions of other competitor, and so only concerns itself
with the effects of its own actions on its own profits. The pure monopolist completely
controls market price and output, and need not even be concerned about the possibility of
entry because entry is effectively blocked.
          Many markets display a blend of monopoly and competition simultaneously. Firms
become more interdependent the smaller the number of firms in the industry, the easier
entry, and the closer the substitute goods available to consumers. When forms perceive their
interdependence, they have an incentive to take account of their rival’s actions and to
formulate their own plan strategically.
          When firms are behaving strategically, one of the first things we need to do is ask
ourselves how we should characterize equilibrium in situations like this. On the face of it,
one might be tempted to reason as follows: Because firms are aware of their
interdependence, and because the actions of one firm may reduce the profits of others.
Putting the legality of such collusion aside, there is something tempting in the idea of a
collusive equilibrium such as this. However there is also a problem.
          In the games theory the information is incomplete when some players don’t know
the earnings associated with distinctive strategic combinations. Incomplete information
creates strategic problems when some players possess some private information which is
inaccessible to other players. Therefore, the games theory studies this sort of situation in
which the information is not only incomplete, but also asymmetric.
          For example, considering the static games with incomplete information, there is at
least one participant which is not sure about the earnings function related to the other
participants. At the same time, this game type proves that there can be private information at
the „i” player level. This kind of information can refer to his earning and/or the earnings of
the other playing participants.
        The patterning of different market structures can be realized with the help of
sequential games in which the decision of one player can stress upon a particular sort of
information and, thus, can modify the decisions of the other players who perform choices
subsequent to the player’s one. The Bayesian equilibrium can specify the rationality
meaning of different behaviors within strategic situations with incomplete information.
        The dynamic games with incomplete information in steps partially resemble the
dynamic games with complete, but imperfect information characterized by players
performing simultaneously, in different steps, but considering, for example, a game with
two economic actors, one player has private information while the opponent doesn’t have
access to it. Considering the following game whose matrix can be defined as follows (fig.
1):
                                  Fig. 1 - The game matrix
                                                             Player 2
                                                        s21            s22
                        Player 1         s11           (3,2)          (0,0)
                                         s12           (0,3)          (0,2)
                                         s13           (2,4)          (2,4)

           This particular game, fig.1, has two pure pairs of strategies which create Nash
types of equilibrium - (s11,s21) and (s13,s22), both of them being perfect sub-games. The pair
(s13,s22) represents a perfect sub-game because player 2 doesn’t know the actions of player 1
when choosing between s21 and s22. In mixed strategies cases, when player 1 plays s11
strategy and player 2 plays s21 strategy, with the possibility of minimum 2/3, the pairs
(s11,s21) and (s13,s22) remain in Nash equilibrium types [5] .
        Dynamic games with incomplete information have numerous economic applications.
For example, we can consider the oligopoly game type with a „leader firm”, in which only
this firm possesses private information, while the „satellite firm” will always notice the
decisions of the leader firm on the market.
         Studying the market car ,,lemons’’(the market in which the seller has private
information about the quality of goods supplied, while the buyer has not) Akerlof (1970)
demonstrated that, in such a situation, the buyers have to make an expectation on the quality
of the car and that, in equilibrium, only bad quality cars are sold. Rothschild and Stiglitz
(1976) applied this approach to insurance markets and the key common conclusion of these
studies is that, under certain assumptions, a bad allocation of information could lead markets
to failure[4 ].
        We can have two different types of asymmetric information between two economic
agents. The first is the so called ,,hidden action’’ situation. One person, called the,,
principal’’ cannot control all the actions that another person, called ,,agent’’ has to make to
achieve the goals contracted with the principal. The utility of the principal depends on the
results achieved by the agent, who has, however, an informative advantage, in the sense that
his actions are not fully controllable by the principal.
          This situation is described in economic literature as the ,, moral hazard’’ problem. In
equilibrium to make sure that the agent will act as the principal wants, the latter must offer
incentive to the agent, with a loss of social surplus due to the incentive scheme necessary to
neutralize information asymmetry.
           The games theory developed by John von Neumann and Oskar Morgenstern
concerning situations generated by a bargaining process with its own rules, where each
agent maximizes his utility function and the information set given. John Nash argued that
the notion of an equilibrium point is the key ingredient in our theory. This notion yields a
generalisation of the concept of the solution of a two-person zero-sum game.
              An equilibrium point is a profile of strategies in which each agent’s strategy is
the best response to the strategy of the others. In this situation, the role of the information set
available to various players is crucial. In equilibrium only a strategic profile incentive
compatible with the information set would dominate.
           Let us consider that there are „n” competitive firms, each of them maximizing
profits by production adjusting. Therefore, if the pure equilibrium of strategy exists, it can
be determined by solving the equation (1.1):
                      Pqi  Yiqi 
                                     0                         (1.1)
                          qi
                             n 
in which              P     qi  for qi0                   (1.2)
                             i 1 
         Before studying the behavior within the Cournot equilibrium type in which the
number of competitors is increasing, we assume that firms are of approximately equal size,
thus with the same variable average costs. Let us compare the situations when the market is
controlled by some big firms of the same size, with non-cooperative behavior towards
smaller competitive firms.
         The pattern for this comparison needs to reflect that each of the „n” competitors
gains the share„n” from the market.We will consider the request function in a game with „n”
players as follows (equation 1.3):
                           n
                                        n
                                              qi 
                     n  qi   1                         (1.3)
                         i 1       i 1   n

in which: 1(q1)- represents the request function on a monopolist market where the firm
produces only one product. The number of units from the product purchased at a certain
price on a market with „n” persons will be „n” multiplied with the purchased quantity on a
monopolist market, if we apply the conditions of the previous request. Let us assume that
the following conditions are met: 1- is continue, any partial derivate of rank 1 exists and is
continue, having a finite limit.
         These conditions prove the decrease of the request for an increase of any price
level and also that the request is null for a finite value of the price.
The analytical equations of a specific equilibrium of pure strategy can be represented as
follows:
            Pqi  Yiqi 
                           0                                    (1.4)
                qi
                 n 
 in which P  n  qi  for qi0 , which can be represented as follows:
                 i 1 

                     dYi          Pi
           Yi  qi        P  qi                               (1.5)
                     dqi          qi

                                     dYi         d qiYi 
Therefore, we notice that: yi  qi        0unde            P consist of the equilibrium
                                     dqi           dqi
point equations.
         Consequently, if one firm’s price is above marginal cost, both prices must be above
cost and each firm must be strictly undercutting the other, which is impossible. In the
Bertrand model, price is driven to marginal cost by competition among just two firms.
         In the neoclassical theory of consumer and firm behavior, consumers have perfect
information about important features of them commodities they buy, such as their quality
and durability. Firms have perfect information about the productivity of the inputs they
demand. A situation in which different agents possess different information is said to be one
of asymmetric information. As we shall see, the strategic opportunities that arise in the
presence of asymmetric information typically lead to inefficient market outcomes, a form of
market failure Is important the effect of asymmetric information on the efficiency properties
of market outcomes. Many real-life situations involve substantial doses of incomplete
information about the opponents’ payoffs.


3. CONCLUSION

          Games theory is the systematic study of how rational agents behave in strategic
situations, or in game, where each agent must first know the decision of the other before
knowing which decision is best for her. The solution concepts include Nash equilibrium and
strategic decision making. The Bertrand models of duopoly capture strategic decision
making on the part of the two firms. Each firm understands well its optical action depends
on the action taken by other firm.
          In general, when it is possible to make someone better off and no one worse off, we
say that a Pareto improvement can be made. If there is no way at all to make a Pareto
improvement then we say that situation Pareto efficient. That is, a situation a Pareto
efficient if there is no way to make someone better off without making someone else worse
off.
          The idea of Pareto efficiency is pervasive in economics and it is often used as one
means to evaluate the performance of an economic system. The basic idea is that if an
economic system is to be considered as functioning well, and then given the distribution
resources it determines, it should not be possible to redistribute them in a way that results in
a Pareto improvement. Which, if any, of the three types of market competition- perfect
competition, monopoly or oligopoly- function well in the sense that they yield Pareto-
efficient outcome?
          Note that difference between the three forms of competition is simply the prices
and quantities they determine. For example, were a perfectly competitive industry taken
over by a monopolist, the price would rise from the perfectly competitive equilibrium price
to the monopolist’s profit-maximizing price ant the quantity of the good produced and
consumed would fall.
          Our conclusion is that the only price-quantity pair yielding a Pareto-efficient
outcome it’s the perfectly competitive one. In particular, neither the monopoly outcome nor
the oligopoly outcome is Pareto efficient.
           Note well that we cannot conclude from this analysis that forcing a monopoly to
behave differently than it would choose to must necessarily result in a Pareto improvement.
It may well lower the price and increase the quantity supplied, but unless the consumers
who are made better off by this change compensate the monopolist who is made worse off,
this move will not be Pareto improving.
          The games theory can provide explanations of the existing phenomena in real
economy. By applying this theory as a reference in representing economic agents’
behaviors, a broad investigation field has been revealed. Economic agents should no more
be concerned with studying of perfectly competitive markets functionality, but instead with
analyzing the modalities in which they can coordinate decisions in static or dynamic
configurations, within a competitive environment influenced by risk and uncertainty.
                                 4. REFERENCES

[1] Cahuc, P. (2008), La nouvelle microéconomie, La Découverte (Ed.), Paris
[2] Geoffrey A., Reny Philip J. (2000), Advanced Microeconomic Theory, second edition,
Addison Wesley Longman, London
[3] Sîrghi Nicoleta ( 2005), Jocurile in microeconomie, Mirton (Ed.), Timisoara
[4] Stiglitz, J. E., Walsh C. E.,( 2005), Economie, Editura Economică, Bucureşti
[5] *** Revue Cahiers français, 2008, Decouverte de la microéconomie,La Documentation
Française, p. 63-65.

				
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