Showing posts with label Oligopoly. Show all posts
Showing posts with label Oligopoly. Show all posts

Meaning of The Game Theory and Importance of Game Theory

The term ‘game’ represents a conflict between two or more parties. A game is a decision situation with multiple decision makers where each person’s welfare depends on his/her own as well as other individuals’ actions. That is, a game is a decision situation with strategic interactions among all decision makers.

Game theory is a theory of individual rational decisions taken under conditions of less than full information concerning the outcomes of those decisions. This theory examines the interaction of individual decisions given certain assumptions concerning decisions made under risk, the general environment, and the cooperative or non-cooperative behavior of other individuals.

In the words of Richard G. Lipsey and K. Alec Chrystal, “Game theory is an approach to analyzing, rational decision-making behavior in interactive or conflict situation.”

According to N. Gregory Mankiw, “Game theory is the study of how people behave in strategic situations." By ‘strategic’, we mean a situation in which each person, when deciding what actions to take, must consider how others might respond to that action. Game theory is a mathematical technique used to show for example, how oligopoly firms play their game of business.

Importance of Game Theory


Game theory is an analysis that illustrates how choices between two plays affect the outcome of a “game”. Game theory which sounds playful/laughing in its terminology is filled with significance. It has been used by economists to study the interaction of oligopolistic markets, union-management bargaining disputes, countries’ trade policies, international environmental agreements, reputations, conflicts such as games and war and a large number of other situations. Game theory offers insights for politics, warfare, and everyday life as well.
  1. Game theory is commonly used in economics to illustrate interdependent decision-making among oligopoly firms. It illustrates that one firm makes a decision based on the decision expected from the other firm. One key conclusion from the game theory analysis is that firms often make decisions that are “second best” or the “lesser of two evils”. The classic example of such a decision is the prisoners’ dilemma, in which two prisoners both confess to a crime to avoid harsher punishment when not confessing would avoid any punishments.
  2. Thus, game theory has proved to be useful in analyzing suspects of economic behavior such as natural resource depletion and public goods. The theory of cooperative games which allows collaboration between individuals has been used to analyze cartel formation and industrial and labor market collusion.
  3. Game theory is a body of knowledge which is concerned with the study of decision-making in situations where two or more rational opponents are involved under conditions of competition and conflicting interests. It deals with human processes in which an individual decision making unit who can be an individual, a group, a formal or informal organization, or a society, is not in complete control of the other decision making units, the opponents, and is addressed to problems involving conflict, co-operation or both at various levels.
  4. The main objective in the theory of games is to determine the rules of rational behavior in the game situations, in which the outcomes are dependent on the actions of the interdependent players. A game refers to a situation in which two or more players are competing it.
  5. Game theory is quite useful for understanding the behavior of oligopolies. When game theory is applied to oligopoly, the players are firms. Their game is played in the markets, their strategies are their price/output decisions, and the payoffs are their profits. Because the number of firms in an oligopolistic market is small, each firm must act strategically. Each firm knows that its profit depends not only on how much it produces but also on how much the other firms produce. In making its production decision, each firm in an oligopoly should consider how its decision might affect the production decisions of all the other firms.
In summary, a game theory framework can often help us understand the strategic choices available but it does not always help to predict which of many possible outcomes may occur.

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The Cartel or Collusion Model

The cartel is an explicit agreement between the oligopoly firms. Cartel agreements represent the most complete form of collusion among the oligopolists. Under cartel agreements, firms jointly establish a cartel organization to make price and output decision, to establish production quotas for each firm and to supervise the market activities of the firm in the industry, cartel type collusions are formed with a view;

i) Eliminating uncertainty surrounding the market and 
ii) Restraining competitions and thereby ensuring monopoly gains to the cartel group.


For this, the board of control first calculates the MC and MR for the industry; MC for industry in the summation of MCs of individual firms. On the basis of industry’s MR and MC, the total output for the industry determined. The determination of industry output is shown in figure C and the share of each firm in figures A and B. For the sake of convenience, let us suppose there are only two firms in the industry, firm I and II. Their cost curves are given in figure C. The industry output is determined at OQ and price PQ on the pattern of monopoly firm.

The share of each firm in industry, quantity is determined at the level of their own output which equates their individual MC with the industry’s MC. The industry’s MC, CQ is determined by the intersection of industry’s MC and MR at point C. The market share of each firm can be obtained by drawing a line from point C and parallel to X-axis through MC to MC1 to the Y-axis. The points of intersection C1 and C2 determine the level of output for firm I and II respectively. Thus, the share of each of the two firms I and II, is determined at OQ1 and OQ2 where OQ1 + OQ2 = OQ. The total profit can be completed as (PQ – Firm’s AC) and firms output which is maximum. The total profit may be different, but there will be no motivation to change in price quantity combinations, since their individual profit is maximum.

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Concept of Oligopoly and Kinked Demand Curve Model

Price rigidity under oligopoly in terms of kinked demand curve
Price rigidity in the oligopoly market is best explained by the kinked demand curve.

The oligopoly is a reduced form of monopolistic competition. The term oligopoly has a Greek base and means few sellers, oligopoly as such, refers to markets with small number of large firms, each selling either differentiated or homogeneous product.

A few sellers imply a number so small or a few market share of each firm in so large that it can influence the market price. It also implies that each seller commands a sizeable proportion of the total market supply. The products traded by the oligopolists may be differentiated or homogeneous. Accordingly, the oligopoly market may be a heterogeneous oligopoly or a homogeneous (or pure) oligopoly. It seems the following features:
  • Sellers are few in number.
  • Any of them is of such a size that can increase and decrease in his output will appreciably affect the market price. In fact, the size of each seller’s output in relation to the total supply is the test.
  • Each seller knows his competitors individually in each market.
Each oligopolist realizes that any change in his price and advertising policy may lead rivals to change their policies. Hence, an individual firm must consider the possible reaction of the other firms to its own policies. The smaller the number of firms, the more interdependent are their policies. The reactions of rivals will generally be immediate and strong, and tendencies to close collaboration in price determination are appeared.

It is the fewness of sellers that introduces interactions into the price and output decision problem under oligopoly a special form of oligopoly in duopoly, under which only two firms produce a particular product.

Kinked Demand Curve Model


The kinked demand curve model developed by Paul M. Sweezy, has features common to most of oligopoly pricing models. The kinked demand curve analysis does not deal with price and output determination. It seeks to establish that once a price-quantity combination is determined, an oligopoly firm will not find it profitable to change its price in response to a moderate change in cost of production. An oligopoly form believes that if it reduces the price of its product, rival firms would follow and neutralize the expected gain from price reduction. But, if it raises its price, rival firms would either maintain their prices or may even cut their price down. In either case, the price rising firm stands to lose, at least a part of its share in the market. This behavioral assumption is made by all the firms in respect of others. The oligopoly firms would therefore, find it more desirable to maintain their price and output at the existing level.

There are three possible ways in which rival firms may react:
  1. The rival firms follow the price changes, both cut and hike; 
  2. The rival firms do not follow the price changes;
  3. Rival firms do not react to price-hikes but they do follow the price-cuts.

Kinked-demand curve is a demand curve with two distinct segments with different elasticities that join to form a kink. The primary use of the kinked-demand curve is to explain price rigidity in oligopoly. The two segments are:
(i) a relatively more elastic segment for price increase and
(ii) a relatively less elastic segment for price decreases.

The relative elasticities of these two segments are directly based on the interdependent decision-making of oligopolistic firms. Interdependence is the guiding behavioral principle of oligopoly firms in which the decision by one firm is both affected by the decisions of other firms and in turn affects the decisions of other firms. Such interdependence is characteristic of oligopoly firms that practice competition among the few. Interdependence is indicated by the kinked-demand curve, game theory, collusion, and mergers. Merger is the consolidation of two separately-owned businesses under single ownership. This can be accomplished through a mutual, “friendly” agreement by both parties, or through a “Hostile takeover,” in which one business gets ownership without cooperation from the other. Mergers fall into one of three classes –
(i) horizontal – two competing firms in the same industry that sell the same products,
(ii) vertical – two firms in different stages of the production of one good, such that the output of one business is the input of the other, and
(iii) conglomerate – two firms that are in totally, completely separated industries.

According to the kinked demand curve model, firm determines the price and output by intersection of MC and MR. But intersecting point lies on the discontinuous segment of MR. In this model, the demand curve faced by oligopolists has kink at the prevailing price. It means, the upper section of the kinked demand curve has higher price elasticity than lower part. Because, each oligopolist believes that if he reduces his price below the prevailing level, his competitors will follow him, and will accordingly lower their prices. So that an oligopolist firm which lowers the price could not increase its share of the market. Whereas if he raises the price above the prevailing level, his competitors will not follow him and they do not increase their price. So, an oligopolist will lose a considerable part of his customers. Because of this, an oligopolist tends to keep prices constant even if the cost and demand conditions are changed. This model is illustrated in figure.


In the figure, dED is the demand curve faced by an oligopolistic firm and has a kink at point E which represents the prevailing market price. Above this point, demand curve dE is more elastic and below this point, it is less elastic. dABMR is the marginal revenue curve of the firm. MR has two segments; the upper segment dA corresponds to the upper part of the demand curve dE. The lower segment BMR corresponds to lower part of kinked demand curve ED. The kink at point E on the demand curve results in discontinuity ‘AB’ in the MR curve. Oligopolist firm can reach equilibrium position and determine the selling price, and quantity and maximize the profit by equating MC with MR. In the given figure, SMC cuts the discontinued segment of MR at point ‘C’ and the firm determines price QE and selling quantity OQ. This QE level of price will not be changed by firm. If SMC curve rises to SMC1 because of increasing costs and SMC curve goes down to SMC2 because of decreasing cost, this will not affect the pricing decision of the oligopolist. These two curves SMC1 and SMC2 allow the firm to fix the price QE and quantity OQ.

We may conclude that an oligopolist faced with a kinked demand curve will be extremely unwilling to change his price. For a fall in his price will cause no large increase in his sales whereas a price increases will cause a substantial decline in his sales. Thus, neither a price increase nor a price reduction will be an attractive proposition for the oligopolist. During inflationary periods, however, oligopoly firms often follow one another’s price increase, to this extent, the kinked demand curve analysis can be said not to hold true.

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Modern Oligopolistic firms typically seek to maximize their sales subject to minimum profit constraints | Boumol's Theory of Sales Maximization

Modern Oligopolistic firms typically seek to maximize their sales subject to minimum profit constraints.

Boumol’s theory of sales maximization is an alternative theory of firm’s behavior. The basic premise of this theory is that sales maximization, rather than profit maximization, is the plausible goal of the firm. As pointed by him, there is no reason to believe that all firms seek to maximize their profits.

Business firms pursue a number of incompatible objectives and it is not easy to single out one as the most common objective pursued by the firms. His observation shows that more managers seek to maximize sales revenue rather than profits. He argues that in modern business management is separated from ownership, and managers enjoy the discretion to pursue goals other than profit maximization. According to Boumol, business managers pursue the goal of sales maximization for the following reasons:
  1. Financial institutions consider sales as an index of performance of the firm and willing to finance to the firm with growing sales.
  2. Profit figures are available only annually, sales figures can be obtained easily and more frequently to assess the performance of the management. Maximization of sales is more satisfying for the managers than the maximization of profits which go to the pockets of the shareholders.
  3. Salaries and slack earnings of the top managers linked more closely to sales than to profit.
  4. The routine personal problems are more easily handled with growing sales. Higher payments may be offered to employees. Sales figure indicate better performance. Profits are generally known after a year.
  5. If profit maximization is the goal and it rises in one period to an unusually high level, this becomes the standard profit target for the shareholders which managers find very difficult to maintain in the long-run.
  6. Sales growing more than proportionately to market expansion indicate growing market share and a greater competitive strength and bargaining power of a firm in a collective oligopoly.

Under sales maximizing objective, output is greater and price is lower under the objective of profit maximization. Hence, Boumol has described two types of equilibrium under sales maximization objective which are;
  1. Without profit constraint to sales maximization, & 
  2. There is profit constraint to sales maximization

In the figure, total profit curve (TP) measures the vertical distance between the total revenue and that cost at various levels of output. At first, total profit rises and after a profit falls downwards.

If the firm is a profit maximizer, it would produce the level of output OA. However, in Boumol’s model, the firm is sales maximizer, but it must also earn a minimum level of profit. The acceptable level of profit is OM. The firm will produce the level of output OB which maximizes its sales revenue. The firm earns profit BE, which is less than the maximum attainable profit AH. At this point, output OB total revenue is BR1. The figure shows that sales or total revenue maximizing output OB is larger than profit maximizing output OA.

The firm aims at sales maximization subject to a profit constraint as Boumol contended. If OM is the minimum total profit, which firm wants, then ML is the minimum profit line. This minimum profit line ML cuts TP curve at point E. There, the firm produces and sells OB output.

At output OB, the firm will have total revenue equal to BR1, which has less maximum possible total revenue of CR2. It should be noted that the firm can earn minimum profit ON even by producing ON output. But total revenue at output OH is much less than at output OB. In summary, two types of equilibrium appear to be possible. One in which the constraint provides no effective barrier to sales maximization. The firm is assumed to be able to pursue an independent price policy that is to set its price so as to achieve its goal of sales maximization (given the profit constraint) without being concerned about the reactions of competitors.

A profit maximizer produces the output OB defined by the equilibrium
 

Given that the marginal cost is always positive, it is obvious that at the level OB, the marginal revenue is also positive. That is TR is still increasing at OB, since its slope is still positive. In other words, the maximum of TR curve occurs to the right of the level of output at which profit is maximized.

The sales maximize sells at a price lower than profit maximize. The price at any level of output is the slope of the line through the origin to the relevant point of the total revenue curve (corresponding to the particular level of output).

Criticisms of Boumol's Theory of Sales Maximization

This model is not also free from certain weaknesses as below:
  1. As pointed by Boumol, sales maximize will in general produce and advertise more than a profit maximize, which is invalid. Hawkins comments that a sales-maximizer may choose a higher, lower or identical output and a higher, lower or advertising budget. It depends on the responsiveness of demand to advertising rather than price cuts.
  2. In case of multi-products, Baumol has argued that revenue and profit maximization yield the same results. But Williamson has shown that sales maximization yields different results from profit maximization.
  3. This model fails to explain observed market situations in which price are kept for considerable time periods in the range of inelastic demand.
  4. This model ignores the interdependence of the price of oligopolistic firms.
  5. It ignores not only actual competition, but also the threat of potential competition from rival oligopolistic firms.
  6. This model does not show how equilibrium in an industry in which all firms are sales maximizers, will be attained. Baumol does not establish the relationship between the firms and industry.

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