8. (И.К.)Models of oligopoly and game theory applications

An oligopoly is a market form in which a market or industry is dominated by a small number of sellers (oligopolists).[citation needed] Because there are few sellers, each oligopolist is likely to be aware of the actions of the others. The decisions of one firm influence, and are influenced by, the decisions of other firms. Strategic planning by oligopolists needs to take into account the likely responses of the other market participants.

Characteristics of Oligopoly:

1 A few large producers. Usually three, four, or five firms occupy the market, e.g. "Big Three" in the U.S. aluminum industry and companies such as Nokia or Motorola in the cell phone industry, as well as companies in the video game console market. The four largest firms in the market occupy greater than 40% of the market.

2 Homogenous OR differentiated products. Some oligopolistic industries offer homogenous, or standardized, products, e.g. those of steel, zinc, copper, lead, industrial alcohol. Other industries, e.g. those of automobiles, tires, electronics, breakfast cereal, offer different products and place an emphasis on nonprice competition, such as advertising.

3 Price maker, but still mutually interdependent. The small number of firms let oligopolies to set prices and output levels, to some extent. However, because there are rival firms, oligopolies must take note at how they react to its change in price, output, product or advertising.

4 Strategic Behavior: self-interested behavior that takes into account the reactions of others.

5 Mutual interdependence: profit doesn't depend entirely on its own price and strategies.

6 Relatively high entry barriers. Most important barriers are economies of scale, patents, brand loyalty, access to expensive and complex technology, and strategic actions by incumbent firms designed to discourage or destroy entering (new) firms. Additional sources of barriers to entry often result from government regulation favoring existing firms making it difficult for new firms to enter the market.

7 Profit maximisation conditions: An oligopoly maximises profits by producing where marginal revenue equals marginal costs. MR=MC.

Modeling. There is no single model describing the operation of an oligopolistic market. The variety and complexity of the models is due to the fact that you can have two to 102 firms competing on the basis of price, quantity, technological innovations, marketing, advertising and reputation. Fortunately, there are a series of simplified models that attempt to describe market behavior under certain circumstances. Some of the better-known models are the dominant firm model, the Cournot-Nash model, the Bertrand model and the kinked demand model

Dominant firm model

In some markets there is a single firm that controls a dominant share of the market and a group of smaller firms. The dominant firm sets prices which are simply taken by the smaller firms in determining their profit maximizing levels of production. This type of market is practically a monopoly and an attached perfectly competitive market in which price is set by the dominant firm rather than the market. The demand curve for the dominant firm is determined by subtracting the supply curves of all the small firms from the industry demand curve.^[7] After estimating its net demand curve (market demand less the supply curve of the small firms) the dominant firm maximizes profits by following the normal p-max rule of producing where marginal revenue equals marginal costs. The small firms maximize profits by acting as PC firms–equating price to marginal costs.Cournot-Nash model

Main article: Cournot competition

The Cournot-Nash model is the simplest oligopoly model. The models assumes that there are two “equally positioned firms”; the firms compete on the basis of quantity rather than price and each firm makes an “output decision assuming that the other firm’s behavior is fixed.”^[8] The market demand curve is assumed to be linear and marginal costs are constant. To find the Cournot-Nash equilibrium one determines how each firm reacts to a change in the output of the other firm. The path to equilibrium is a series of actions and reactions. The pattern continues until a point is reached where neither firm desires “to change what it is doing, given how it believes the other firm will react to any change.”^[9] The equilibrium is the intersection of the two firm’s reaction functions. The reaction function shows how one firm reacts to the quantity choice of the other firm.^[10] For example, assume that the firm 1’s demand function is P = (60 - Q₂) - Q₁ where Q₂ is the quantity produced by the other firm and Q₁ is the amount produced by firm 1.^[11] Assume that marginal cost is 12. Firm 1 wants to know its maximizing quantity and price. Firm 1 begins the process by following the profit maximization rule of equating marginal revenue to marginal costs. Firm 1’s total revenue function is PQ = Q₁(60 - Q₂ - Q₁) = 60Q₁- Q₁Q₂ - Q₁². The marginal revenue function is MR = 60 - Q₂ - 2Q.^[12]

MR = MC

60 - Q₂ - 2Q = 12

2Q = 48 - Q₂

Q₁ = 24 - 0.5Q₂ [1.1]

Q₂ = 24 - 0.5Q₁ [1.2]

Equation 1.1 is the reaction function for firm 1. Equation 1.2 is the reaction function for firm 2. To determine the Cournot-Nash equilibrium you can solve the equations simultaneously. The equilibrium quantities can also be determined graphically. The equilibrium solution would be at the intersection of the two reaction functions. Note that if you graph the functions the axes represent quantities.[13] The reaction functions are not necessarily symmetric.[14] The firms may face differing cost functions in which case the reaction functions would not be identical nor would the equilibrium quantities.