ECONOMICS BY MUJTABA: Game Theory of Oligopoly

Game Theory of Oligopoly

Game theory is mainly concerned with predicting the outcome of games of strategy in which the participants (for example two or more businesses competing in a market) have incomplete information about the others’ intentions.

Game theory explores the reactions of one player to change in strategy by another player. It is therefore necessary in any theory of oligopoly, to understand the consequences of those reactions. One method / tool to analyze oligopolistic behavior is Game Theory.

1) Dominant Strategies: A dominant strategies is where a single strategy is best for players irrespective of what strategy the other player adopt.

Consider this table

DOMINANT STRATEGIES
Firm ‘A’s Strategy	A Profit in Millions £	B Profit in Millions £	Firm ‘B’s Strategy
Price Raise	+£ 5	+£ 5	Price Raise
Price Raise	+£ 3	+£ 3	Leave Price Unchanged
Leave Price Unchanged	+£ 2	+£ 1	Price Raise
Leave Price Unchanged	£ 0	£ 0	Leave Price Unchanged

ﻡ If a firm ‘B’ choose to raise the price firm ‘A’ will earn extra £ 5 if it raises its price too better than £ 2 extra if it choose to keep the price unchanged.

ﻡ If firm ‘B’ choose to keep its price same, firm ‘A’ can make extra £ 3 m profit by raising its price. If both firms keep the price same then they will not be getting any extra profits.

ﻡ Which strategy should firm ‘B’ choose?

2) Nash equilibrium: Neither player is able to improve their position given the choice of the other player.

Consider this table

Nash Equilibrium
Firm ‘A’s Strategy	A Profit in Millions £	B Profit in Millions £	Firm ‘B’s Strategy
Lower Price	+£ 5 m	+£ 2 m	Lower Price
Lower Price	-£ 1 m	-£ 1 m	Leave Price Unchanged
Leave Price Unchanged	-£ 2 m	-£ 1 m	Lower Price
Leave Price Unchanged	£ 0 m	£ 0 m	Leave Price Unchanged

Dominant strategy equilibria don’t occur that often. In most games the strategy of one firms depend on the strategy by other firm adopt.

ﻡ Assume that firm ‘B’ choose to lower its price, the best strategy for firm ‘A’ will be to lower its price too, as it will increase the profit by £5m. if it keeps its price same there will be a fall of £2 m. Therefore the best strategy for firm ‘A’ is to reduce price if firm ‘B’ reduce its price

ﻡ What is the best strategy for firm ‘B’ if firm ‘A’ chooses to lower its price?

Both firms lowering price is a Nash Equilibrium, named after a US mathematician John Nash. In Nash equilibrium, neither player is able to improve their position given the choice of the other player.

However in this example there may be more than one Nash Equilibrium. If both firm leave their price unchanged is a Nash Equilibrium.

If a firm is sticking to one single policy (Pure Strategy) then there will be no Nash Equilibrium.

Price Stability: In oligopoly firms maintain price stability over a pricing season, which may last for 6 months or one year.

If oligopolistic firm raise price it has the risk of losing the market share, if other competitor did not raise price. This move will reduce firm’s profit.

If oligopolistic firm lower its price it starts price war. However it may gain market share but the profit of the firm falls. As the profit will fall down the firm may not be able to compete in the market and hence again at a time it has to increase its price leading to more loss of market share than before.

Hence price change is the risky strategy.

A zero sum game which leads to price stability
Firm ‘A’s Strategy	A Profit in Millions £	B Profit in Millions £	Firm ‘B’s Strategy
Price Raise	+£ 10	-£ 10	Price Raise
Price Raise	-£ 2	+£ 2	Leave Price Unchanged
Leave Price Unchanged	+£ 1	-£ 1	Price Raise
Leave Price Unchanged	£ 0	£ 0	Leave Price Unchanged

This table shows a particular type of game “Zero Sum Game”. In this game the profits / gains of one player are matched by equal and opposite losses for other player. When gains and losses are added it equals Zero.

Q. Explain why and what strategy should firm A pursue?

Q. Explain why and what strategy should firm B pursue?

Non Price Competition: Price competition is absent in oligopoly. Price war can be damaging for firms in oligopoly. Firms in oligopoly may adapt different methods like advertisement.

For instance: If firm A launches an advertisement and has gained some extra market share due to advertisement, firm B will be provoked to make advertisement. If firm B makes more successful advertisement and gains more market share than firm A it will be like a back fire for firm A. This explains in oligopoly firms may not try to drive out other firms as it can be risky and they themselves can be victim of such move.

Branding: Ideally oligopolistic firms would like to turn themselves into monopolists with full control over the market. One way of doing it is Branding their product.

Strong brand is difficult to create and consumes more time; hence firms prefer to take over firm and their branded product at high cost too. For example: Jaguar Cars, Arcellor.

Collusion: Another way in which oligopolists can turn itself into a monopoly is by colluding with other firm. Forming Cartels was the practice carried out in British manufacturing industry before 1950s then this was made illegal.


Firm ‘A’s Strategy	A Profit in Millions £	B Profit in Millions £	Firm ‘B’s Strategy
Low Price	+£ 15	+£ 10	Low Price
Low Price	+£ 25	+£ 5	High Price
High Price	+£ 10	+£ 20	Low Price
High Price	+£ 20	+£ 25	High Price

In this table if firm ‘A’ will lower its price against high price strategy of firm ‘B’ as they will get maximum benefit but firm ‘B’ will not let it happen as its profit will be only £5m. however a high price strategy by firm A will be worse of when firm ‘B’ will lower its price as it will make the lowest possible profit of £10m. In fear of opponent firms strategy both the firm will stick to low price strategy. The best strategy for both firms will be to collude and come to a conclusion that both firms will raise price so as they will earn maximum profit.

Same situation can be analyzed by the example of what is often called the Prisoner’s Dilemma. Substitute profits for prison sentences and prices for pleading guilty or not guilty. If 2 prisoners kept apart in different cells plead not guilty, then they will be released through lack of evidence. However, if one prisoner pleads guilty, then he will get reduced sentence and the other will get a heavier sentence. If both plead guilty they will get heavy sentences. If they could get together (i.e. collude) they would choose to plead not guilty. But in isolation they cannot trust the other prisoner, so each chooses to plead guilty and they both suffer.

Cartels are usually unstable because it would normally be in the interest of one of the player to attempt to cheat on the agreement made. In the table if firm ‘A’ secretly lower its price directly or in the form of offers he can get £25m which is £5m extra.

The firm who can be cheated by other firms must be able to enforce the rules agreed by the cartel. For example OPEC, in 1980s and 1990s was beset by some countries cheating by some countries. Prices and output quota was given to each country in Cartel. But some countries secretly produced more and sold at lower price which increased their market and profits. But this step lowered the price of oil in world market. In 1986, Saudi Arabia which had tended to agree to production cuts in OPEC punished the cheating countries in OPEC suddenly increased production. Prices collapsed and all other countries were worse off. It subsequently cut down the production to raise oil prices, but it had shown what could happen to cheats if they refused to stick to policies laid down by Cartel.

Multi – firm, multi – strategy options

Till now we were discussing two firm two option situations. In reality there are likely to be more than two firms and more than two policy option. For example if there are two firms and 6 options the possible situation would be (6x6=36). If there are 3 firms and 6 options the possible situations available will be (6x6x6=216). Hence it is difficult to provide one unified model which would explain price and output decision in industry.