Oligopoly: Collusion and Game Theory

Collusion
It is an anti-competitive behaviour in an oligopoly in which firms aim to jointly maximise profit by collectively agreeing to restrict output or fix prices. If it is possible for the players to reach an agreement to collude it is called formal collusion. But it is illegal in many countries to engage in any form of anti-competitive agreement such as price-fixing or supply restriction. Collusion is bad for the consumers as the price fixed may be exorbitant; oligopolists may agree on a very low price in order to hide the profitability of the business, thereby discouraging other firms from entering the industry. It hurts the colluders who suffer from X-Inefficiency due to complacency and lack of competition. Government watchdog agencies will investigate and punish any firm found wanting, e.g. the Competition and Markets Authority (UK) and the Justice Department (USA). What can be seen most times is tacit collusion where there is no formal agreement among the dominant firms to collude.  They all tend to charge the same as the leading firm in the industry; this is not illegal as there is no written agreement among the firms.

Conditions necessary for collusion to work
Few firms
It is only successful if the number of firms in the industry is not large. Agreements can be easily reached and monitored only if there are few dominant firms like in an oligopoly. It will be difficult to bring too many firms to a table to reach any meaningful agreement. Besides, detecting cheating by the participants would become a herculean task if the number is too large.

Monitoring mechanism
Since the aim is to maximise profit by keeping price as high as possible there must be a mechanism for monitoring players and ensuring that cheating is not allowed. for example, the Organisation of Petroleum Exporting Countries (OPEC), a cartel of oil-producing countries, gives production quotas to members to restrict supply and maintain high crude oil prices. If some member countries exceed the quota in order to sell more, total supply will increase and the price will be driven down. Consequently, the benefits of the association will be lost as members get low prices for their crude oil sales. 

Inelastic demand
The product involved in the market should have an inelastic demand. A rise in the price of an inelastic product will lead to a smaller percentage decrease in quantity sold, thereby increasing the revenue of the seller. Collusion is not beneficial if the product has a fairly elastic demand as a rise in price will lead to a bigger fall in quantity leading to a reduction in revenue for the seller.

The demand must not be volatile
It is not only the supply that determines the price of a product. A fall in demand can reduce the price of the product and sellers have no control over this. For instance, weak demand for crude oil by the major importers of crude oil may spell doom for oil-exporting countries. Slow growth in China a few years ago reduced the demand for crude oil, forcing the global prices of crude oil to tumble. 

High barriers to entry
High barriers enable the firms to protect their market share and continue to enjoy the benefits of collusion. Low barriers to entry will encourage more firms to join the industry and increase market supply. Increased market supply will force down prices which is not beneficial to the firms that collude.  This is why OPEC sometimes cooperates with non-OPEC members to keep crude oil prices as high as possible. 

It must be legal
Collusion is illegal in most countries due to antitrust laws that seek to promote fair business practices and competition. Collusion takes different forms such as price-fixing, restricting supply, sharing the market and other anti-competitive practices.  Government agencies charged with the responsibility of implementing antitrust laws will fine the firms that are found culpable. But tacit collusion is legal. 

Game Theory
Game theory helps to analyse the independence among firms in an oligopolistic market.  A game involves participants (players) contending to get ahead of one another while adhering to some rules. They contest to obtain advantages  (payoffs) such as more profits. In choosing a plan of action (strategy), the players take cognisance of other competitors’ likely reactions. A firm contemplating, for instance, cutting its price has to anticipate the reactions of other firms. It has to envisage the likely consequence of others cutting their price in response or leaving their prices unchanged. 

A zero-sum game is one in which the gains of one player are equal to the losses of the other player. When the gains and losses of the players are totalled, zero is obtained. A non-zero game is one in which the gains of one player are not equal to the losses of the other player. In other words, a player’s gain does not come at the expense of the other player.

Game outcome-Dominant strategy equilibrium
A dominant strategy is the best line of action for a player regardless of its competitor’s option. Table 1 below shows the payoff matrix for Firm A and Firm B. The first number in each cell (green colour) is the profit for Firm A while the second number (red colour) is the payoff for Firm B if each decides to advertise or does not advertise. 

Table 1: Payoff table for Firm A and Firm B

In order to determine Firm A’s strategy, one has to ascertain its best choice if Firm B advertises or does not advertise. If B advertises, firm A will make $20 if it advertises or $10 if it does not advertise. It will pick the option to advertise since it produces a higher payoff of $20 (see Table 2 below). 

Table 2: Firm A’s strategy if Firm B advertises

If B does not advertise, firm A will make $25 if it advertises or $15 if it does not advertise. It will choose the option to advertise since it produces a higher payoff of $25 (Table 3 below). Therefore, the dominant strategy of A is to advertise as it will always get the higher profit whether B advertises or  does not advertise. 

Table 3: Firm A’s strategy if Firm B does not advertise

Firm B’s strategy is the better option if Firm  A advertises or does not advertise. If Firm A advertises, Firm B will make $15 if it advertises or $5 if it does not advertise. It will pick the option to advertise since it produces a higher payoff of $15. 

Table 4: Firm B’s strategy if Firm A advertises

If Firm A does not advertise, Firm B will make $25 if it advertises or $10 if it does not advertise. It will select the option to advertise since it produces a higher payoff of $25 (Table 5 below). Therefore, the dominant strategy of Firm B is to advertise as it will always get the higher profit whether A advertises or not.

Table 5: Firm B’s strategy if Firm A does not advertise

Game outcome-Nash Equilibrium

This occurs when a player has to choose his own strategy only after considering its competitor’s choice. A game may have no nash equilibrium or more than one nash equilibrium.  

Table 6: Payoff table for Firm A and Firm B

If Firm B advertises, Firm A will make $20 if it advertises or $10 if it does not advertise. It will choose  to advertise since it produces a higher payoff of $20 (Table 7 below). 

Table 7: Firm A’s strategy if Firm B advertises

If Firm B does not advertise, Firm A will make $25 if it advertises or $30 if it does not advertise. It will pick the option not to advertise since it produces a higher payoff of $30 (Table 8 below). Firm A has no dominant strategy. It will advise if B advertises; it will not advertise if B does not advertise. 

Table 8: Firm A’s strategy if Firm B does not advertise

If Firm A advertises, firm B will make $15 if it advertises or $5 if it does not advertise. Firm B will pick the option to advertise since it produces a higher profit of $15 (Table 9 below). 

Table 9: Firm B’s strategy if Firm A advertises

If Firm A does not advertise, Firm B will make $25 if it advertises or $10 if it does not advertise. Firm B will pick the option to advertise since it produces a higher payoff of $25 (Table 10 below). The dominant strategy for B is to advertise.

The Nash equilibirum is advertising strategy for both firms. This is where their strategies happen at the same time. It is shown by the asterisk in Table 10.  It is the best strategy or response for each given the strategy of the other player. Neither can be better off in terms of profit by choosing  a different option from the equilibrium.

Table 10: Firm B’s strategy if Firm A does not advertise