GAME THEORY IN OLIGOPOLIES

An Oligopoly is a type of market dominated by a few firms that produce homogenous products, which are mutually interdependent, and every decision taken by one firm, affects the other firms in the market in one way or another.

The behaviour of firms depends upon how firms respond to the actions or anticipated actions of rivals for a particular market over time and can follow two different routes – in some industries, there may be cut-throat competition between aggressive firms, while in others, there may be cooperation or collusion or formation of cartels.(fixing profit maximising prices)

Game theory is the formal study of conflict and cooperation. Where each player (firm) knows that the final outcomes of their decisions will depend on the decisions of the other players. (firms)

The ‘Prisoners Dilemma’ helps understanding Game theory.

In this example two individuals A and B have been arrested on suspicion of having committed a crime which carries a maximum prison sentence of 8 years.

A and B are being detained in separate parts of a prison and have no chance of communicating with each other.

If anyone confesses to the crime, they will receive a small sentence of two years and their partner will receive a prison sentence of 8 years and if both of them confess, both receive a sentence of five years. What are A and B supposed to do here? What is the best strategy for each in these circumstances?

The possible strategies for each are indicated in the two player pay-off matrix given.

‘A’ would reason as follows,

“It is best that I confess because in the best case scenario I will receive a small sentence of two years if B does not confess, and in the worst scenario I will receive a sentence of five years rather than 8 years if B also confesses.”

‘B’ will also follow the same path of reasoning and also conclude that the best strategy for him is to confess.

The final result is that both A and B will confess and receive a sentence of five years each as illustrated in quadrant D of the matrix.

Clearly, this is not the best outcome (pay-off) for A and B. The best outcome would be for them to co-operate or collude and both agree to not confess, which would give them a smaller sentence of two years, However, in the absence of any ability to communicate with one another this is unlikely, and even if they could communicate with one another they would each have to trust in the other's willingness to stick to the deal.

This application of Game theory helps us understand behaviour of oligopolistic markets.

Let’s take X and Y, two companies selling similar products to be the players.

The game takes place in the market and the pay-off is the expected final profit for each firm resulting from their respective strategies.

Currently, both companies are charging the same fare, $100, We assume that they are not prepared to co-operate with one another and are independently considering the impact of reducing their fares to $90 on their profits.

In deciding whether to leave fares at $100 or lower them to $90, each company will need to take into account the likely response of the other company to the decision it makes. The pay-off matrix below shows the profits made (in $millions) by the two firms as a result of leaving their fares at $100 and reducing them to $90.

Strategies available for the firms are similar to the prisoners in the earlier example, and the best strategy, also known as the dominant strategy is to reduce their fares, irrespective of what the other company does and hence the final outcome would be them ending up in quadrant D with a $20 million profit. This position of theirs is known as Nash equilibrium.

Nash equilibrium is when, in a non collusive / non cooperative situation the best strategy for the firms is to maintain its present behaviour given the present behaviour of the other firms in the market because no player can change their decisions and get a better payoff.

The final position in this game is shown in quadrant C with both companies reducing their prices and achieving profits of $20 million, and now, neither company will have any incentive to change its strategy because increasing prices would lead to loss in market share which would lead to losses and decreasing their prices would lead to a price war which they may lose. Therefore prices remain rigid.

We see that the two companies have failed to achieve the best possible outcome for both of themselves which is shown in quadrant A with both firms leaving their fares at $100 and making profits of $30 million.

However, in reality, it is not a single-move game but one which is repeated over time, it is likely that the companies will come to realise that their mutual interests are best served by cooperating or colluding either tacitly or through a formal cartel. (although the latter is illegal in most countries)

Game theory helps us explain that in an oligopoly, firms are affected not only by their own production decisions, but by the production decisions of other firms in the market as well.

The prisoner’s dilemma explains why cooperation is difficult to maintain for oligopolists even when it is mutually beneficial by showing that the dominant strategy of each actor is to defect even though acting in self-interest leads to a sub-optimal collective outcome.

It also helps show us how mutually interdependent firms in an oligopoly are, by showing that firms, when deciding on a course of action, must also consider how others might respond to that action. The Nash equilibrium helps us

understand that no player can do better by unilaterally changing his or her strategy and therefore explaining the reason behind prices being stable in an oligopoly.