Competitive Oligopolies: Prisoners Dilemma (Game theory)

In this video I explore how the prisoners dilemma shows how firms in an oligopoly behave through dominant and non-dominant strategies.

Competitive Oligopolies - Prisoners Dilemma (Dominant and Non-Dominant Strategies)

The Prisoners Dilemma is a form of Game Theory used to show how firms in an oligopoly are interdependent. We will look at how the Prisoners Dilemma shows how firms can have a dominant strategy or not have a dominant strategy.

A dominant Strategy

A dominant strategy is were a firm has an incentive (to gain market share and increase profits) no matter what the other firm does. 

		Firm A
Firm B		£2.00	£1.50
	£2.00	£200k each	£100k (B) £1mil (A)
	£1.50	£1mill (B) £100k (A)	3 million each

So both Firm A and B have an incentive to keep their price at £1.50 regardless of what the other firm keeps. But you might be wondering then what has this got to do with interdependence? The ‘pay-off matrix’ shows that if Firm A decided they wanted to keep their price at £2.00 so they can pursue other objectives such as Corporate Social Responsibility then Firm B can only make a maximum profit of £1million this shows their interdependence. As, if they were not interdependence their maximum amount of profit would not be reliant on the price set by rival firms.

No Dominant Strategy

This when a firm has to react to what another firm does in order to be better off. So the difference is that if they had a dominant strategy no matter what another firm does they will be better off at Price X, but here they can only be better off at Price X if the rival firm also charges at Price X or the other firm will need to follow suit to recapture lost market share and profits. This might sound a bit confusing so I will explain this using the ‘pay-off matrix’ below.

		Firm A
Firm B		£1.50	£1.30
	£1.50	£3 million each	£1.5m (B) £5m (A)
	£1.30	£5m (B) £1.5m (A)	£1 million each

So if again we look at firm B who is deciding whether to price at £1.50 or £1.30. This decision will be based on firm A (unlike when the firm was choosing between £2.00 and £1.50 and had a dominant strategy). For example, if firm B charges at £1.50 it might loose out because firm A is charging at £1.30 and if it chooses to charge at £1.30 it might loose out again if the firm B is charging at £1.30. So this strategy also shows interdependence because it shows how a firm bases its prices on competitors. The non-dominant strategy which seems to be more common also shows why firms have an incentive to collude as well as cheat and engage in non-price competition.