A payoff matrix is a tool used for analysing interdependent behaviour shown between firms in an oligopoly market structure.  Game theory shows the potential strategies a firm could follow and the resulting behaviour of an interdenpendent firm. 

In short 'if firm A does ............. what should firm B do?

Game theory and a payoff matrix can be used to model a number of business strategies such as

• Whether to invest in R&D.
• How much to spend on advertising.
• Whether to hire new workers.
• Whether to run promotions and to what extent.

The standard example of game theory relates to pricing decisions, the diagram below shows some interelated outcomes that firms may in regard to charging a lower or higher price.

Payoff matrix showing the outcomes for two firms.

1. Initially each firm in the oligopoly is charging a higher price and each receive £40m in revenue.
2. This is an example of tacit collusion - there is no direct agreement for both firms to charge a higher price however they have mathced each others prices naturally.
3. Both firms understand that they are able to greatly increase their revenue by competing on price and choosing a low price, £60m in revenue.
4. The firm that lowers price first would benefit from first mover advantage.  The firm with the lower price would see an increase of £20m in revenue whilst the firm keeping the higher price would see a reduction in revenue of £25m. 
5. The first mover advantage is likely to be very short term.  the firm with the higher price would reduce their own prices as quickly as possible to minimise their losses.
6. Now both firms settle on the lower price and both have revenue reduced by £30m down to £10m.
7. What are firms likely to do given all of this information? Overtly collude to keep the selling price at the higher price.  Overt collusion is a formal agreement between firms to not compete on price.  Overt collusion negatively impacts consumers' welfare and is illegal. 
8. Firms overtly colluding may be referred to as cartels.