Game theory is a concept in applied mathematics that can be used to study and interpret a variety of behaviour.
We’ve all seen examples of it in popular culture – the Oscar winning 2001 film A Beautiful Mind is an account of the life of Nobel laureate John Nash who made important contributions to the subject.
In business and economics game theory is most commonly used to study aspects of decision making – particularly between competing parties in activities that involve bargaining.
Many of the games or strategies involve outcomes where co-operation, or mutual agreement benefit all parties, while over-competitive behaviour punishes all but one of the parties involved.
Game theory can most commonly be seen in business in so-called "price wars", where it would be mutually beneficial for all competing parties that manufacture or sell the same product to agree on a price.
Despite this favourable outcome, all parties enter into a battle to get a competitive edge over their rivals by lowering their prices further.
A commonly expressed facet of game theory is the zero-sum game, or nil-sum game. This is where the sum of all gains for one party, or parties, must equal the sum of all losses suffered by a counterparty, or counterparties.
Game theory can therefore be used to explain the behaviour of stock markets – essentially, a very complex zero-sum game. Single transactions do not necessarily conform to this rule, but the market as a whole does.
Examine some of the games and a hint of the type of behaviour that characterises investor sentiment emerges: holding on to losing positions, failing to maximise profit because of ill-timed exits, and failing to accurately assess the balance between risk and reward.
Let's look at a few of the classic examples of game theory that explain this type of behaviour.
1. The Prisoner's Dilemma
Game theory starts with this decision-making strategy.
Two prisoners – let's call them Convict 1 and Convict 2 – accused of the same crime are held in separate rooms and cannot communicate with each other.
They are each told that if one testifies against the other he can go free. If Convict 1 refuses to testify against Convict 2, but Convict 2 agrees to testify against Convict 1, Convict 1 will get three years in prison while Convict 2 goes free and vice versa.
They are also told that if both testify against the other, they both get a two year sentence, while if both refuse to testify, they both get one year in prison.
So imagine you're one of the prisoners. The best strategy is co-operation: if you both refuse to testify you get just one year each.
Yet research shows that most people will testify against the other – this can be for two reasons:
- In the vain hope that the other refuses and you go free
- For fear that if you stay silent, the other party testifies giving you three years
Even though the reward is greater if you stay silent, you have to be sure that your counterparty will also do so, but this is too great a risk to take.