The prisoner’s dilemma is probably the best known problem in game theory and was originally formulated in the 1950s by two mathematicians, Merrill Flood and Melvin Dresher, working in America.

It is a depressing piece of maths because if the prisoners involved follow their own self interest with cold logic, they are forced to betray each other every time, yet end up worse off than if they had been more magnanimous.

The scenario is that two suspects are held by the police who do not have enough evidence for a successful conviction and hope to convince one or other to break ranks and testify against his fellow inmate. The police separate the suspects and make both the same offer.

They are told that if one of them testifies against the other and the second remains silent, then the betrayer will be freed but the silent accomplice will get a ten-year term in jail.

If both keep silent they will both serve just six months on a reduced charge but if each betrays the other they will go down for five years apiece.

The dilemma is that each is better off confessing than remaining silent but if both confess, the outcome is less good than if both had remained silent.

It turns out that they do not have a real choice and, if we exclude any damage to their reputation or lingering affection for the other player, the rational choice leads the players to betray each other every time. This leads to a worse outcome for both of them than if they had acted cooperatively.

The most obvious parallel in business is pricing. Does one player (or retailer) betray a competitor by reducing prices in the hope that the competitor will go out of business? And does the competitor follow suit, so that both make less money?

Even if the competitor believes his product reflects value for money at its current price, his dilemma is whether to maintain the price and risk losing market share, or cut the price and his profits.