# What is the Prisoners Dilemma, and what significance does it have for understanding economic behaviour?

What is the Prisoners Dilemma, and what significance does it have for understanding economic behaviour?

The prisoner’s dilemma represents a simple economic example of the applied mathematics of game theory. As with all economics models, if rationality of the consumer is assumed, it can be seen that each player will seek to maximise their own utility without thought for the ‘greater good’. In effect this will disadvantage both parties and leave them worse off than they could have been. This behaviour applies to our modern day economics for example in price wars in an oligopoly where unless collusion occurs, the two companies will always loose out in the short game.

The prisoner’s dilemma was originally illustrated by Merrill Flood and Melvin Dresher in 1950. It tells the story of two captured prisoners, who are offered a deal by the police to give the other up in return for freedom whilst the other will receive 10 years. If both parites admit to the crime they will recive 5 years each and if they both stay silent only 6 months. Each prisioner must decide which option to take without knowing which the other will choose. The options can be summerised in a decision matrix, as shown in figure 1 below.

Figure 1- Prisioners dilemma matrix

When we consider the assumption that each prisoner will only seek to minimize their own sentence it is predictable that both will choose the dominant stratergy of betraying their accomplice this is because it can be seen to be the best solution for the individual. If your accomplice has stayed silent it is in your interests to betray and if they have betrayed it still makes sense to follow to reduce your own sentence. Therefore if each individual plays for themselves both will betray and serve for 5 years. However this is not the optimum pay off for the pair as they will be serving more time than if they had trusted each other to stay silent. The prisoner’s dilemma game is unique in that the equilibrium gives a sub-optimal Pareto solution meaning that rationality leads the player to betray even though both would be better of by co-operating.

However the outcome changes slightly when given the chance to play more than one game, known as the ‘Iterated prisioner’s dilemma’. If the players have memory of at least one previous game, a co-operative outcome can eventually be reached as shown by Robert Aumann in 1959. With outcomes judged solely on self interest of both parties, it is shown that greed stratergies are much less effective than those of co-operation and fogiveness. Staergies that lead to success in this long game are being ‘nice’ in that you should not defect before your opponant does, ‘retailiating’ as if you are ...