A classic example in game theory is that of the prisoners' dilemma. Two people are arrested for a crime, but the police suspect they have been involved in other crimes and hope to obtain confessions from them. The two prisoners are separated and cannot communicate with each other. The police make them an offer. If they both confess tothe other crimes, they will each receive a three-year sentence. However, if one confesses and the other denies, the one who confesses will receive one year, and the denier will receive ten years. If they both deny the other crimes, they will each receive a two-year sentence for the crime they were arrested for committing

Their choice is either to deny or confess. But the result of either action will depend on what the other one does. Both denying will achieve the best outcome. But neither of them can afford to take that risk, because if only one denies while the other confesses, the denier will receive a ten-year sentence. Think about the choice another way: denying means either two years (if the both deny) or ten years (if the other confesses), confessing means either one year (if the other denies) or three years (if they both confess). They each want the best outcome for themselves. So one chooses on the basis of what the other might do: if one confesses and so does the other, it is three years; if one confesses and the other denies, it is one year. This is better than risking 10 years. Therefore they will both confess. (This is known as the Nash equilibrium.) This avoids either one having to do to prison for ten years but it means they both can agree a three-year term when it could have been two.

Think about two firms in an oligopoly, Mega and Maxi. If they both advertise, they will each make $2m profit. If they both do not advertise, they will make $6m profit. But if Mega advertises and Maxi does not, Mega will make $10m and Maxi will make only $1m. If Maxi advertises and Mega does not, Maxi will make $10m and Mega will make $1m.

i. What will the two firms do: advertise or not?

ii.What kind of outcome is this for each firm? What kind of outcome is it in terms of economic welfare?