‘Game-theory’ can be used to explain ‘interdependence’ and ‘price-stickiness’, which are both characteristics of oligopolies.

A game has three central components - players, outcomes and the need for a strategy. Game 'theory' is the formal study of games where a player's outcomes are determined by decisions they take and those taken by other players.

Games may involve co-operation between players, or may involve conflict between players.

The ‘Prisoner’s Dilemma’ is an early example of a game which can be applied to oligopolists.

The term 'prisoners dilemma' was first used by Canadian American mathematician, Albert Tucker, in 1950. In this game, two individuals – lets call them Bill and Bob – are arrested for a petty crime and placed in separate cells.

During their interrogations, the police officer suspects the two of committing a more serious crime. The officer offers them a chance to confess to the serious crime, and get a reduced sentence.

If they both confess, they will get a 3-year sentence – if they both deny they will only get 2 years for the lesser crime.

If one denies, and the other confesses, the one confessing will get one year, and the one denying will get 10.

The outcomes can be laid out in a ‘pay-off matrix’.

What would you do? If you think about it long enough, it is best to confess. While it is tempting to deny, it doesn’t take long to work out that, if you do, and the other confesses, they achieve the best outcome of a one-year sentence.

Confessing is the only rational option! ‘Confessing’ is also ‘Nash equilibrium’, after the late American mathematician John Nash.

Here, equilibrium exists when players have arrived at a position where any change will result in a worse outcome.

Hence, if both prisoners decide to confess, they will not change their mind as ‘denying’ makes them instantly worse off!

When applying this to oligopolists you can see that, once a price is set, there is little gain to be made by changing it. True, oligopolists could collude and raise price together, but only if they trust their rivals not to cheat.

In the matrix below, two rival firms can either raise price or lower price.

The payoffs are shown based on whether they raise or lower.

Without any co-operation, the rational option is for both to lower (both get $70m) given that if one lowers and the other raises the one that raises will only get $30m.

However, if they can collude, and agree to raise price together they can get the best outcome of $80m each. Hence, the temptation is to collude.

Any fines on firms caught colluding will alter the pay-off matrix to make colluding less beneficial.

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