# Game Theory

Game theory is a branch of mathematics that provides a framework for analysing what choices rational individuals will make, when the outcome ("payoff") depends on both their choice and the choices of other "players".

Game theory has many applications in economics and and some in finance - it has uses in exchange rate theory, for example.

A simple example of how game theory works is given by the prisoners' dilemma game. This is a hypothetical situation in which two criminals caught by the police may each confess and give evidence against the other. The possibilities are:

1. If neither confesses both will face a minor charge that carries a one year prison sentence.
2. If one confesses and the other does not, the one who confesses will go free, the other can expect to be convicted and get a 10 year prison sentence.
3. If both confess, both will go to prison, but will receive more lenient (say 5 year) sentences.

A game theorist will represent the possibilities as a strategic form game:

 Player A Co-operate Defect Player B Co-operate -1,-1 0,-10 Defect -10, 0 -5,-5

The players are the two criminals, "cooperate" means helping the other player (e.g. by not confessing), "defect" means the opposite, the payoffs are shown in the table, first the payoff for player A, then that for player B.

It is obvious that the two players (the prisoners) will be best off if they both "cooperate" (try to help each other), as they will then both receive light sentences.

However, from the point of view of each player, he or she is better off if he or she defects regardless of what the other player does. The strategy of defecting dominates the alternative.

The result is that, assuming rational and non-altruistic players, they both defect.

There are game theory analyses that take account of cooperation. These are cooperative game theory, the use of which is less common that non-cooperative game theory.

Simple dominance is only one possibility. Another common outcome in economics and financial economics is a Nash equilibrium.