ABSTRACT
In this chapter, the authors look at game theory, introducing the reader to the Nash equilibrium and the dominant strategy equilibrium, using a range of examples to illustrate these. Finally, they consider the use of mixed strategies, considering when it is optimal for participants to randomise strategies with a degree of probability attached to each. A key idea in the study of game theory is the Nash equilibrium, which is a solution to a game involving two or more players who want the best outcome for themselves and must take account of the actions of others. In such a situation, game theory indicates that both players should mix their strategies, with the penalty-taker aiming for a corner with a two-thirds probability, while the goalkeeper should dive with a 5/9 probability. There is debate in the academic literature about the relative advantages and disadvantages of where to shoot and where to dive.
