pure strategies in game theory

Question

I'm really lost and spent ages trying to understand this:

• what is the exact definition of a pure strategy in game theory?

• how can one find/identify a pure strategy in a pay-off matrix? i.e. what difference is there between a pure strategy and a normal strategy?

• if one is definite of choosing a pure strategy, then how come there are 2 pure strategies in the battle of the sexes?

thanks!!

Answer 1

Given a game matrix, a pure strategy means that you are always making the same choice. For instance, in rock-paper-scissors, always playing rock is a pure strategy. There are exactly three pure strategies in that game.

By contrast, a mixed strategy is one where you randomly choose which strategy you are going to make. For instance, a mixed strategy would be to play rock 80% of the time and scissors 20% of the time. There are an infinite number of mixed strategies for any game with more than one pure strategy. (A game with only one strategy would be pretty trivial to investigate anyways.)

Answer 2

A pure strategy is when you choose one of your options. The alternative would be a mixed strategy. That is where you choose your option at random, according to a certain probability distribution.