Explain the difference between pure strategy and mixed strategy in game theory?

Answer 1

Suppose you and your younger brother/sister are playing a game which involves picking various colours from a bag of smarties. The reward, (ie payoff/profit/utility), you or your brother/sister gets depends on a combination of the colours you both pick. Little brother/sister is getting bored and awkward and he/she continually picks one colour and you know that he/she is going to pick that colour. Little brother/sister is playing pure strategy. You know what he/she is going to do, whereas you, being very keen to make the game fun, pick various colours different number of times with different frequencies in a given game. You are playing with mixed strategies. You are picking different colours with at different probabilities. After a while little brother/sister gets even bored in the next game and decides to pick a different colour and sticks to the same colour, meanwhile you change and pick different colours with different number of times again brother/sister is playing pure strategy and you are playing with mixed strategy. Strategy in this case means an activity such as picking a colour which is part of the rule of the game