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Showing posts from April, 2019

Is it ever optimal to play a mixed strategy?

In the early days of its (modern) history game theory focused a lot on zero-sum games. These are games in which total payoffs always add to zero no matter what the outcome. So, in a two player setting - your gain is my loss and vice-versa. It was arguably natural for game theory to focus on zero-sum games because they represent the epitome of conflict. The main reason the focus fell on such games is, however, more one of convenience  - zero-sum games have a solution . This solution is captured by the minimax theorem and all that followed. Basically it amounts to saying that there is a unique way of playing a zero-sum game if all players want to maximize their payoff and are rational . Most games do not have a 'solution', because there are multiple Nash equilibria and so there is not an obvious correct way to play the game. In this sense zero-sum games are 'nice' or 'convenient'. But does it make sense to behave according to the minimax theorem? The simple an