In game theory, a pure strategy is an unconditional choice of strategy for a player. In other words, the player chooses that strategy for sure. That distinguishes it from mixed strategy, where the player randomises their actions, choosing each of the possible strategies with some probability (which might be zero). There are lots of examples of mixed strategies. One that I use in my ECONS101 class is the choice for a tennis player over whether to serve down the middle, into the body, or out wide. If they chose one strategy for sure, they would reduce their chances of winning. Instead, they should randomise - sometimes choosing the first strategy, sometimes the second, and sometimes the third.
Another example from sports is the penalty kick in football (or soccer, if you prefer). The penalty taker must choose which side to kick towards, and the goalkeeper must choose which way to defend. I've discussed this game and the mixed strategy equilibrium before (see here and here).
The key problem with mixed strategy is that it genuinely involves randomisation. You cannot reason a pure strategy solution to a mixed strategy game. If you do, you end up with something like this:
I'm not sure where the video comes from (TV or movies, or something else), but it is very similar to a story related in the book Soccernomics, by Simon Kuper and Stefan Szymanski (as Robbie Butler notes here). The solution to mixed strategy games is not to try and solve them with pure strategy, but to randomise.
[HT: Jadrian Wooten at Critical Commons, via the Economics Media Library]
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