Mixed strategy
Randomising over strategies, which is the only equilibrium available in games of pure conflict.
Often misread asComputing your own mixture from your own payoffs, on the reasonable-sounding grounds that it is your decision.
How to see it
Being unpredictable on purpose
Rather than picking one action, you pick a probability for each and let the draw decide. In games where being read is fatal this is not indecision but the actual best play, and the right probabilities are the ones that leave the opponent with nothing to exploit.
The checkYour mixture is pinned down by the other player's payoffs, because its job is to make them indifferent.
Try itWork out the keeper's probabilities in a penalty kick. If you used the keeper's own payoffs you have gone wrong; check instead that the kicker's expected payoff comes out the same whichever side they aim at.
Games that show it
Know these first
Leads on to
Easily confused with
Sources
- Nash, J. (1950). PNAS 36(1), 48-49.
- von Neumann, J. & Morgenstern, O. (1944). Princeton UP.