Game Theory 101 (#11): Calculating Payoffs

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How do we calculate payoffs in mixed strategy Nash equilibria? The process has three simple steps:

1) Find the probability each outcome occurs in equilibrium.

2) For each outcome, multiply that probability by a particular player's payoff.

3) Sum all of those numbers together.

That's all it takes!

It is always a good exercise to calculate payoffs in mixed strategy Nash equilibria and compare them to the payoffs for pure strategy Nash equilibria, or even non-equilibrium outcomes. Is the mixed strategy Nash equilibrium efficient? Are there pure strategy Nash equilibria that are better for both players? What about non-equilibrium outcomes?