Lecture 9 - Mixed Strategies in Theory and Tennis

We continue our discussion of mixed strategies. First we discuss
the payoff to a mixed strategy, pointing out that it must be a
weighed average of the payoffs to the pure strategies used in the
mix. We note a consequence of this: if a mixed strategy is a best
response, then all the pure strategies in the mix must themselves
be best responses and hence indifferent. We use this idea to find
mixed-strategy Nash equilibria in a game within a game of tennis.