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.

📑 Lecture Chapters:

Mixed Strategies: Definition [00:00:00]
Mixed Strategies: Examples [00:06:02]
Mixed Strategies: Direct and Indirect Effects on the Nash Equilibrium [00:22:20]
Mixed Strategies and the Nash Equilibrium: Example [00:27:05]

Source: Ben Polak, Game Theory (Yale University: Open Yale Courses). Licensed under CC BY-NC-SA 3.0.