10. It is possible for a player’s pure strategy to be dominated by a mixed strategy. For the following game, Player I’s strategy of playing Top and Middle, each with probability 1/2, dominates the pure strategy of playing Bottom. Calculate the expected value for each of these strategies against Player II playing the pure strategies Left and Right. Use your answer to explain why Bottom is dominated by the mixed strategy.
Player II | |||
---|---|---|---|
Left | Right | ||
Player I | Top | 2 | 8 |
Middle | 8 | 2 | |
Bottom | 4 | 4 |