7. If a player has more than two strategies in a game and one is dominated, it is possible that no single strategy is dominant. Fill in the payoffs in the following two-person zero-sum game in which Player I can choose between Top, Middle, and Bottom and Player II can choose between Left and Right so that both Top and Middle dominate Bottom, but neither Top nor Middle is dominant.
| Player II | |||
|---|---|---|---|
| Left | Right | ||
| Player I | Top | ||
| Middle | |||
| Bottom | 2 | 2 | |
7.
Answers will vary. For example, payoffs of 4, 3, 3, and 4 for (Top, Left), (Top, Right), (Middle, Left), and (Middle, Right) give the desired property.