1. In the following two-person zero-sum game, the payoffs represent gains to row Player I and losses to column Player II.

What is the maximin strategy for Player I?

2. In Skills Check 1, the minimax strategy of Player II is to play the _________ column.

3. In the following two-person zero-sum game, the payoffs represent gains to row Player I and losses to column Player II.

What is the minimax strategy for Player II?

4. In Skills Check 3, the maximin strategy for Player I is to play the _________ row.

5. Does the game in Skills Check 1 have a saddlepoint? What about the game in Skills Check 3?

6. Do any of the above games have a saddlepoint?

7. In which two games does neither player have a dominant strategy?

8. How many of Player I’s strategies are dominated in the third game?

9. Which strategy of Player II is dominant in the third game?

10. Strategy _________ of Player I is dominant in the third game.

11. The third game has

12. If a game has a saddlepoint, then _________ is the value of the game.

13. In the game of Matching Pennies, Player I wins a penny if the coins match; Player II wins a penny if the coins do not match. Given this information, it can be concluded that the matrix representing this game has

14. A mixed strategy uses randomization to ___________________.

15. Which of these games does not have a saddlepoint?

16. A game is fair if its saddlepoint is equal to __________.

17. In the following game of kicker-versus-goalie, the kicker’s likelihood of being successful in kicking certain goals is given in the game matrix. Recall that the kicker can kick to the goalie’s left or the goalie’s right and the goalie can dive to the left or to the right .

Which is the best strategy for the kicker?

18. In Skills Check 17, the goalie’s optimal strategy is to dive to the left with probability . What is ?

19. In Skills Check 17, if the kicker and the goalie use their optimal mixed strategies, then, on average, the kicker successfully kicks a goal with probability _________.

20. In Skills Check 17, if the kicker uses her optimal strategy, do you know beforehand whether she will kick the ball to the goalie’s left or to the goalie’s right? (Yes or No)

21. In the following game of batter-versus-pitcher in baseball, the batter’s batting averages are given in the game matrix. The batter tries to maximize his batting average while the pitcher tries to minimize the batter’s batting average; this is a zero-sum game. The pitcher decides between throwing a fastball and a curveball. When the batter is in the batter’s box, he guesses which pitch is coming (either a fastball or a curveball). If he guesses correctly, then his batting average is higher. For example, it is easier for him to hit a fastball when he correctly guesses that one is coming. However, if he guesses incorrectly, then his batting average goes down.

22. For Skills Check 21, find the optimal mixed strategy for the batter. Using this strategy, the batter will guess fastball with what probability?

23. In Skills Check 21, the pitcher’s exact optimal strategy is to ____________.

24. In the following game of batter-versus-pitcher in baseball, the batter’s batting averages are given in the game matrix.

25. In Skills Check 24, the pitcher’s optimal strategy is to _______.

26. In Skills Check 24, given your answer to Skills Check 25, the optimal strategy for the batter is to ______.

27. Consider the following partial-conflict game with ordinal payoffs (in which a player rank-orders the outcomes 1, 2, 3, and 4).

Both players might select because ___________.

28. In Skills Check 27, what strategy constitutes a Nash equilibrium?

29. In the following game, Player I has the preferences of the row player in the Prisoners’ Dilemma, and Player II has the preferences of the column player in Chicken.

Does the player with a dominant strategy benefit more than the player without one?

30. In Skills Check 29, the strategies associated with (4, 2) constitute a Nash equilibrium, but those associated with (3, 3) do not because ____________.

31. A game tree is used to

32. Suppose that Chicken is played sequentially instead of simultaneously. Use backward induction to determine the equilibrium outcome for the game tree for Chicken.