1. Prisoners’ Dilemma sometimes is written with the apostrophe between the and the : Prisoner’s Dilemma. The latter placement of the apostrophe indicates that a single player faces the dilemma; the former placement indicates that all players face the dilemma. Argue both positions. Which do you think is a better representation of the problem?

2. The game-theoretic descriptions of interactions between batters and pitchers in baseball used in the exercises of this chapter are simplified. The original cover of Boston Red Sox legend Ted Williams’s The Science of Hitting included Williams’s batting average for different regions of the strike zone; for current players, this information is available on ESPN’s website through their game tracker, where it is possible to follow Major League Baseball games while they are being played. Can you use batting average information to better model the batter- versus-pitcher game by including pitch location (and the batter’s guess of location)?

3. Former San Francisco Giants slugger Barry Bonds has been much maligned for his use of performance- enhancing drugs. But he also was shrewd about how baseball was played. Once, before an at-bat, he described to a teammate exactly how he would be pitched; the at-bat resulted in a homerun. This suggests that the batter-pitcher interaction may be better modeled as an extensive-form game, like a truel. Pitchers often describe using pitches to set up a hitter. ESPN’s website includes a game tracker feature so that users can follow a game being played in real time; this feature tracks the sequence of pitches thrown during an at-bat. Explain how to develop such an extensive-form game model of the batter-pitcher interaction. What information would you use in your model? Should the information be limited to one at-bat or for all at-bats in the game? Should it extend to previous games?

4. Consider a conflict that you had—with a parent, a boss, a girlfriend or boyfriend, or some other acquaintance—in which each person had to make a choice without being sure of what the other person would do. What strategies did you seriously consider adopting, and what options do you think the other person considered? What plausible outcomes do you think each set of strategy choices would have led to? How would you rank these outcomes from best to worst, and how do you think the other player would have ranked them? In two to three pages, analyze the resulting game, and state whether you believe you and the other person made optimal choices. If not, what interfered with your or the other person’s rationality?

5. It is sometimes argued that game theory does not take account of the (irrational?) emotions of people, such as anger, jealousy, or love. What is your opinion about this question? In one to two pages, give an example, real or hypothetical, that supports your position, paying particular attention to whether the players acted consistently with or contrary to their preferences.

6. In tennis, one player often prefers to play from the baseline while her opponent prefers a serve-and-volley game (i.e., likes to come to the net). The baseline player attempts to hit passing shots. This player has a choice of hitting “down the line” or “crosscourt.” The net player must often correctly guess in which direction the ball will go to cover the shot. In one to two pages, formulate this situation as a matrix game and discuss appropriate strategies for the players.

7. Quentin Tarantino’s films Reservoir Dogs (1992) and Pulp Fiction (1994) both have truels, but the choices that the characters make in each film are completely different. Does the truel analysis offer any insight into why? Discuss in one to two pages.