SITUATION: MUGGING
Notorious for being cheap, the comedian Jack Benny would tell the fol- lowing story: “I was walking down a dark alleyway when someone came from behind me and said, ‘Your money or your life.’ I stood there frozen. The mugger said again, ‘Your money or your life.’ I replied, ‘I’m thinking, . . . I’m thinking.’”
Simon is walking home late at night when suddenly he realizes that there is someone behind him. Before he has a chance to do anything, he hears, “I have a gun, so keep your mouth shut and give me your wallet, cell phone, and iPod.” Simon doesn’t see a gun, but does notice that the mugger has his hand in his coat pocket, and it looks like there may be a gun in there. If there is no gun, Simon thinks he could give the mugger a hard shove and make a run for it. But if there is a gun, there is a chance that trying to escape will result in him being shot. He would prefer to hand over his wallet, cell phone, and even his iPod than risk serious injury. Earlier that evening, the mugger was engag- ing in his own decision making as he debated whether to use a gun. Because the prison sentence is longer when a crime involves a gun, he’d really like to conduct the theft without it.
The mugging situation just described is depicted as the extensive form game in FIGURE 2.8. The mugger moves first in deciding between three options: not to use a gun; bring a gun, but not show it to the victim; and bring a gun
FIGURE 2.8 Mugging
Mugger
Mugger
Simon
3
2
5
4
2
6
6
3
Gun & show Gun &
hide
No gun
SimonSimon
Resist Do not resist Resist Do not resist
3
2
4
5
Resist Do not resist
30 CHAPTER 2: BUILDING A MODEL OF A STRATEGIC SITUATION
and show it to the victim. In response to each of these actions, Simon has to decide whether to resist the mugger by doing the “shove and run” (resist) or by complying with the mugger’s instructions (do not resist). Simon has two in- formation sets. One is a singleton and is associated with the mugger’s having and showing a gun. The other information set comprises two nodes, one cor- responding to the mugger’s having a gun, but not showing it, and the other to the mugger’s not having a gun. With the latter information set, Simon isn’t sure whether the mugger’s pocket contains a gun.
In specifying the payoffs, the best outcome for Simon is that the mugger does not use a gun and Simon resists; the worst outcome is that the mugger has a gun and Simon resists. For the mugger, the best outcome is that Simon does not resist and the mugger doesn’t use a gun in the robbery. The worst out- come is that he doesn’t use the gun and Simon resists, as then the mugger comes away empty handed.