Bank robberies, surfing and game theory – eliminating options during a kidnapping
From a game-theoretical perspective, robbing a bank to finance a certain lifestyle is not a rational thing to do. Especially if there is an undercover FBI agent on your case and things are slowly getting out of control. Nevertheless, even bank robbers can turn a hopeless situation to their advantage by using game theory, as shown by the bank robbing surfer-gang in the cult movie Point Break.
[Spoiler alert] In order to understand the circumstances of the game-theoretical application, it is important to know what the movie is about. In the movie, FBI Agent Johnny Utah (played by Keanu Reeves), infiltrates a surfer gang which robs banks to finance their surfing lifestyle. Johnny becomes friends with the gang leader Bodhi (played by Patrick Swayze), and develops a passion for surfing. After the gang finds out that Johnny is an undercover agent, they force him to take part in one last robbery before they flee the country. In the end, most of the gang are shot and die in the fleeing process, while Bodhi escapes and is found a year later during a storm at Bell’s Beach in Australia. Johnny is about to arrest Bodhi, who convinces him to let him surf the perfect storm wave one last time. Knowing that Bodhi will die in the waves, Johnny lets Bodhi go.
Overall, the movie shows that robbing banks is not sustainable when your actual goal is to maximise surfing time. Your expected time spent surfing over your lifetime is likely to be substantially shortened when you finance it by robbing banks, since there is a high probability of being arrested or even killed. In general, the bank robbers do not show a utility for maximising behavior in a game-theoretical sense. However, in two scenes in the movie, Bodhi very skillfully applies game-theoretical concepts to turn a hopeless situation to his advantage. In this article, the first of the two scenes is analysed from a game-theoretical perspective. The second scene will be analysed in a follow-up article.
THE SITUATION SEEMS HOPELESS FOR BODHI
In this scene, Bodhi has found out that Johnny is an undercover agent. Bodhi explains to Johnny that Johnny’s girlfriend, Tyler, has been kidnapped by the gang. She will only be released if Johnny participates in the last robbery. Johnny overwhelms Bodhi, and demands that Tyler is let go. This is where Johnny underestimated Bodhi’s game-theoretical strategy. At first, the situation seems hopeless for Bodhi, as visualised in the decision tree in Figure 1.
To find out what decisions will be taken by Bodhi and Johnny, we use backwards induction. We look at the last decision points, where it is Johnny’s turn to decide what to do. To know what Johnny will decide, we also need to know the preferences of the two players.
Bodhi prefers to be free and keep Tyler as a leverage on Johnny. If Bodhi is arrested however, then the leverage is not worth much, so then his priority is to avoid being arrested. Johnny would like to fulfill his job by arresting Bodhi and not have to participate in the bank robbery. His priority, however, is to save Tyler as soon as possible.
With this information, the decision tree above can be solved.
Johnny’s decision points:
Bodhi decides to let Tyler go
If Bodhi decides to let Tyler go, he loses his leverage on Johnny. Johnny can therefore arrest him, and Bodhi would end up in prison. Tyler would live, and Johnny has fulfilled his job. Johnny could also decide to let Bodhi go. Tyler would still live, but Johnny will not have fulfilled his job. At this decision point, it is better for Johnny to arrest Bodhi, which is shown by the green frame in Figure 1.
Bodhi decides to not let Tyler go
If Bodhi does not let Tyler go, Johnny again has two options: arrest Bodhi or let Bodhi go. If he arrests Bodhi, then he has fulfilled his job, but Tyler is still in the hands of the gang and hence her fate is unknown. If Johnny lets Bodhi go, then he does not fulfill his job. Again, Tyler stays in the hands of the gang and her fate is unknown. At this decision point, it is again better for Johnny to arrest Bodhi.
Bodhi’s decision point:
Now that we know how Johnny reacts to Bodhi’s decisions, we can predict what Bodhi will choose. Bodhi knows that if he lets Tyler go, Johnny will arrest him, and Bodhi will go to prison for bank robbery. He also knows that if he does not let her go, he will end up in prison for bank robbery and kidnapping. Hence, Bodhi’s best decision is to let her go, which will only land him in prison for bank robbery.
BODHI USES STRONG COMMITMENT TO ACHIEVE HIS DESIRED OUTCOME
Bodhi’s priority is to remain free, but as the analysis of the decision tree above shows, this is very unlikely to happen. This is where Bodhi applies game theory to improve his situation. Bodhi eliminates the option of letting Tyler go, by telling the gang member who kidnapped Tyler to kill her if he does not arrive at a certain location in Mexico in a few days. In addition, he gets rid of any means of communicating with the kidnapper. By eliminating the option to let Tyler go, Bodhi uses strong commitment to achieve his desired outcome: being let go by Johnny, and keeping Tyler as a leverage so Johnny must participate in the bank robbery. The new decision tree is visualised below.
Again, we can analyse Johnny’s choices.
If Johnny arrests Bodhi, he has fulfilled his job. Tyler, however, is guaranteed to die, since Bodhi would not show up at the agreed location in Mexico. If Johnny lets Bodhi go, he will not fulfill his job, and the fate of Tyler is uncertain. An uncertain fate still means that there is a chance that Tyler survives. Johnny is deeply in love with Tyler, and therefore will do anything to save her life, even if it means not fulfilling his job.
Johnny’s best decision is to let Bodhi go, shown by the green frame in Figure 2. The consequence is that Johnny has to participate in the bank robbery.
BODHI MANAGED TO AVOID HIS ARREST, COMMIT THE LAST BANK ROBBERY, AND GET ON THE PLANE
The outcome is that the bank robbery goes wrong when a security guard and a cop try to overwhelm the robbers. Bodhi and two gang members manage to escape with a large amount of money and make it to the airport, where a plane is waiting for them. Johnny follows them and, after a shootout on the plane field, Bodhi forces Johnny to come with him on the plane.
While the outcome is not perfect for either Bodhi or Johnny, through the strategic move of limiting his own options, Bodhi managed to avoid his arrest, commit the last bank robbery and get on the plane.
This game-theoretical strategic move is achieved by a strong commitment from Bodhi. The strategic move only works if the commitment is credible, which Bodhi achieves through the elimination of any form of communication with the kidnapper.
The follow up scene involving a parachute jump from the plane, will be analysed from a game-theoretical perspective in a second article. Here it will be shown that knowing the preferences and possible choices of the other player, is key to achieving the optimal outcome for oneself.
Title image by Sam Wermut on Unsplash