Learn the answer to the 2023 Biz Quiz.
Question
Business relationships frequently involve promises and threats: A building contractor promises a completion date; an incumbent firm threatens a potential entrant with a price war; a habitually late employee promises to be on time in the future. The question for the recipient of a promise or threat is whether the sender’s actions will credibly match their words. If the potential entrant, for example, believes that the threat of a price war is empty, they might want to enter the market. Whether in business relationships or in life’s relationships, we should seek guidance as senders of promises and threats about how to make them credible (i.e., how to convince recipients that it is in their best interest to carry them out) and as recipients about whether to believe the promises or threats are credible. We can examine this question further by examining a few films and using game theoretic analysis.
The films Die Hard, Crimson Tide, and The Maltese Falcon each contain a scene that depicts a strategic threat made by a primary character—a threat that is the starting move in a game interaction between two characters in the film. What is the threat?
The screenplay of one of the films captures perfectly the strategic interaction between the characters as the move is played. In the screenplay, a description is given for the game theoretic equilibrium of the interaction and the character speaks to the credibility of his threat. Which screenplay?
The character who employs the strategic threat in this film states one of the most elegant and convincing lines in film regarding his motive to carry out a threat, even though it (superficially) appears to not be in his best interest to do so. What is the line?
View the original question webpage.
Answer (Online Only)
- The threat is to kill the information holder.
- The movie is The Maltese Falcon.
- The quote is from Kasper Gutman - “Because, as you know, sir, in the heat of action men are likely to forget where their best interests lie and let their emotions carry them away.”
Spoiler alerts ahead!
The films The Maltese Falcon, Die Hard, and Crimson Tide each contain a scene involving the same strategic threat by a primary character – a threat that is a beginning move in a game interaction between the character and another of the film’s characters. What is the threat?
In Die Hard, thief Hans Gruber threatens to kill Joseph Takagi, the only person who knows the code to a safe containing bearer bonds, if he does not open the safe. In Crimson Tide, submarine commanding officer Captain Frank Ramsey threatens to kill weapons officer Lieutenant Peter Ince, the only person with the combination to a safe containing a tactical firing pin, if he does not open the safe. In The Maltese Falcon, gangster Kasper Gutman threatens to kill Sam Spade, the only person who knows the location of a ceramic falcon, if he does not give up the location of the falcon.
The screenplay of one of the films perfectly captures the strategic interaction between characters in which the move is played (i.e., the screenplay correctly describes the game theoretic equilibrium of the interaction). Which screenplay?
In Die Hard, Gruber kills Takagi for not giving up the code. Gruber then states that he has an alternative option to getting into the safe, albeit one that takes longer than if Takagi has opened it. Gruber’s strategic flaw is that while threatening Takagi, Gruber should have credibly shown Takagi that Gruber would have this alternative. If he would have done so, Takagi would have been more likely to open the safe.
In Crimson Tide, following Ramsey’s threat, after Ince does not open the safe initially, Ramsey states that killing Ince will do Ramsey no good because Ince is the only person with the combination. Ramsey then turns his gun on another character in the submarine’s command center, Petty Officer Hilaire, and threatens to kill Hilaire if Ince does not open the safe. Ince acquiesces and opens the safe. The strategic flaw in Ramsey’s threat to kill Hilaire is that if Ramsey were to do so, he would then have to threaten to kill Ince, but he had already demonstrated in the scene that he would be unwilling to open the safe, even with death on the line. Ramsey and Ince therefore both should understand that Ramsey’s threat to kill Hilaire is ineffective. However, the screenplay subtly touches on the possible effectiveness of Ramsey’s threat to kill Hilaire by developing Ramsey’s character – he’s crazy enough to act irrationally, in this case irrationally killing a crew member, even though the threat to do so should be ineffective. Perhaps the writers of Crimson Tide in establishing Ramsey's instability were inspired by the MalteseFalcon screenplay.
The discussion between Kasper Gutman and Sam Spade about the effectiveness or ineffectiveness of Gutman’s threat is a screenplay masterpiece in which the two narrow down to the realization of Gutman’s irrationality of carrying out his threat because Spade is the only person who knows the falcon’s location. Their discussion ends with Gutman stating, “... sir, in the heat of action men are likely to forget where their best interests lie and let their emotions carry them away.” While the Crimson Tide screenplay might hint at this point, The Maltese Falcon screenplay nails it. Following this Gutman line in The Maltese Falcon, Spade continues by describing what game theorists call mixed strategies in which players randomize over their actions.
The character who employs the strategic threat in this film states one of the most elegant lines in film regarding the optimality of any strategic threat. What is the line?
It’s the line, “... sir, in the heat of action men are likely to forget where their best interests lie and let their emotions carry them away.”
A Game Theoretic Analysis
A figure has trees representing two possible games between Gutman (G) and Spade (S). Specifically, the game that follows Gutman’s threat to kill Spade if he does not tell the location of the falcon and not kill Spade if he does.
In the game, Spade moves first by deciding whether or not to tell Gutman the location of the falcon. Then, conditional on Spade’s decision, Gutman decides whether or not to kill Spade. The part-a tree has the payoffs for Gutman in which he is mindful of his best interests. The part-b tree has Gutman’s payoffs if he forgets where his best interests lie. The double lines in each of the trees, represent the two possible games and show the subgame perfect Nash equilibrium.
If Gutman is mindful, then he will not kill Spade, regardless of whether he tells Gutman about the falcon’s location. Spade does not tell the location. However, if Gutman forgets where his best interests lie, then he would carry out his threat. Anticipating Gutman’s response, Spade tells Gutman the location.
What should Spade do? The answer depends on the probability that he believes Gutman is mindful and the probability he is forgetful, which Spade can influence.
Lehigh students interested in the analysis of the more sophisticated game with mixed strategies and two possible Gutman types should take one of the College of Business’s two game theory courses — Eco 358 (introduction) or Eco 463 (advanced).
Editor's Note
Our randomly selected winner from all of our correct submissions from our 2023 issue was Miles Cox '24, finance. Congratulations!