Monday, February 19, 2024

Game Theory, Jaws, and Girard, with an assist from Lévi-Strauss: A quick sketch

While thinking about the next installment in my series on great literary critics (which has become another inquiry into the nature of literary criticism), I found myself thinking about that essay in which I offered a Girardian interpretation of Steven Spielberg’s Jaws. I smelled an opportunity: Why not add Lévi-Strauss and game theory into the mix?

Lévi-Strauss is obvious since I’d already discussed him in the series, but game theory? How’d I get there? I don’t really know, it just happened.

But I had taken a look at some of Girard’s remarks about Much Ado About Nothing in his Shakespeare book, A Theater of Envy, where he talks of Beatrice and Benedick as playing a game with one another (p. 81):

Outside observers shrug their shoulders and declare the entire game frivolous. It certainly is, but our condescension itself may well be part of a strategic positioning that is always going on, “just in case” the game might have to be played. The game, perhaps, has already begun. We always try to convince others that we ourselves never play this kind of game, but these disclaimers are necessarily ambiguous; they resemble too much the moves that we could have to make if we were already playing the game.

Girard does not invoke game theory, and games of course are common enough. We talk about them all the time. Back in 1964 Eric Bern had a bestseller with Games People Play: The Psychology of Human Relationships, though it's not a game theory book, not in the sense I have in mind in this essay. But Girard was also concerned about who knows what, with what things are public knowledge, and what things are secret, with how public knowledge confirms individual beliefs, those are all matters of importance in game theory. Moreover and after all, game theory is an abstraction over games in the common-sense use of the term and in a way very similar to the way Turing’s account of computation is an abstraction over an activity otherwise performed by people using pencils and paper.

But just how and why I came to think of game theory is not all that important; what’s important is that I thought of it. Once there I thought of the work of Michael Chwe, a brilliant political scientist who published a very interesting book I’d read some years ago, Rational Ritual: Culture, Coordination, and Common Knowledge (2001) and has more recently published Jane Austen, Game Theorist (2013), which I’ve not read. But I have skimmed through his article, Rational Choice and the Humanities Excerpts and Folktales (2009); Chwe uses the relationship between Beatrice and Benedick as one of this examples. Moreover, if you search on “game theory and literature,” you get hits. The conjunction of game theory and literature is thus not so strange, not so unexplored, as one might think. If literature, why not film?

Since I’ve already done a Girardian analysis of Spielberg’s Jaws, why not revisit the film with game theory in mind? That’s what the rest of this post is about. I don’t actually conduct a game theoretical account. Game theory is a technical discipline, but this is not technical. It is, however, informed by game theory, but it is not technical. It is a long though, so take your time.

Caveat: If you’re looking for Girard and Lévi-Strauss, they’re here. But the essay is mostly about games. You can find more Girard in my original essay on Jaws, linked above.

The larger game, Nature and Culture

We can think of the larger game, the one that frames the whole story, as being between Nature and Culture, to use terms favored by Claude Lévi-Strauss. The shark is Nature’s primary agent in this larger game and the town of Amity is Culture’s primary agent. That, I know, is a bit of a strange way of putting things. Setting aside the fact that Amity is a town of some thousands of people (with many more to arrive during the summer tourist season), why not think of it as a game between Amity and The Shark?

I fear I could, and probably should, go on about that at some length. But this is not the place. If we were talk about a Real-Life situation, that’s what I would do. But we’re not, we’re talking about a fiction. I assume that people watching movies do so with the same neurobehavioral equipment they use to negotiate their way in Real-Life, but fictions have affordances that Real-Life lacks. For one thing, fictions are always complete, in some sense, and one’s life continues beyond and outside of one’s vicarious experiences (to borrow a term from William Flesch, Comeuppance) of the fiction. Real-Life is not like that. When you’re dead, that’s the end.

Beyond that, one (generally, often) has a knowledge of the events in the fictional world denied to characters within that world. Take the beginning of Jaws. A young woman goes skinny dipping in the ocean at night. Her body is found next day, washed up on the beach. No one in Amity knows what happened to her. Sheriff Brody sets out to find out. The audience, however, does know what happened. She was killed by a shark. It’s not that we saw the shark; we didn’t. But, we see her struggle and we know it had to be a shark. How do we know that? Because THAT’s what the film is about. It's called Jaws and the posters featured an image of a shark with its mouth open, displaying all those sharp teeth.

THAT changes the valence of everything we see and our experience of it. It gives those events an emblematic resonance that similar events are not likely to have in reality, unless, of course, we so interpret them. I’m using the terms Nature and Culture to capture that resonance. The shark is Nature’s agent and Amity is Culture’s agent. 

* * * * *

“Wait a minute, hold on there. You can’t do that. In what sense is Nature playing a game against Culture?”

“Good question. In the first place we would certainly treat the shark as a game player, with preferences and so forth.”

“But that’s not what you’re talking about, no?”

“Right. Stay with me here. The people of Amity, that is, Team Culture, doesn’t know what’s going on. It makes perfect sense to think of Amity as playing against an unknown opponent, trying to guess its moves, influence its behavior, and make moves of its own. That's what people do.”

“OK. I can see that. And that’s how an audience would see it.”

“Right. Then we might try modeling Team Nature, that is, the shark, with a view to provoking Team Culture into sending out some people to hunt the shark in its own territory.”

“Hmmm. I have to think about that. You’re saying that unknown and unseen force wants to lure people on...”

“Yes. That gives a teleological cast to the affair.”

“And of course there IS teleology involved. The film-maker, Steven Spielberger is up to something, yes?”


Together: “Curiouser and curiouser.”

The Amity game, Team Safety vs. Team Livelihood

But the town of Amity does not act as a unitary entity. It acts through the actions of individuals. And those individuals are not in agreement about how to respond to the dead body. We can thing of the town as divided into two teams, each headed by an official. Team Safety is headed by Sheriff Brody, an official hired by the city. He wants to close the beach until whateveritis has been dealt with. Team Livelihood is headed by the mayor, an elected official who is also Brody’s boss. The mayor wants to keep the beaches open. Why? Amity is a tourist town and, as such, much of its income derives from the summer tourist trade. Closing the beach even for a couple of days could damage the tourist trade badly.

That’s the first choice that has to be made, with Team Safety and Team Livelihood opposed to one another. Team Safety’s thinking is dominated by the short-term risk of people being killed. Team Livelihood’s thinking is dominated by mid-term and long-term risk of economic disaster, which could lead to bankruptcies, job loss, depopulation, and perhaps even some people dying (e.g. suicide, can’t afford medical care). The decision is made difficult by the fact that the town doesn’t know what’s going on and so the teams have no way of reliably estimating the effects of their actions. Culture, if you will, doesn’t know what Nature is up to.

At this point we might think about drawing up the payoff matrix that is a standard feature of game theoretic analysis. What actions are available and what value do the players put on those actions? But I’m going to leave that as an exercise for the reader who is more skilled in these matters than I am. Once that happens, we can then revise the matrix as Team Safety learns more about what Nature is up to (by bringing in a shark expert) and as Team Livelihood has to deal with the consequences of Nature’s next action: the shark kills a young boy without, however, revealing itself.

The mayor calls a town meeting. Of course Sheriff Brody is there. The discussion reveals that the townspeople are divided between Team Safety and Team Livelihood. The mother of the slain boy puts up a $3000 bounty on the shark; adjusted for inflation, that’s roughly $17K in current dollars. Sitting in the back of the room, shark-hunter Quint gains the room’s attention by scratching his fingernails on a blackboard. He’s says that it’s foolish to send a bunch of amateurs after such a deadly shark, but he’ll hunt it down for $10,000. That’s roughly $57,000 in current dollars. That’s the salary, including benefits, of a mid-level municipal employee. A small town like Amity is not likely to have that amount floating around in some contingency fund where it can be casually accessed. The beach is closed and the hunt begins. Score one for Team Livelihood.

The town’s streets are jammed with would-be shark hunters attempting to get to the harbor to hunt down the shark. Yes, they want the money, but they also want the glory of winning the tournament. That’s is where Girardian thinking comes into play. Though I’ve not been able to track it down, I remember hearing a deputy say that he couldn’t tell the locals from the foreigners, a clear sign of mimetic confusion.

Now we have the mimetic payoff. Some fisherman kill a shark. They’re posing on the dock for a photograph with the shark. The photo will go national. The mayor insists that he be in the photo. They open the beaches once again. Team Livelihood scores again.

Team Safety is not convinced. Brody’s expert, Matt Hooper, has examined the shark and said it’s not large enough to have been the one that killed the girl and the boy. They need to autopsy the shark to be sure. The mayor (Team Livelihood) is not convinced. No autopsy. Brody and Hooper sneak out at night and Hooper does the autopsy; no remains of the boy. It’s not the shark.

Hooper and Brody board Hooper’s boat later that night and look for the shark. They don’t find it, but they do discover a sunken fishing boat and the dead body of a local fisherman, Ben Gardner, who’d gone after the shark earlier that day. Hooper pulls a shark’s tooth stuck in the boat’s hull, but looses it. The next day they are unable to convince the mayor that Gardner had been killed by the shark. Team Safety and Team Livelihood are now operating on the basis of very different information.

Team Livelihood’s concern about economic viability may well be influencing how they interpret the evidence. Spielberg certainly believes us to believe so. But that’s distinct from the fact the we in the audience are certain that a shark is involved, though we’ve not yet seen it. While the fictional game between Safety and Livelihood is being played out within the film, the game between Nature and Culture exists only in the minds of the audience. And there, maybe it's not so much Nature vs. Culture as Things We Can’t Control vs. Things We Can. That seems to be a semantic issue.

Fourth of July comes, the beaches are jammed with tourists. The shark kills again. Score one for Safety. Brody is angry; the mayor is chagrinned. The mayor agrees to hire Quint for that $10K that’s going to put a dent in his budget.

Sacred resonance

At this point Safety and Livelihood are in agreement on how to proceed. We are now roughly 3/5s of the way through the film. The rest of the film takes place at sea and involves four characters, Quint, Brody, Hooper, and the shark. Quint and the shark end up dead; Brody and Hooper make it back to shore. But, and this is an important point, we don’t see them re-enter the town. We see them swimming for shore while hanging on to a piece of Quint’s now-destroyed boat. Then, as the end-credits role, we seem then walking from the ocean onto a deserted beach.

This, after all, is a standard (mythic) story. The town is threatened by a monster. A hero kills the monster and then returns to town, triumphant. There’s a big celebration. Everyone’s happy. For all we know that may have happened in Amity. But Spielberg doesn’t show that; it’s not part of the story he’s telling. That story’s up to fans – and there IS fanfic for Jaws, though I’ve not looked into it.

Thus the shark hunt is a private event between three men and the shark. No one in Amity is witness to these events, but we are. If I were arguing at greater length, I’d argue that that disjunction gives a sacred character to their mission. We know, but Amity doesn’t. Ours is the larger, more inclusive vision.

Moreover I’d point to the story that Quint tells on the boat, about being in the Navy during WWII when he served aboard the USS Indianapolis. It was returning from a secret mission transmitting materials for “Little Boy,” the first atomic bomb detonated over Japan, when it was sunk by a Japanese submarine. Those who didn’t die were left in the ocean where they were preyed upon by sharks. Quint was one of them. That story-telling is the single longest sequence in the film. One doesn’t put a sequence like that into an adventure film, which is what Jaws had become at this point, unless it is very important. It resonates, and that resonance contributes to the sacred aura of the film.

[As an exercise, I leave it to the reader to craft a more detailed argument on that point.]

The adventure game

Let’s return to Amity. Brody and Hooper show up at Quint’s shack as he prepares to set out after the shark. Quint doesn’t want them on his boat, the Orca. He doesn’t need them; they’ll just be in the way. Hooper gives proof of his seamanship by tying a sheepshank and Brody points out that he’s paying for the voyage. That is to say, we’ve got a negotiation. We could draw up a pay-off matrix for this interaction. And we should.

“Too detailed, not necessary,” you say. I disagree. I’m not going to do it now, but it would be worthwhile. These three men are negotiating their relationship. That negotiation continues on board the Orca as they interact with one another, and the with the shark. The negotiation doesn’t stop until evening comes and they go into the cabin where they share a meal. Share a meal, very important. After the meal they get to drinking, Hooper and Quint have a little competition over who’s got the most impressive scars, Quint tells his story about the Indianapolis, and they join together in song, “Show me the way to go home...” And then the shark rams the boat.

No, it’s games all the way down. Quint clearly sees himself in a duel with the shark. He’s thinking about the shark in strategic terms and imagining how the shark is thinking about him. That’s how hunters think, they have to. Animals are agents, and hunters study them so they can think like them. Quint, in effect, has a payoff matrix he’s using to guide his interactions with the shark.

How many games are we dealing with, and how are they related? The three men are negotiating their relationship. It’s my understanding that, in game theory, three-person games are considerably more complicated than two-person games. Of course, we aren’t witnessing an interaction between three autonomous individuals. We’re witnessing a staged interaction, that’s taking place under very constrained circumstances. How are we, in the audience, modeling that interaction?

That’s one game, one that started in Quint’s harborside shack in Amity. There’s the game between Quint and the shark, in which Hooper and Brody are just accessories to Quint. And then there’s the final state of the voyage, with Quint and the shark both dead, while Hooper and Brody are both alive.

Are we dealing with another game, one in which Quint and the shark are on one team, which loses, while Brody and Hooper are on the winning team. What teams are those? How was that game set up? Could that be the Nature-Culture game?

Once again, Lévi-Strauss + Girard

Here’s how I am currently thinking about it. I’m making this up as I type. Who knows what I’ll think tomorrow or a week from now.

In his original approach, as set forth in his seminal 1955 paper, “The Structural Study of Myth,” Lévi-Strauss imagined individual mythic stories as proceeding from a maximum opposition through a series of substitutions for terms in the opposition where the substituted terms approach one another until they reach a point of minimal contrast. That ends the story. Think of Quint-shark and Brody-Hooper as a reduced a form of the Nature vs. Culture binary that frames the whole story. Quint-shark is on the side of Nature while Brody-Hooper is on the side of culture. That’s not quote how Lévi-Strauss did things, but it’s in the spirit of his analytic approach, which is all I’m after.

But we Must also think of Quint-shark as the Girardian scapegoat, the pharmakon. I note that Quint was depicted as a disagreeable person, something of an outsider in Amity, shark-hunting is not economically significant. He’s an expendable member of the community. He caught the shark, himself got caught and killed by the shark, and the good sheriff then managed to finish off the shark. The sacrifice has been made, shark AND shark-hunter, and town thus has been saved. There will be tourists this summer. Livelihood restored, but it cost Safety the life of one disagreeable shark hunter. 

That is to say, Team Safety, playing for Team Culture, had to sacrifice a life in the short term so that Team Livelihood could preserve the mid- and possibly long-term economic health of the town. Team Livelihood, also playing for Team Culture, had to give up $10,000 and suffer a temporary reputational loss (following from the deaths allowed by its open-beach policy) in order to achieve the same mid- and long-term ends.

What of the basic conflict raised by the shark, between safety and livelihood? That conflict is not gone. Another shark could activate it. There is a larger point, however. Nasty conflicts are part of life. They can’t be avoided. Through Jaws we get to face such a conflict, and to see it expiated, if you will. That’s the best we can do, no? In the end, we’re dealing in myth, not history, not science.

Where is this going?

I don’t know. It’s just an essay, an intellectual trial balloon. I see three issues, each requiring more discussion than I can give them here:

1. Game theory was devised for the purpose of analyzing the behavior of independent actors? In what way is it sensible to apply it to the behavior of fictional actors who are completely at the disposal of their creators?

2. Given that that is a sensible thing to do, what is the relationship between these three bodies of theory, Lévi-Strauss, Girard, and game theory, in the context of this kind of investigation?

3. How much of Girard’s thought can plausibly be reconstructed or augmented in game theory terms?

On the first issue, I’ve already mentioned it above. It is not unreasonable to assume that we use the same neuro-psychological mechanisms to follow the actions of imaginary people as we use to follow the actions of real people. We surely have psychological mechanisms for regulating our interactions with others. To the extent that game theory sheds light on them, it should be useful in thinking about how we understand imaginary actions as well as in thinking about the real actions of friends, family, and acquaintances. I recommend the concept of vicarious experience that William Flesh develops in Comeuppance: Costly Signaling, Altruistic Punishment, and Other Biological Components of Fiction (Harvard 2007) for insightful discussion of this issue.

On the second issue, one underlying question is whether or not there are analytic and descriptive roles for each of those bodies of thought in the study of imaginary stories, such as those in myths, folktales, novels, and, in the present case, movies (albeit, a movie derived from a novel). It is not at all obvious to me that the kind of work Lévi-Strauss has done on myth can be derived from either or both of those other two bodies of thought. One might, of course, think that Lévi-Strauss’s approach to myth is simply wrong; but that’s a different kind of issue. If his approach is useful, then it is useful and cannot, as far as I can tell, be derived from Girard and certainly not game theory. And so I believe it goes with the others as well.

In particular, game theory is of a piece with the computational ideas that emerged after World War II. As far as I can tell, Girard has not dealt with those ideas at all. Lévi-Strauss has come a bit closer, as I’ve explored in this working paper, Beyond Lévi-Strauss on Myth: Objectification, Computation, and Cognition, but did not quite make it.

That brings me to the third issue, which is what was on my mind when I decided to write this piece. In effect, is Girard a latent game theorist?

I heard Girard lecture about mimetic desire and sacrifice when I was an undergraduate at Johns Hopkins. I read Violence and the Sacred quite carefully when the English translation came out in 1977. By that time, however, I had become deeply enmeshed in the co-called cognitive revolution and Girard did not speak to that. That’s the last time I gave serious attention to Girard until I wrote that essay on Jaws. Now that I’ve finished this essay, I have to wonder whether or not, as I’ve just asked: Is Girard a latent game theorist? I’m not the person to do it, I’ve got other things that are more compelling to me at the moment, but someone needs to think seriously about investigating that question by reanalyzing a collection of examples that he uses.

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