Unless you’re a regular viewer of Numb3rs, you may be wondering what game theory is. Wikipedia has a reasonable description of it, but if you’ll indulge me, I have a specific example I prefer to use. I got it from Discover magazine, but it is also explored here.

In this scenario, 5 pirates have 100 coins to divide up. They have decided on the following immutable terms: a) the most senior pirate gets to divide up the coins however he likes; b) the pirates will all vote to accept or reject the division; c) if the motion passes, the pirates divvy up the coins and get on with their lives, and if it fails, the most senior pirate is executed, the next in line tries again and the process is repeated; d) the most senior pirate holds the tie-breaking vote. Keep in mind as you approach the problem that these pirates each want to collect as many coins as possible, and they are strictly logical; human nature doesn’t affect their decision at all. I’ll just leave that with you for now. The answer will be posted in the comments below.

In a nutshell, game theory says that our behaviour and the decisions we make change based on what we know, what we know other people know, whether we know other people know we know they know we know, and so on. The curious thing about this particular mathematical problem is that it yields a seemingly unpredictable answer. It might seem most “fair” to just give each pirate 20 coins and call it a day, but mathematics doesn’t answer the terms of the question in the same way emotions do. The end result: unexpected outcomes in strategic human behaviour can be derived by following game theory, as opposed to following our ideas of “human nature.”

This lends itself extremely well to certain types of storytelling. Here’s a simpler example of game theory than the pirate example above: imagine there’s a buried treasure, and you and I are both on the hunt for it. If I don’t know you’re looking for it, I will obviously concentrate all my efforts on finding the treasure. Once I discover you’re also looking, my behaviour changes: I decide to take you out, and once you’re safely in the hospital, I can take my time looking for the treasure. If you discover I’m looking for the treasure as well, you may do the same. And then, when you discover that not only am I looking for the treaure, but I’m also trying to disable your efforts, you will be on the alert and become defensive. But it’s not until I become aware that you know I’m trying to disable you that I change my strategy, and instead of trying to ambush you, I return my efforts to simply beating you to the treasure. At each stage, the actions of both parties depend not only on their goals, but their understanding of what the opposing party knows and doesn’t know. The story practically writes itself!

Ironically, a straightforward procedural like Numb3rs doesn’t rely very heavily on game theory. Suspense stories and thrillers, on the other hand, use it often – more and more frequently, I would argue. Perhaps the best example of a show with writing founded almost entirely on game theory is Lost (heavy spoilers ahead). The characters all have secrets – secrets that come out gradually. There are cons, crosses and double-crosses, moles and plants. At every stage of the story, characters simply act in response to the knowledge they have, and then change their behaviour when they obtain new information. They also make unlikely alliances, not unlike the pirates in the example above.

To provide a specific example of game theory in use on Lost, I’ll turn to the character of Benjamin Linus. From the beginning, Ben uses game theory to parse his options. He lies about his identity, knowing that the group taking him in has no way of knowing better. The group responds with distrust, but without proof to contradict him can only hold him captive. When identification belonging to his assumed identity is found, the group’s behaviour changes – Ben’s life is threatened. Ben’s behaviour changes in response: he refuses to eat or speak to anyone. Ultimately, Ben is freed because he has given orders to his allies to kidnap Michael’s son. To obtain the release of his son, Michael agrees to free Ben; obviously, if the rest of the group was aware that Michael was doing the bidding of Ben’s allies, they would have prevented him from freeing Ben. After Michael’s role in Ben’s escape is discovered, it is only because he’s under Ben’s protection that the group doesn’t attack him – another reversal of behaviour in response to new information. Meanwhile, Ben and his allies have established a decoy camp, in order to conceal the real location of their base. Oh, there’s more … but you get the point. Secrets are jealously guarded, then revealed at strategic moments – but even when someone’s secret has been found out, they may not know until that person decides it’s in his interests to reveal that he knows. Who knows what, and when they know it: the flow of information forms the central structure for all the events that unfold in the narrative.

Naturally, this works better with some types of storytelling than others. But anything involving secrets and / or deception, by definition, is to a degree based on game theory. It can be simple – a murderer will lie to cover up his crime. But when the network of secrets and deception becomes more complicated, game theory takes on more and more importance in untangling and deciphering the ways that characters relate to one another.

Secrets and deception … the natural extreme of stories of secrets and deception is, of course, the soap opera. I quote from Channels of Discourse: Reassembled (pp. 111-112 (italics in original, bold added):

“As regular soap opera viewers know, in any given episode there are likely to be several major plot lines unfolding. The text ‘cuts’ among them constantly. The action in one scene might simply be suspended for a time while we look at another plot line. Later in the episode we might rejoin the action in scene one as if no time had elapsed in the interval, or we might join that plot line at a later moment in time.

“The gaps that structure the soap opera viewing experience — between episodes and between one scene and the next — become all the more important when one considers the complex network of character relationships formed by the soap opera community. In a sense, the soap opera trades narrative disclosure for paradigmatic complexity. Anything might happen to an individual character, but in the long run it will not affect the community of characters as a whole. By the same token, everything that happens to an individual character affects the other characters to whom he or she is related.

“When I first began to watch soap operas regularly, I was struck by the amount of narrative redundancy within each episode. One episode of Guiding Light, I remember well, consisted basically of scenes in which different members of the community learned that two couples were about to be married. I could understand why this information might be repeated in subsequent episodes — not every viewer is able to watch soap operas every day — but why was it necessary to repeat it over and over again within the same episode? This is a puzzle only for the inexperienced soap opera viewer. The regular viewer, familiar with the paradigmatic structure of that particular soap (that is, its network of character relationships) will know that who tells whom is just as important as what is being related. Having been conditioned to think of a narrative primarily in syntagmatic terms (what happens when), I did not realize that in soap operas, what happens is important only as it affects the soap’s network of character relationships. Each retelling of the information ‘Skip and Carol are to be wed’ is viewed against the background formed by all the characters’ interrelationships. Thus the second and third retellings within the same episode are far from being paradigmatically redundant.”

Robert C. Allen may not even be aware that he’s describing game theory, but these interrelationships, and the fact that information about events being passed on to new characters is an important development unto itself, can be better understood using game theory.

Suspense and soap operas are not alone in genres that can be analysed using game theory. Comedy is also often predicated on humorous misunderstandings, the French farce being a notable subgenre. Certain episodes of the show Frasier exemplify this structure well. But two simple examples from The Cosby Show come to me off the top of my head.

In the first, Cliff overhears Elvin and Sondra telling Claire that Elvin is planning to ask for Sondra’s hand in marriage. They decide to play a prank on Cliff – when Elvin announces the plan, Claire will pretend to be incensed, and Cliff will be forced to come to Elvin’s defense. Of course, they don’t realise Cliff is listening in. Cliff turns the tables on them, pretending to agree with Claire, going off on Elvin and telling him he’ll never let him marry Sondra. The humour lies in the fact that Cliff knows, they don’t know he knows, and of course we know they don’t know he knows.

Same show, different episode – It’s Cliff and Claire’s anniversary. Claire has put together an extravagant gift for Cliff, so the stakes are high. Cliff prefaces the presentation of his gift to Claire with a story. He tells the story in the third person: the story of a young man, strapped for cash, and his girlfriend, who only wanted a wooden barrette with a glass bead. As much as he loved her, he couldn’t afford to get her the gift, but he promised to get it for her one day. Fast forward to today – he has scoured the country, spent decades looking for this barrette, and now, he’s able to present it to her. It’s very romantic. But Claire is having none of that – she flies into a rage, tearing into the package. “That was not me. That was Eunice Chantilly. I wanted a green plastic bracelet, not this tacky wooden piece of –” She freezes. She looks at what she’s holding in her hand: a green plastic bracelet. She melts, and everyone has a good laugh and Cliff’s touching gesture, and his clever delivery. In this example, unlike in the first, we the audience don’t know that Cliff actually knows the correct item, and is only feigning the error, meaning the final reveal is a reveal to us as well as to the other characters.

Nothing’s ever as funny if you try to analyse it, but it’s certainly interesting to note that game theory can be used to break down comedy as well, if it involves secrets, deception, mistaken identity or hilarious misunderstandings. Shows like Lost, Guiding Light and The Cosby Show require more math skills than I have to fully describe them, but merely knowing that game theory applies even to narrative provides insight into the way these genres of storytelling convey meaning about the unfolding events, the characters, and their relationships.

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