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A Game Theory of Thrones

Is the game of thrones a zero sum, positive sum, or negative sum game?
April 12, 2015, 12:00pm
​Stark versus Lannister: round one. Image: Kyle McCoy

​SPOILER ALERT: This article contains show spoilers from season one to season four of Game of Thrones_, and includes preview videos of season five._

The epic juggernaut that is Game of Thrones will return for its fifth season tonight on HBO, and its many millions of fans could not be more stoked. Few television series have ever cultivated such a massive and enthusiastic fanbase, which is currently about 18.4 million strong and with every season grows stronger—House Tyrell style.

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One of the main reasons that Game of Thrones has become such a cultural phenomenon is that George R. R. Martin's world has a little bit of something for everyone. Fantasy fans get sorcery, shadow babies, and increasingly rebellious dragons. Horror fans get frequent bloodbaths and suspenseful glimpses of the undead. Romance fans get a variety of star-crossed love plots destined to end in tragedy.

But perhaps Martin's greatest strength—and by extension the show's most compelling hook—is portraying the brutal economy of politics. The characters in Game of Thrones may inhabit a fantastical universe, but their moral compasses and tactical decisions grant them a certain verisimilitude, or a Stephen-Colbert-style "truthiness," if you will.

Because of the story's overall plausibility, it is easy to apply game theory scenarios to the world of Game of Thrones as one might to real world situations.Indeed, the very title of the show derives from Cersei Lannister's warning to Ned Stark that, "in the game of thrones, you win or you die—there is no middle ground."

Cersei lays out the ground rules to the game of thrones. Image: YouTube/GameofThronesquotes

Here, Cersei is spelling out one of the fundamental games of game theory: a zero sum game, in which there can only be one winner and one loser. Sadly for Stark fans, Ned learns the truth of Cersei's words the hard way, and it seems that the Lannisters have won the game at the end of the show's first season.

Blogger Ben Sweeney wrote a thought-provoking essay about this zero sum game in 2012, in which he deconstructed the game theoretical tactics of the Starks and the Lannisters, and suggested that the dichotomy between family honor and family shame in Westeros is its own macro zero sum game.

But now that we are a few more years along in the plotline, it's time to question whether the game of thrones really is a zero sum game. Maybe it can be viewed this way on a short timescale, but if you widen the aperture to include the latest seasons, it's clear that game winners often experience extreme reversals of fate—Tyrion or Tywin Lannister are pertinent examples.

Sneak peek of Tyrion and Varys's whereabouts in season five. Image: HBO/GameofThrones/YouTube

Additionally, the whole ominous mantra that "the North Remembers" seems to suggest that while many individual Starks are off the board, House Stark as a whole remains in the game.

One of the main points that Sweeney makes in his essay, for example, is that the Lannisters have very little family solidarity compared to the Starks. In fact, there is outright hatred between key players like Joffrey, Tyrion, Tywin, and Cersei. Accordingly, the Lannisters mostly play the game as individuals, and from the perspective of the more united Starks, that makes their game inherently negative sum—meaning that there will only be losers at the end.

Given that season four ends with a very publicly fractured House Lannister, that perspective may well yet be validated. And while the high Stark death toll has been grueling to watch, it does make the family ripe for martyrdom. Surviving Starks like Arya, Sansa, Bran, Jon Snow, or feral Rickon could find themselves harnessing and riding that tide of Northern vengeance like their very own populist dragon. In this scenario, the Lannisters may win the zero sum battle, but the Starks win the zero sum war.

Of course, none of these speculations account for the many other major forces in the show and books, like the upstart Tyrells, the White Walkers, the involvement of Dorne, or those winged WMDs across the Narrow Sea. That's why my own personal "game theory of thrones" is that the fight for the Iron Throne will be an entirely negative sum game. Forget who is sitting on the Iron Throne at the end—I'll be disappointed if there even is an Iron Throne left in the ashes.

I think Martin is gleefully nihilistic enough to consider this route, though it's possible he will instead opt for a positive sum game, in which multiple forces rule together. The Game of Thrones fan community often vaults up Jon Snow and Daenerys Targaryen as potential future allies, though that partnership seems a little too obvious. Regardless, it's fair to say that the jury's still out on whether the overarching game of thrones is zero sum, positive sum, or negative sum.

Of course, there are also loads of other interesting game theory scenarios embedded throughout the Game of Thrones universe, including a few instances of the so-called "stag hunt game" (which shall be hereafter be known as the official game of House Baratheon).

House Baratheon video roundup. Image: HBO/GameofThrones/YouTube

The stag hunt game is a kind of a reverse prisoner's dilemma, in which two cooperating players will receive a bigger joint payoff if they work together than they would if they worked separately.

The idea is that two players have to individually decide whether to hunt a stag or hunt hares. If both choose to go stag-hunting, there will be a bigger total payoff of meat for everyone, but it will require both players to down one. If one chooses to hunt hares and the other chooses to hunt stag, the hare-hunter will end up with a better payoff because hares can be caught by only one hunter, whereas stags require two.

In a way, the Red Wedding was itself the result of a stag hunt scenario, albeit a three-player one. Walder Frey, Roose Bolton, and Tywin Lannister could have continued to work separately in consolidating their power across smaller regions—chasing hares, as it were. But by throwing in their lot together, these three centers of power end up with a bigger total payoff by killing off the Stark leadership in one fell swoop.

An even more straightforward example pops up in "Walk of Punishment," the third episode of season three. Robb Stark has instructed his uncle Edmure Tully to wait for Gregor Clegane's forces to come to Riverrun, but when Clegane seizes the nearby fortress of Stone Mill, Edmure takes the fight to him, and delivers a decisive winning blow.

Though this seems like a stag win from Edmure's perspective, as it turns out, he has only caught the hare. Robb's plan was to purposefully lure Clegane into the west and cut his forces down guerilla-style, but the Battle of Stone Mill instead allows Clegane to escape and head back east. This is a pretty cut-and-dried example of the stag hunt in narrative action, and a great excuse to re-watch Edmure Tully getting verbally eviscerated.

Judging by the previews to season five, it appears that Daenerys Targaryen, collector of magisterial titles, may even have her own stag hunt in the works. "I'm not going to stop the wheel," she declares confidently in the below trailer. "I'm going to break the wheel."

Game of Thrones season five trailer. Image: HBO/GameofThrones/YouTube

Daenerys is clearly declaring herself a stag-hunter with that statement. But her problem is going to be finding someone to play that game with her, because it takes more than one player to nab a stag. Will Player No. 2 end up being Tyrion Lannister? A redeemed Jorah Mormont? The budding assassin Arya? The rogue dragon Drogon? Perhaps we'll find out over the next ten weeks.

Dozens of other game theory scenarios can be spotted in Game of Thrones, from Jaime abandoning Brienne in a Bolton-themed prisoner's dilemma (which he later gallantly reneges on) to the fact that the War of the Five Kings represents a brutal war of attrition scenario. Let's not even get started on all the assurance and trust games Petyr Baelish is simultaneously playing, or what Varys's "little birds" will turn up next, because that is a whole other level of gameplay.

Regardless of how the chips fall, it's clear that Cersei's initial assessment that the game of thrones only has two outcomes—win or die—is clearly breaking down at this point. Tywin's fate demonstrates that you can win and die, and Daenerys is intent on doing this (╯°□°)╯︵ ┻━┻ to the game table.

Clearly, the fight for the Iron Throne is sure to be remain bloody, brutal, and packed with gratuitous nudity and plot twists. I cannot goddamn wait.