In the world of Westeros, were some people better at the game of death than others?

Game (Theory) of Thrones

SPOILER ALERT: This article contains show spoilers for Game of Thrones. It also includes information from the novels.

Game of Thrones is more than simply a thrilling television show full of action, drama, fantasy, and suspense. It’s also a startlingly accurate representation of politics and violence in impoverished countries.

When you play the Game of Thrones, you win or you die — there is no middle ground.

The above quote by Cersei Lannister suggests that the Game of Thrones is a zero-sum game but, is it really true? Let’s find out.

CERSEI LANNISTER V/S NED STARK

To demonstrate the game theory’s power, let us return to one of the very first conflicts that triggered the sequence of events that led to the pandemonium that transpired later in the story: the death of Lord Eddard Stark. In season 1, before King Robert’s death when he was out hunting, Ned Stark (show’s initial protagonist) confronts Cersei Lannister (show’s antagonist) about her incestuous relationship with her twin brother Jamie Lannister and how Joffrey is not the true heir to the throne.

Ned now has two options before him: One, he can reveal Cersei’s secret and hostility towards the Lannisters but risk his family’s safety (because both his daughters are in Cersei’s care). Or two, he does not choose to reveal the secret which will ensure his daughters’ safety at the cost of his honor. Cersei, on the other hand, now that she knows that Stark understands that Joffrey isn’t the lawful heir to the kingdom, has two easy choices: whether to place Joffrey on the throne or not, with risk the impending insurrection led by Ned.

Thus, there are four different scenarios that can unfold once both players make their decision.

• If Ned reveals the truth and rebels against the Lannisters while Cersei names Joffrey king. This would be the worst-case scenario for Ned because even though he retains his dignity, he risks his and his family’s safety. And not to mention that he becomes an adversary of a cruel king like Joffrey, who will be the most powerful man in Westeros (the seven kingdoms) at that time.
• If Ned reveals the secret about the Lannisters and Cersei confesses to her crimes and installs the legitimate successor Stannis on the throne. It would be a horrible outcome for the Lannisters because they would have lost all the power. Ned will be in a much better position, but his family would still be in danger from Cersei and Tywin Lannister.
• A more ideal scenario for both the players is if Cersei makes Joffrey king and Ned doesn’t reveal the truth and maintains good connections with the Lannisters in the near run, at least until he saves his family. But Ned loses his honor in return. Cersei gets her wish, with Joffery being proclaimed King.
• A rare but preferable scenario can be if Ned doesn’t reveal the truth but Cersei names Stannis (the rightful heir) the king. It is the best scenario for Stark as he saves his family as well as his honor. Cersei, on the other hand, in the future can overthrow Stannis and make Joffery king but for once have to sacrifice the throne.

The pay-off matrix below illustrates the game:

The first conclusion we can draw from this pay-off matrix is that this isn’t a zero-sum game as we assumed from Cersei’s quote. Due to a multitude of considerations such as honor and family being considered in assessing the amount of these payoffs, the payoffs of Ned and Cersei do not add up to zero.

And if we further analyze the pay-off table, we can see that Cersei should always make Joffrey king, regardless of what Ned does, and Ned should never rebel against the throne, regardless of what Cersei does. Thus, Nash Equilibrium exists at this condition. But in reality, Ned Stark chose honor over his and his family’s lives and safety, and as a result, he was beheaded. As he was unable to recognize and adapt to the dominant strategy, he can not be considered a good player of the game. Cersei, on the other hand, showed herself to be a better player by choosing the best approach for her.

LITTLEFINGER: THE EQUILIBRIUM BREAKER

Initially, the great three houses (namely, Stark, Targaryen, and Lannister) were at a Nash Equilibrium (living together in peace) linked together with marriage and devoted allegiance to one another. Littlefinger, on the other hand, is able to turn the houses against one another and wage battles without ever setting foot on a battlefield by murdering Jon Arryn, leading Ned Stark to the South, and inciting tensions between the Stark and Lannister families.

He was one of the most fundamental and pivotal players in the struggle for power whose strategy contains a significant amount of strategic fabrication. He was aware that he was functioning in a system filled with inconsistency and noise. Thus, he has a “non-stationary” strategy, which means that not only each action in each round but also the rule for selecting each action varies from round to round. This strategy allowed him to cast aside the prescriptive standards of behavior, whether it’s the Starks’ Moral Absolutism or the Lannisters’ tit-for-tat strategy. Non-stationary strategic players draw on their previous experiences as well as evidence obtained from other players’ actions in previous rounds to form opinions about their future options. This is the reason why Littlefinger is just as likely to cooperate in the face of cheating as he is to retaliate in the face of a long history of collaboration. He has proven to be adept at always cheating in the last round after a long chain of cooperation, which is one of the clear advantages of using this shifting tactic. We see in the last round that Joffrey Baratheon, Dontos Hollard, Lysa Arryn, and Ned Stark were all betrayed by him.

Lord Petyr Baelish (aka Littlefinger)’s policy can be stated as:

1. If you believe me, I will betray you.
2. If you don’t believe me, I will not betray you.
3. Once you start believing me again, I will not betray you.
4. And when I have gained your confidence and you still believe me, I will betray you.

His game plan against both Starks and Lannisters can be easily summarized using the following pay-off table:

His strategy corresponds to the remarks he made in Season 7:

“Sometimes, when I try to understand a person’s motives, I play a little game. I assume the worst. What’s the worst reason they could possibly have for saying what they say, or doing what they do? Then I ask myself, ``how well does that reason explain what they say and what they do?”

Littlefinger’s keen eye for uncertain payoffs and interest in conflicts, as well as the reality that Nash Equilibrium (in this case, peace) does not always reflect each individual’s optimal interest, allowed him to shatter the equilibrium between the three houses. Due to this strategy and his knowledge of game theory he could:

• eliminate his possible opponents one by one.
• create tension and conflicts between the remaining players (or houses).
• acquire other players’ confidence and boost his power.

And before you know, you have been littlefingered.

DAENERYS STORMBORN V/S CERSEI LANNISTER

When Daenerys comes to understand that there is an army of dead marching forward ready to annihilate mankind, she joins hands with Jon Snow to kill the white walkers. She recognizes that in order for everyone to live, they must put their differences aside and work together. Daenerys offers a truce despite having a tactical edge over Cersei. Thus, in the last episode of the penultimate season of the series, we see a council meeting where Jon and Daenerys redeem themselves as negotiators. Now both the queens (Daenerys and Cersei) have two options; they can either co-operate and join forces or betray each other.

As a result, once both of them have made their decision, four possible situations can develop:

• If both of them join forces: This would be the ideal scenario for both the players because they would then defeat their common enemy. They would then be at odds with each other again and would have an equal chance to capture the throne.
• If both of them betray one another: In this scenario, The Night King will divide and conquer and both the queens will lose. It is worth noting, though, that Cersei is the character who would rather see the kingdom crumble than surrender the throne to Daenerys. Thus, from this mutually guaranteed devastation Daenerys suffers loss whilst Cersei doesn’t.
• If Cersei co-operates but Daenerys betrays: In this strategy clash, Cersei loses everything including the throne to Daenerys. Daenerys is almost certain to assassinate her and then utilize Cersei’s armies to assist in combat against the undead.
• If Daenerys co-operates but Cersei betrays: In this last scenario, Daenerys loses everything. However, Daenerys has demonstrated a willingness to make sacrifices for the greater good, implying that she might find it useful to hold back the undead if it meant that those she cared about may live.

According to these scenarios, the following pay-off table can be devised:

If we analyze the pay-off table, we can see that Cersei should always betray Daenerys regardless of what Daenerys does. Thus, she has a dominant strategy of betrayal. On the other hand, Daenerys has no such dominant strategy.

If Daenerys had spent more time analyzing Cersei’s decision-making process, she would have known that any attempt at negotiation was doomed from the start to the Betray/Teams Up Nash Equilibrium. With this combination of methods, neither player gains by just modifying their own decision, which is why it is the equilibrium. But she ultimately chose her heart over her head and was duped. Cersei realizes that betrayal is her dominant strategy, and in the season’s finale, she reveals that she simply lied to Daenerys about her willingness to aid. Thus, Cersei once again proved to be a better player.

A LANNISTER ALWAYS PAYS HIS DEBTS

Tit-for-tat is a strategy that can be used in games with repeated plays or a sequence of games that are similar. The concept of tit-for-tat states that if two players work together, they will be more successful. Players that use the tit-for-tat approach start the game by cooperating in the first round, then simply repeat the actions of the other player in subsequent rounds. The principles of revenge and altruism are at the heart of this technique. When confronted with a dilemma, an individual cooperates when another member has previously cooperated and defaults when the opponent has previously defaulted.

“A Lannister always pays his debt.”

This is an excellent illustration of this tactic. This technique is the center of the Golden Rule and also finds its affirmation when Tywin Lannister advises Joffrey:

“Joffrey when your enemies defy you, you must serve them steel and fire. When they go to their knees, however, you must help them back to their feet. Elsewise no man will ever bend the knee to you.”

The tit-for-tat strategy may have the impressive benefit of setting up an unending game of cooperation, but it is also vulnerable to a terrifying chain reaction of revenge, where neither party ever forgives the other’s decision to cheat. This flaw of the strategy is accentuated when two players are operating in a system that allows for ‘noise’. Noise is a signaling error in which one player’s cooperative move is incorrectly seen by the opponent as cheating.

According to the pure tit-for-tat strategy, if player 2 misinterprets a cooperative move as cheating, he will retaliate by cheating, setting off a chain of non-cooperative interactions that will last the rest of the game. In the world of Game of Thrones, in Westeros, two or more self-interested parties unite and promote exactly this kind of noise, as other parties urgently strive to inject themselves into other games, hoping to disrupt the signal between two otherwise collaborating players.

As a matter of fact, the fundamental source of discord between the Starks and Lannisters was a systematic signaling error. Jamie’s cooperative moves in executing the mad king were wrongly interpreted by Ned Stark as treason motivated by vengeance.

FORGIVING TIT-FOR-TAT STRATEGY

By devising a method that allows for a fixed number of betrayals before revenge is punished by revenge can be the only way to solve the tit-for-tat strategy’s flaw which is miscommunication and ‘noise’. One such technique is forgiving the tit-for-tat players in order to stop the loop of revenge. It is called the “forgiving tit-for-tat” strategy which Starks frequently uses and was more than often botched. This tactic, on the other hand, leaves the forgiving player vulnerable to exploitation by a pure tit-for-tat player.

Thus, it can have disastrous consequences as if the forgiving player is induced to give a perceived defector a second chance, as Ned Stark did with Littlefinger, or assume that other players are also using the forgiving strategy when they are pure tit-for-tat players, as Rob Stark was with Walder Frey.

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References:

1. https://blogs.cornell.edu/info2040/2017/09/19/game-theory-in-game-of-thrones-season-1/#:~:text=The%20article%20quotes%20a%20famous,Lannister%20can%20win%20the%20game.
2. https://medium.com/@mayurajaysaxena/lord-petyr-baelish-a-game-theoretic-explanation-fad763cc296#:~:text=Baelish's%20policy%20is%20simple%3A,I%20will%20not%20betray%20you.
3. https://www.theverge.com/2019/4/29/18522103/game-of-thrones-got-season-8-hbo-final-battle-of-winterfell-daenerys-targaryen-cersei-lannister
4. https://www.livemint.com/Opinion/f4y0unB6m7fCBOFEE3QiFI/How-not-to-negotiatethe-real-Game-Of-Thrones.html