Decisions Matter: Game Theory
in Billions – Part II

In case you missed Part I, you can see it here.

We are getting into more intricate territory in Season 1 Episode 6 The Deal with Wendy now getting involved in the game with her two boys! 😀

Paul Giamatti, Maggie Siff and Damian Lewis at a Billions photo shoot at TCA 2017

Costly Signaling

We see Bobby playing a textbook signaling game in The Deal like Chuck does in The Pilot. He invites Wendy to a meeting at a very unusual spot: A spa pool. Bobby wants to make sure no one is listening but also, and more importantly, wants to find out whether Wendy is loyal or not. We know where Axe stands on loyalty from what he said to Mafee earlier: “You don’t try to be loyal. You just are. Or you’re not.” It is loyalty that rules Bobby Axelrod’s billions.

Axe stacking the cards against Wendy to test her shows he wants to trust her. Wendy’s value to the firm and to Axe is absolute. Her “bold statement” of “I have built this company as much as you did” is a “true statement” and Axe cannot drop her like, say, he drops Victor. There are many Victors. There is only one Wendy. So Axe sets up the game and reasons if Wendy does not meet him in her birthday suit, she is not to be trusted; if she does, she is willing to pay a cost to show him she is loyal.

Why would meeting Axe at a spa pool be costly for Wendy?

It is costly not because she is getting into a pool naked with her boss. If I can think of a possible photo/video opportunity there, Wendy can, too! That is why one may see Wendy meeting Axe naked as an “out of character” behavior for her. But, no, this is pure Wendy: she knows this is the only way she can get her message across to Axe: “I am loyal.” So is her job THAT important to her? Hell yes. Her answer to Axe’s “Why are you still sticking around?” speaks volumes: Wendy believes she has built Axe Capital as much as Axe has. She found meaning in putting him together when his world was completely shattered. She still does. THAT IS why she is here: “Meaning matters to me more than happiness.” In other words, meaning gives her more happiness than happiness itself.

The bond between Axe and Wendy is very intriguing thanks to the simultaneously sincere and strategic nature of their connection. You may like my four-part series scrutinizing this special relationship.

Zero-sum and Non-Zero-sum Games

Wendy is a rational player. She makes the decision that would benefit her the most after doing her own cost/benefit analysis and taking into account what others might be doing.

And that is WHY she opens “the book on Axe” to Chuck as the latter plans the plea deal his office would make with Axe. Wendy tells Chuck that not giving Axe a small win will only make him play a different game with rules unknown. Axe may get out of it with a loss but makes the other side suffer even more:

source: Showtime

“Axe comes from nothing. So he unconsciously fears, no, he may even expect, that he’ll have nothing again.”

Wendy advises Chuck not to play a strictly competitive zero-sum game with Axe. Two actors are in a zero-sum game if each participant’s gain or loss is exactly balanced by the losses or gains of the other participant. That is, one is a winner while the other is a loser. Think of the plea deal as Axe and Chuck cutting a cake. Wendy basically advises Chuck to give Axe a slice while he himself gets the rest of the cake.

source: Showtime

Chuck seems to be listening at the moment; however, he does exactly what Wendy tells him NOT to do at the deal table when Axe and Wags chat about the fee not being a shark bite, not a bee sting, not even a horsefly, and maybe a red ant that cannot ruin the picnic.

source: Showtime

By agreeing to get into a plea deal, Axe comes to the table with the biggest check ever written to the US government for insider trading fees. He knows Chuck is getting the big chunk of the cake but he will have a slice in the form of home office. This is his small win. BUT when Chuck declares out of blue there will be no family office for Axe and he will not be able to manage even his own money, he tears the check and leaves the table. No cake. No deal.

As Wendy rightly guesses, Axe will now set up his own game with rules unknown to Chuck. The name of the game will be “Donnie.”

Finite Timeline

What lies at the center of The Donnie Game revealed in Season 1 Episode 10 Quality of Life is finite timeline.

source: Showtime

It is Donnie’s pancreatic cancer that catalyzes Axe’s new game plan. He knows the US Attorney’s office will leave no stone unturned until they find some insider trading on him. So why not having Donnie give them a true story bit by bit knowing he would not live long enough to testify against Axe? This way, Axe will stop the US Attorney’s Office from looking elsewhere and it will also make Chuck look like an idiot in the end. Two birds with one stone.

source: Showtime

I know. This seems like a pretty cold-hearted play: Axe is basically using a sick man, a man that has been loyal to him for years, to save his ass. You may call Axe a predator. But you may also call him a rational man. Offering his sick friend an option to leave the world in peace. Axe is not tricking Donnie. What he is doing is just to keep his own quality of life (the title of the episode) and provide an equally good quality of life for Donnie’s family when he is gone. You may call Donnie a victim. But you may also call Donnie a rational man. He knows he is dying and he is making a deal with the boss to guarantee a “game changer” for his family… Remember how Walter White starts his “blue” business in Breaking Bad? People may do things that they are not proud of just to make sure their families are okay after they are gone. It is rational. And it is painfully human. Donnie wants his family to be taken care of. Axe is giving him that. I would call this a win – win situation with the hope that I do not sound like an insensitive asshole. I am just a game theorist that believes in rational choice.

Suppose Donnie knew his options: dying soon with his family receiving $50M from Axe and living for a few more months with his family receiving no money. Given that he is a rational player, I believe Donnie would choose the first option. And I think this is the calculation Axe does on behalf of Donnie when he tells Dr. Gilbert they may not want to share with him the information about experimental treatment that could give him a few more months. That said, this is playing God on Axe’s part. Donnie has the right to have access to the information and, even though I believe his calculation would be the same as Axe’s, he should be able to make his own decision.

When I told Mr. Koppelman and Mr. Levien at Billions PaleyLIVE that, as a game theorist, I was very impressed about how they use game theory in the show, Mr. Koppelman teased me saying I already told him that and he was glad to see I was still impressed! And, believe me, Damian was about to fall from his chair laughing 😀

I am thrilled to report I am still behind my words after Season 2!

Commitment Problems

Season 2 opens with the two leads having  what we call commitment problems in game theory. A commitment problem is a situation in which people cannot achieve their goals because of an inability to make credible threats or promises.

Knowing that he bent quite a few rules in the Axelrod case, Chuck is concerned that one of his Assistant Attorneys (AAs) may feel the urge to talk to Oliver Dake who is investigating his office’s methods of conduct. So when the head of criminal prosecution at the Southern District leaves public service for a 7-figure salary, Chuck makes it clear to his AAs that the Head of Crim job is now within their reach.

source: Showtime

Using a chess game in which his opponent cheated as a metaphor, Chuck tells them his constructive approach towards the cheater ensured that the cheater would not cheat again. So they can side with the cheater, ahem, Chuck (constructive approach) and one of them can be awarded Head of Crim job or they can side with Dake (destructive approach) and deal with Chuck’s replacement.

Bryan asks the key question:

“How do you know he did the right thing after you left?”

This is Chuck’s commitment problem. It is hard for him to convince Bryan because Chuck cannot make a binding promise that he will not bend the rules again. My advice for Chuck at the time was to delay filling up the  position, if possible, until the end of the investigation to make sure the AAs stay loyal  believing they have a real shot for the job. Chuck did exactly that and appointed Kate as the Head of Crim once he was sure he owned Dake.

Axe has a similar commitment problem with Wendy. Axe, after gloriously blowing their relationship in Season 1, shows up at Wendy’s new digs at the beginning of Season 2 to apologize and tell her he needs her back at Axe Capital.
The commitment problem is Axe cannot make a binding promise  that he will not do wrong with her again. When Wendy shows him the finger, Bobby sets up a new game to corner her: Bringing up law suits against Chuck only to drop them when Wendy makes it a condition to return to Axe Capital Motherfucker indeed. And a very smart one at that.

Optimal Play 

Well, I could not be happier that a game theory term makes it to the title of Season 2 Episode 3: Optimal Play. Optimal Play, also known as Best Response, is the strategy that produces the most favorable outcome for a player, taking into the account the strategies of other players in the game. While the Alpha Cup Poker tournament, which I will talk about in detail here, sits at the heart of this episode, my recap of this particular episode talks about several characters, from Kate to Lara, making their optimal play in different contexts.

source: Showtime

Axe, who holds a grudge against Todd Krakow who has been trying to recruit Wendy, finds his secret weapon to break Krakow at the poker table: Taylor. Axe has a feeling, pulls up their resume and finds out Taylor was a multi-table poker prodigy, 16 tables at a time, in high school. They played live with students as well as professors in college, too. Axe wants to rely on Taylor’s game theory strengths but he cannot convince them to play. However; when he finds out Wendy will be coaching Krakow at the poker game, he facetimes Taylor to let them know they are playing for Axe Capital at the Alpha Cup.

I do not play poker, but I know how relevant it is to game theory. You are holding a hand, and what you play is not just based on your own hand but on your opponent’s hand as well as their play. But you obviously do not see their hand. So what you do is to try to “read” your opponent, understand what kind of player he is, form beliefs about their hand and predict what play they will make based on that hand. And you give your best response to THAT. You also know every play you make is a signal to the other side about you as a player and so you need to mix up your play and not let your opponent “read” you. It is about probability. It is about information. It is about strategy. It is about optimal play.

Billions makes it as authentic as possible with (at least) two professional poker players, Phil Hellmuth and Brandon Cantu, plus extras with poker experience. And, hey, we would not expect anything less from Koppelman and Levien, who gave us Rounders! I watched it again before Season 2 hit our screens and one quick connection is Texas Hold’em. If you want to learn the rules, this little video is quite helpful.

Shuffle and Deal! Axe wins against Jim “China is a pig on LSD” Chanos where as he loses to Krakow. I do not think Axe deliberately loses to him but he collects information about him as a player and strategically plays to his high confidence levels to double the wager and make him sit against Taylor who wants to be THAT biker who takes their hands off the bike and let the others ride on by.

Krakow does not give Taylor the opportunity to be THAT biker. I agree with Axe that, yes, they were probably not nice to Krakow when he was a kid, but even then, he should have started it! 😀 Krakow’s inability to control his anger makes him an easy read, and when one reads their opponent, they do not need the best hand to win. This is what you get from Taylor for being a bully, Todd.

source: Showtime

The most impressive game we have seen in Billions is, hands down, Chuck’s long game in Season 2. We will talk about it next week along with what kind of strategic games we may expect in Season 3.

Next: Decisions Matter: Game Theory in Billions – Part III

Author: Damianista

Academic, Traveler, Blogger, Runner, Theatre Lover, Wine Snob, Part-time New Yorker, and Walking Damian Lewis Encyclopedia :D Procrastinated about a fan's diary on Damian Lewis for a while and the rest is history!

4 thoughts on “Decisions Matter: Game Theory
in Billions – Part II”

  1. Love this – can’t wait for part 3. Also – any idea if they will hold another event like PaleyLIVE! I would make the trip up from DC to attend if they did.

    1. Thank you for reading! I really love talking about The Donnie Game in particular. I have no idea if there will be any event before Season 3 premiere. Fingers crossed! They usually announce it way earlier, like a few weeks ago, on Twitter and other social media outlets. But we will roll the drums if we hear anything!

  2. I had pending reading this. It’s great as usual. I love the way you dissect everything and cleverly relate each math to each chapter, making it look like it is easy and obvious. I insist, I would love to have you as teacher.
    By the way I once tried playing poker, but my problem is not reading others, is masking my very own emotions! 😉

    1. Thank you for your kind words! Part III, the last one in the series, is coming tomorrow. I have just finished writing it.
      You are absolutely right. It is not only about you reading your opponent but also you should not let your opponent read you. You should have poker face! 🙂

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