“Game theory is about how people cooperate as much as how they compete... Game theory is about the emergence, transformation, diffusion and stabilization of forms of behavior.” — Herbert Gintis
This quote is an extract from Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction (2000).
Dear Traders, Friends, and Colleagues: Happy Sunday!
Thank you for the overwhelming support on my previous work; I think it was a record article. It seems you enjoyed the podcasts list, so I’ll share more materials like this in the future when the occasion presents itself.
Today, I want to discuss with you Game Theory and my current work on this topic. Before being a trader, or a programmer, I’m a mathematician by formation. I learned about Game Theory in school more than a decade ago. Funnily enough, I never tried to implement it in my trading research. Why? I don’t know. But I feel that now is the time to start this new chapter. That is another reason I love trading so much.
In which other disciplines could I be so excited to start from 0 again, with so much to learn, even though I’m already learning new skills every month?
What is Game Theory?
Game theory is a branch of mathematics that studies strategic decision-making. It provides a framework for analyzing situations in which multiple parties, called players, make decisions that influence one another. Game theory has applications in many fields, including economics, political science, psychology, and everyday life.
The history of game theory can be traced back to the 18th century, with the work of Swiss mathematician Leonhard Euler on the theory of cooperation and competition. However, the modern study of game theory is usually considered to have started with the work of John von Neumann and Oskar Morgenstern, who published the book "Theory of Games and Economic Behavior" in 1944. This book introduced the concept of a "zero-sum game" in which the other player's loss exactly balances one player's gain.
Since the publication of von Neumann and Morgenstern's book, game theory has significantly developed and become a highly influential field. It has been used to analyze a wide range of phenomena, including auctions, negotiation, and voting. Game theory has also been applied to studying biology, computer science, and international relations.
The Prisoner’s Dilemma
One well-known example of game theory is the "Prisoner's Dilemma." This is a scenario in which two prisoners are being held by the police and are being offered the following deal: if one prisoner confesses to the crime and the other remains silent, the prisoner who confesses will go free while the other one serves a longer sentence. If both prisoners confess, they will both serve shorter sentences than they would have if they had both stayed silent. If both prisoners remain silent, they will both serve a shorter sentence than they would have if they had both confessed.
In this situation, the prisoners are faced with a dilemma: if one prisoner confesses and the other remains silent, the first prisoner will go free while the second one serves a longer sentence. However, if both prisoners confess, they will both serve shorter sentences than they would have if they had both stayed silent. The optimal strategy for each prisoner is to confess since this will result in the shortest possible sentence.
However, if both prisoners confess, they will both end up serving longer sentences than they would have if they had both remained silent. This illustrates the concept of a "non-cooperative game," in which the optimal strategy for each player is to act in their own self-interest, even if this leads to a worse outcome for both players.
Of course, what matters to us is the application of Game Theory to Trading.
Game Theory Applied to Trading
Before I start this chapter, I want to caveat that I’m very new to the world of options, having started just at the beginning of the year. I had absolutely no prior experience except the mathematical theory behind it that I studied in school with the Black & Scholes formula. Fun times. I’m just sharing my progress, mistakes, and projects I’m building along the way.
I decided to approach Game Theory applied to Trading through the lens of options.
All credit to @DoubleWideCapital, who sparked my curiosity a few weeks ago with this post.
A more detailed explanation is available here for those of you who are interested: Perfiliev's article on Gamma Exposure.
As you know, I’m exclusively trading $NQ (except for swings on cryptos from time to time, without too much success so far). Therefore, my work on Game Theory and options is focused on QQQ 0.00%↑ and $NQ. I will share a few theories on some stocks like TSLA 0.00%↑ and AAPL 0.00%↑ , though, as I want to have more data points to test my assumptions in the coming months.
First, some definitions.
QQQ 0.00%↑ is the ticker symbol for the Invesco QQQ Trust, which is an exchange-traded fund (ETF) that tracks the performance of the NASDAQ-100 Index. The NASDAQ-100 Index is a stock market index that consists of the 100 largest and most actively traded non-financial companies listed on the NASDAQ stock exchange.
$NQ is the ticker symbol for the NASDAQ-100 Index. The Invesco QQQ Trust is designed to track the performance of the NASDAQ-100 Index, so the value of QQQ is closely related to the value of $NQ. If the value of the NASDAQ-100 Index goes up, the value of QQQ is likely to go up as well. Conversely, if the value of the NASDAQ-100 Index goes down, the value of QQQ is likely to go down as well.
I started by adding a new module to @Alfred: Options.
I now have Futures, Stocks, and Options. Quite cool to see the progress over the last couple of months of work. It’s definitely worth it, as it allows me to gather and process information much more quickly than if I did it manually.
On the 8th of January, I extracted the Open Interest by strikes for QQQ 0.00%↑ for the 13th of January (the following Friday). You can see the puts in red and calls in green. I also added the previous closes with the vertical dashed lines.
The way I interpret it, and chances are I’m wrong, is that most options will expire worthless if we close between 260 and 270. From the perspective of $NQ, it would mean closing within the 10800-11100 range.
I developed a homemade formula calculating the max pain areas on $NQ based on the options analysis from QQQ 0.00%↑. My goal for the next few weeks is to test it live. Here's what I posted on the 7th, and here's what happened during that week.
Here’s what happened the following week.
Results: One of the strongest weeks in months as we completely broke out of that range.
Of course, I won’t conclude with one observation; I’m just learning by trial and error. It’s fun, and you should try it too.
This article is simplified, and I have a lot to learn in this field; we can all have our definition of “game theory”. To me, it’s about reacting to areas where most players are hurt—one of my core principles for my reversal strategies.
I often receive messages on how I find strategies through programming. Well, that’s exactly how I do! Research, Learning, Coding, Thinking. Repeat.
I hope you enjoyed this article because I loved writing it. I’ll see you next Sunday.
It would really mean a lot if you could share this article. One of my goals for 2023 is to have 5,000 subscribers on this Substack, and I would be grateful if you could help me grow it.
Until then, stay safe.
- Retail
PS: I had a few people reaching out to me on Twitter asking why they were not receiving my emails anymore.
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Thanks for the write-up. The options positions in SPX dwarf those in the various NDX instruments. Since NDX is strongly correlated to SPX, such analysis should perhaps better be done on SPX.