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Game Theory

Game Theory in Trading – The Science of Decision-Making

Game Theory helps us better understand how rational people navigate social situations and make decisions when the stakes are high. But what does it have to do with trading the markets? More importantly, how can improved decision-making help you become a better trader?

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What is Game Theory?

Game theory seeks to explain the mathematical and psychological factors driving the decision-making of independent actors in a competitive setting. 

The concept is based on the premise that rational players in a game or a situation aim to maximize their payoff and minimize their losses. It also looks at how these players make decisions in response to the different strategies employed by their competitors. The results of these analyses help predict human behavior in a strategic setting.

Origins and Development

In their book Theory of Games and Economic Behavior, scientists John von Neumann and Oskar Morgenstern explored how game theory can be used to better understand changes in the economy. The book was published in 1944. Neumann also applied some of the methods of game theory to his predictions about World War II using a mathematical model to deduce the victory of the Allies forces. 

In the 1950s, mathematician John Nash further developed the idea of game theory as a model that can be used to understand the results of situations where multiple factors can influence an outcome. He introduced the Nash equilibrium – a concept where a game’s optimal outcome is one where players have no incentive to deviate from their initial strategy after considering an opponent’s choice. The 2001 movie A Beautiful Mind tracks the life of John Nash (played by actor Russel Crowe). 

Game theory has proven incredibly far-ranging and has even been widely utilized across various social and real-world situations that have nothing to do with games. These include military tactics, politics, economics, and more. 

At almost every turn, we find ourselves in social situations that require us to make the right decisions to achieve our goals. As famed poet Charles Lamb so aptly put it in his ‘Essays of Elia’

“Man is a gaming animal. He must always be trying to get the better in something or other.”

Components of Game Theory

There are three primary components in game theory:

  • Players — the game participants represent the main element of game theory. 
  • Strategies — the different tactics employed by the players in the game pursuant to their objectives. This component also includes how players would respond to the strategies used by their opponents. All strategies must be developed in line with the game rules. 
  • End Results — the payoffs/losses or the outcome of the game. All players are assumed to already know the potential results and their implications before participating. 

Game Theory Examples

When you hear the term “game,” your mind automatically associates it with amusements and sporting events. However, in game theory, the word “game” encompasses a much larger scope. Basically, it applies to any situation where there is a need to predict the thought process of participants who compete or collaborate with each other. 

From a business point of view, for instance, game theory can help business managers figure out the most optimal solution from the available choices. This can be done by analyzing the costs and benefits to each competitor in their industry and attempting to predict how interactions between different participants affect the actions and responses of others. 

To better understand game theory and what it entails, here are a few examples worth knowing about:

The Prisoner’s Dilemma

The prisoner’s dilemma is the most famous game theory scenario. It is a paradox in decision-making analysis in which two people must decide while keeping in mind that the decision of the other can impact their own outcome. Generally, the Prisoner’s Dilemma concludes that two individuals with competing incentives who chose to act in their own self-interest will likely produce a suboptimal outcome.

In the classic example, there are two prisoners, let’s call them Karen and Roger. They’ve both been arrested for robbing a jewelry store. The Prisoner’s Dilemma represents the game of social interaction between them when the district attorney decides to press the matter by offering each of them a set of choices.

He tells Karen and Roger that they’re both going to get two years in jail for the original crime. However, if either of them snitches on the other, they won’t get jail time, whereas the other person will get ten years. They both get two years of jail time if they snitch on each other. And if they both decide not to snitch on each other, then they will only get two years.

Then Karen and Roger are split up. They don’t know what the other person will do, so they have to make their decisions independently. Now Karen and Roger have had a wild time stealing jewelry, but they don’t have any special loyalty to each other. There’s no particular reason to think either of them won’t stab the other in the back. And yet, they both have to make a decision that favors them the most, regardless of what the other person decides. 

Game theory then arranges their choices and their potential consequences into a grid known as the Payoff Matrix. 

Prisoner’s Dilemma Payoff Matrix

Here is the graphic representation of the prisoner’s dilemma: 

Karen/RogerConfessDon’t Confess
Confess5 years / 5 years0 Years /10 years 
Don’t Confess10 years / 0 Years2 years / 2 years

If Karen and Roger choose not to snitch on each other, they’ll serve only two years. In theory, this is the best overall outcome combined since it means the least time in prison. However, they must also factor in that there’s a chance that the other person may snitch on them when making their decision.

So how do both Karen and Roger get an optimal outcome regardless of what the other decides?

According to game theory, the optimal solution is for both to confess and therefore serve a 5-year jail time each. Here’s why. By choosing to snitch on each other, Karen and Roger have hit the Nash equilibrium. This means each party picked a choice, having considered the other party’s potential choice(s). This approach actually makes sense.

So from Karen’s perspective, if she confesses and Roger doesn’t, she gets zero jail time. If she confesses and Roger confesses, they both get five years. Of course, she can choose not to confess, but it’s quite risky because if Roger confesses, she gets ten years. She doesn’t know for sure that Roger wouldn’t confess, so she’d rather play it safe such that she gets an optimal outcome regardless of Roger’s decision.

The reverse is also true from Roger’s perspective. He can’t take the risk that Karen won’t snitch, so it is in his best interest to confess and potentially get zero jail time or a max of five years. 

Chicken Game

Also known as the game of chicken, it models two drivers in opposing directions headed toward a single-lane bridge.

Both have the same strategy — they want to get on the bridge, so each driver expects the other to swerve away so they can pass through. But neither is willing to make way for the other since they would be called a chicken (coward). And yet, it is in everyone’s best interest that conflict be avoided because they would both lose if they decided to continue and have a head-on collision. 

Here’s how the possible outcomes look:

Driver A / Driver BSwerve Don’t Swerve
Swerve0/0-2/+8
Don’t Swerve+8/-2-10/-10

If both drivers decide to swerve, there is no impact hence a score of 0. However, this isn’t the desired outcome for any of them because it means neither will use the bridge. If they both decide not to swerve, they are headed towards the worst possible outcome and both lose. 

So using game theory, the optimal solution would be for one of the drivers to swallow their pride and swerve, even if that means being called a chicken. 

Game Theory in Trading

At its core, trading securities is all about making the right decisions. Your choice of what to trade, when to buy or sell, and how much to commit can make the difference between a huge payday and a colossal loss. 

That’s why game theory in trading is so important. It can help traders make optimal decisions even when they don’t know for sure what decisions other traders will make. And yet those decisions can significantly impact the overall outcome of their trading activities.

Using game theory, traders can also better understand market behavior and how it would be affected by certain changes or developments. For example, when the market is volatile, traders have a number of fixed options — hold, buy more, or sell.

The ideal outcome involves maximizing their profit (and minimizing loss). Their decision is contingent on the thought process of other traders and whether they decide to alter their trading strategy in pursuit of their own optimal outcome. Game theory can help traders map out how these options might play out and their resulting impact so they can make informed trading decisions.

Game Theory and the Stock Market

One of the best applications of game theory in trading is the stock market. In stock trading, buying and selling should only be done after the trader has decided on a sound strategy. 

Game theory helps predict the decisions other players might make related to the market. Based on these decisions, they can choose the strategies that best fit the most likely scenario.

The literature on game theory in trading has been expanding too.

In their publication, A Game-Theoretical Approach for Designing Market Trading Strategies, Authors Garrison W. Greenwood and Richard Tymerski discussed how the mathematics and psychology of game theory could be used in conjunction with digital technology and technical analysis indicators to optimize stock market performance. 

A 2021 study, Modeling the Stock Market Through Game Theory by Kylie Hannafey, goes a step further by explaining how the Nash equilibrium can be applied to businesses in the stock market.

Conclusion

Traders and investors always look for good stock market trading strategies to maximize profit and minimize losses. Used properly and in conjunction with other reliable tools and resources, game theory can help you make better trading decisions. That said, there’s simply no way to predict the market flawlessly. Sometimes, even with all the right signals, traders end up getting it wrong.

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