Last Updated on 7 September, 2021 by Samuelsson
Sure, you’ve heard of game theory. It rings true in everything we do — from relationships to politics to economics. And sure, trading is also a game where we all try to come out tops: from devising a strategy, learning the rules, finding trends before anyone else does, managing risks, and trying to beat everyone else to the punch, we are in one gigantic competition.
So, game theory applies here too. What’s more, in the game of trading, your emotions take the lead, but to be able to compete effectively and win the game, you have to manage the emotions and follow the rules of the game. But it is not easy to manage the emotions and trade with our brains unless we understand how the game is played.
To start to undermine our own self-destructive habits, it helps to understand how the game is geared toward those who figure out the game and make the rules. But what exactly is this game theory, and how can you apply it in your trading?
What is game theory?
Game theory is a framework for explaining social situations and interactions among competing players. Essentially, it is the process of modeling the strategic interaction between two or more players in a situation containing set rules and outcomes. The theory, in some respects, is considered the science of strategy and optimal decision-making by independent and competing actors in a strategic setting.
The game theory is used in a number of disciplines, but it is most notably used in the study of behavioral economics. Its application in economics is far reaching, including the analysis of the macroeconomic situations in a country and between countries (trade wars and deals), microeconomic situations, and fundamental analysis of industries and sectors, as well as any strategic interaction between two or more firms.
But the theory can also be applied in trading to explain how traders compete in the zero-sum game. As a theoretical framework for conceiving social situations among competing players, it explains the process through which independent and competing actors in a strategic setting make optimal decisions. Using game theory, real-world scenarios, such as pricing competition, product releases, and many others, can be laid out and their outcomes predicted.
It was mathematician John von Neumann and economist Oskar Morgenstern who propounded the game theory in the 1940s. But it was mathematician John Nash who is regarded by many as providing the first significant extension of the von Neumann and Morgenstern work.
Understanding game theory
As we stated earlier, game theory has a wide range of applications, including psychology, evolutionary biology, war, politics, economics, and business. But despite its many advances, it is still a young and developing science. The focus is on the game, which is a model of an interactive situation among rational players.
According to game theory, the actions and choices of all the participants affect the outcome of each. The key to the game is that one player’s payoff is contingent on the strategy implemented by the other player, so the game identifies the players’ identities, preferences, and available strategies and how these strategies affect the outcome.
Depending on the model, various other requirements or assumptions may be necessary, but first, let’s take a look at some of the important definitions.
Game theory definitions
Before we go further, let’s define a few terms commonly used in the study of game theory:
- Game: This defines any situation with two or more players that involve known payoffs, with the result dependent on the actions of the two or more players.
- Players: A player is a strategic decision-maker within the context of the game.
- Strategy: This is a complete plan of action a player will take given the set of circumstances that might arise within the game.
- Payoff: This is the payout a player receives for arriving at a particular outcome; it can be in any quantifiable form — dollars, utility, or anything.
- Information set: The term information set is most usually applied when the game has a sequential component. It implies the information available at a given point in the game.
- Equilibrium: This is a point in a game where both players have made their decisions and an outcome is reached.
Assumptions in game theory
Just like other concepts in economics, there are some assumptions in the game theory. One of them is the assumption of rationality — it is assumed that players within the game are rational. There is also an assumption of maximization, which implies that the players will always strive to maximize their payoffs in the game.
Furthermore, when examining games that are already set up, it is assumed on your behalf that the payouts listed include the sum of all payoffs associated with that outcome. With this, any “what if” questions that may arise are excluded.
While the number of players in a game can theoretically be infinite, most games will be put into the context of two players. So, one of the simplest games is a sequential game involving two players, but a game with multiple players can easily be reduced to a two-player game with a “them vs. him/her” approach.
The Nash Equilibrium
Nash Equilibrium is a situation where an outcome has been reached, and in that state, no player can increase payoff by changing decisions unilaterally. This can also be considered a “no regrets” state in the sense that once a decision is made, the player will have no regrets concerning decisions considering the consequences.
In most cases, the Nash Equilibrium is reached over time, but once it is reached, it will not be deviated from. After learning how to find the Nash Equilibrium, we try to understand how a unilateral move would affect the situation. But can we say that makes any sense? It shouldn’t, and that’s why the Nash Equilibrium is described as “no regrets.”
Generally, there can be more than one equilibrium in a game, but this usually occurs in games with more complex elements than two choices by two players. For simultaneous games that are repeated over time, one of these multiple equilibria is reached by some trial and error. This scenario of different choices over time before reaching equilibrium is the most often played out in the business world and the financial markets.
Trading as a game
For most traders, trading is all about looking for a good entry signal. So, whether they are using fundamental or technical analysis, the emphasis is always on finding out when to enter the market — finding an entry signal.
But trade entry only covers half of the trading process — there are two parts of any trade: getting in the market, and getting out of the market. While many focus on the first one, the more important of the two is arguably the last one. Here’s why: no matter how we refine our entry, what determines whether we make profit or loss is where we exit the trade.
So, flipping the game, you can re-purpose many strategies from giving you an entry signal to giving you an exit signal. For example, as your strategy shows you buy signals in the market, the opposite setup can show you sell signals, which you use to exit from the market. But this is just a simple solution to a more complex problem that still emphasizes entry and not exit. What if you play the exit game?
Just like poker players, each time you trade, you take a risk; it can go in your favor as well as it may not. In other words, you can win, or you can lose. So we’ll call each time you trade a “game”. There is no limit to the number of times you can play the “game”, and each time you play, you either win or you lose. If the odds are in your favor (if you have a trading edge), you are likely to win more over a large number of trades, and if you make more money per win than you lose per loss, you don’t even need to win more before you can make money. As you can see, while people try to know when to enter a trade, the main thing should be when to exit the trade.
In rare cases, some people can make a killing on just one trade, but that is just a matter of luck. For the majority of traders, money is made from trading several times and accumulating many wins gradually. That repetitive act of trading several times is called iterations.
So, by combining your edge, risk management, and repetitive trading, you have the game theory. This is one of the reasons people who are good at poker are good at trading; it focuses on the outcome, risk management, and playing enough hands — more than just the start of the trade. But unfortunately, with everyone so eager to jump into the market, most trading strategy articles online focus on trade entry and neglect to talk about the “back” side of trading, risk management, and how to get out of the market at the appropriate time.
Using game theory in trading: focusing on the risk, exit, and emotional control
As we stated earlier, any time we have a situation with two or more players that involve known payouts or quantifiable consequences, we can use game theory to help determine the most likely outcomes. To understand how game theory can be applied in trading, we will approach it in two ways:
- The 50/50 chance game
- Using statistics to manage emotions and trading approach
Playing the 50/50 chance game while managing risk
With the game theory, you can approach trading as a game with a 50/50 chance of win or loss, and thus, you can forget your entry signals altogether. Here’s why: the market can basically go up or down, so in its very rudimentary form, there is a 50:50 chance of success in any random trading — just like flipping a coin.
Now, taking the coin-tossing example further, let’s say the head represents a win and the tail a loss. Each time we toss the coin and get the head, we receive $10, but each time we get the tail, we lose $5. Since the bet has a 50% chance of winning and a 50% chance of losing and each win offers twice what you lose in a losing bet, we can feel good to play the game.
This is basically what you can do in trading; you can reduce your trading to these win-or-lose variables by specifying your risk and reward in each trade and knowing that you can either win or lose. You do this with the help of a stop loss and profit target, which are basically exit points. Your entry can be as random as tossing a coin; the focus should be on the exit points because what makes this a “good” or a “bad” strategy isn’t how accurate it is in predicting the outcome but how it can handle your risk exposure.
So, as you make more and more trades, your 50% chance of winning is going to play out and with higher returns per win than what is lost in a losing trade, you have a winning edge in the game. But there’s a catch — you have to bet in a way that you can have to opportunity to bet as many times as possible so that your odds can play out. Let’s break it down: if you bet with 50% or even 10% of your capital at once, you can only make a few trades before the capital dries up if you are unlucky to have a streak of losing bets, which can actually happen.
Someone who has mastered the game would know that he has to risk a very small percentage of his capital in each play. Something like 0.5% or 1% is enough. That way, he can play enough time to give his odds the chance to play out. Coming back to our example where you bet $5 to win $10, you will need to have a $500 capital to play at 1% account risk or a $1,000 capital to play at 0.5% account risk.
So, you can lose two, three, or four times in a row and still have money to play more bets. But losing four bets in a row would be pretty unlucky; there is only a 6.25% chance of that happening. However, you still have more money to keep playing and can win in your next game. Over time, if you play enough, you’re going to win twice as much money as you lose, making you profitable.
In summary, the key factors are focusing on your exit and playing with an amount you can afford to lose without it affecting your trading capital so much. If possible, avoid using leverage.
Using the game to determine the right trading approach and
Understanding how to apply game theory in trading can help you determine the right approach to your trading at any point in time based on the outcome of your previous moves. For example, if you are using a trend-following strategy, when you have a big win, it’s normal to expect your next 2 or 3 trades to be losers. In this case, you may reduce your bet size to minimize the anticipated losses while still giving yourself the opportunity to grab a win if it occurs.
Also, if you have been buying dips in a trend, you should know when a trading range has set in so that you switch to a suitable strategy for a ranging market. Another example is if there is prolonged choppiness, you should expect a big trend to follow. So, in that scenario, you position your trades for breakout opportunities.
Using the game to manage your emotions
The game theory can also help you to manage your emotions when trading. If you have been playing with a focus on exit and know that your odds will always play out the more you play, when you have a streak of losses, you would be expecting a winning streak. That knowledge can help you manage your emotions. As you lose, you know that a winner, or possibly a winning streak is around the corner.
Limitations of using game theory in trading
One of the biggest issues with game theory is that, as with most other behavioral theories, it relies on the assumption that people are rational actors that are only interested in satisfying themselves and maximizing utility. But humans are social beings that can also act for the common good, rather than self-interest.
On the aspect of trading, playing based on randomness and a 50/50 chance of winning or losing may not work in the financial market. Randomly placed trades may not really have a 50% chance of being a winner and a 50% chance of being a loser, especially when there is an expected size for a win and a different size for a loss.
To put it all together, the game theory can be applied in trading. But if you focus only on when to get into the market, then you are banking on luck to become profitable, which is no different from gambling. When you focus on how you exit the market, you are invariably using the relevant statistical variables to determine your odds of making money in the long run.