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Is the market a perfect information game?

Updated: Apr 22, 2020

Game theory is increasingly becoming an important area in data science, and is something that warrants my interest of late. If you are wondering what game theory is, here is an example. You are standing in the queue for one of the cashier lanes in NTUC. The lane besides you seems to be moving faster. You took a look at it and wonder if you should leave your current queue to join the next lane.

That's game theory.

Essentially, it means a set of strategic framework which a country or a company or a person undertakes to make decisions.

Of course, game theory is a huge topic and I'm not going to discuss everything about game theory here. What I would like to concentrate on today is one aspect of game theory. That is perfect information.

What is a perfect information game and what is an imperfect information game? A perfect information game represents a game where players are perfectly informed of all the events which have previously occured and nobody has any advantage of any information over the other. A good example of a perfect information game will be chess. All the players has clear visibility of the events which are happening on the chessboard. Similarly, mahjong will be a good example of an imperfect information game. In mahjong, players do not have full understanding of all the events which are happening. For example, you do not know the starting hands of all the players and that already violates the definition of a perfect information game.

So, is the market a perfect information game?

To answer that question, I like to look at 3 different markets namely the stock market, forex market and cryptocurrency market.

Let's start off with the stock market.

At the first glance, most people will be thinking that the stock market is a perfect information game. You could get all the historical information about any stock you want on the internet. However, what people do not realise is that we do not know much about our "opponents" in this case. "Opponents" represent the other investors or traders or even institutions who are participating in the stock market. We have no visibility/understanding of their portfolio size, intentions or objectives. Thus, we are not perfectly informed in this case. And in certain cases, the retail investors like you and me might not even get full understanding of all the information unlike the insider traders (while I know it's generally the objective of law and regulations to eliminate this as much as possible). The quality of information varies between the retail investors, funds and institutions, thus violating the perfectibility of the information.

In an ideal perfect information model, uncertainty also do not exist. However, we know this is definitely clearly not in the case in the stock market, or in fact most/all markets. Uncertainties constantly manifest itself in several forms, both in real world events (eg. sudden drop in oil prices, abrupt escalation in world tensions etc) and market movements (eg. liquidation in positions by funds etc). And often, such events are almost impossible to understand/anticipate in advance. If the market is truly a perfect information model, we will all have very predictable trends and even predictable returns/outcomes. Clearly, it isn't so.

Hence I'm not of the opinion that the stock market is a perfect information game.

How about the forex market?

The forex market is comparatively a much bigger market than the stock market. The average volume for forex market is around $5 trillions per day while the average volume for all the stock markets around the world is around $200 billion per day. Due to this sheer humongous volume, the forex market is less likely to be affected or influenced by institutions or funds as compared to the stock market as it's almost impossible for a single party to move much of such a big market.

In terms of complexity, the forex market concentrates mainly on few major currency pairs such as EUR/USD, GBP/USD etc while the stock markets around the world have thousands and thousands of stocks. Operationally wise, the forex market is open 24/7 while the stock markets around the world are all open at different times of the day and this inevitably has an effect on information available to all (for eg. if US market tanks the night before, the Asia market traders will adjust their trades and react accordingly- this will not happen in a 24/7 market like Forex).

Since the forex market is much less likely affected by any single party with a much simpler mode of operation, the information is much more perfectly provided/available to all the players in the market. Hence, the forex market is deemed to be a more perfect information game than the stock market though fundamental issues like uncertainties (as discussed earlier on) certainly do still exist in the forex market and will doom it to never be a perfect information game.

Lastly, the cryptocurrency market.

The cryptocurrency market is the exact opposite of the forex market. The total capitalisation for cryptocurrency market is around $250 billion. To put things into perspective, this is only roughly 20% if the market capitalisation of Apple! Hence, you could imagine how small of a fraction is the cryptocurrency market in terms of the forex market and how easily it could be affected by institutions, funds or even ultra-rich individuals.

In terms of distribution, the cryptocurrency market is also heavily controlled/manipulated by whales. To give you an example, Bitcoin accounts for roughly 60% of the cryptocurrency market. Out of which, 1000 people owns about 40% of all the bitcoins as you can read here. The number of unique users for bitcoin is roughly estimated to be between 2.9 and 5.8 billion. This means that 3.45e-9 to 6.8e-9 % of the users control about 40% of all the bitcoins. Not to forget, since bitcoin accounts for roughly 60% of the cryptocurrency market, it means that this same 1000 users already account for 24% of the cryptocurrency market!

With such a huge skew of distribution, these whales have all the power to move the market on their own and have a much higher tendency to share/have access to information which is not available to the general retail investors. This heavily violates the perfectibility of the information to all the players in the market. Hence, the cryptocurrency is a perfect example of an imperfect information game and that is also why many advise against investing in cryptocurrency.

Having said all of these, does this means that everyone should be flocking to forex this particular instant and abandon the stock and cryptocurrency market? Well, I won't be advocating any actions here. But I guess what's important here to know how well are you positioned as a retail investor in these various different markets. What you like to do with this information is then....entirely up to you! #datascienceinvestor

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