Bitcoin and Nash Equilibrium, Keynesian Beauty Contest

Foreword: In a market without a consensus of valuation, the behavior of investment is more like the Keynesian beauty contest. Everyone invests in assets that others think are valuable. At the same time, there is no clear Nash equilibrium to form the final stability. This leads to the possibility of a high valuation at the current stage, who will tell the story. This also reflects the early chaos of the entire cryptocurrency market, which does not have a consensus reached by all to value the project. However, as the project progresses, once everyone has a consensus on the valuation of the project, its price will gradually reach equilibrium. Of course, this also means that the stage of true maturity comes, and it is almost impossible to get a high-magnification return at this time. From this perspective, it can now be said that it is the golden age of cryptocurrency. The author of this article, Tony Sheng, is translated by the "Blue Fox Notes" community "Sima Qing".

The "money bubble theory" is a popular bitcoin bullish theory, as follows:

1. Speculation leads to an increase in asset prices and a bubble;

2. The bubble will not be completely “broken”, as the volatility will decline and the price will stabilize as new buyers enter the market.

3. Once the price is stable, it will be used by the public as currency.

JP Koning has written critical articles about his doubts about whether the Keynesian Beauty Contest model can lead to stability. He believes that the price of Bitcoin cannot be established in the second step of the bubble theory. This article is good and worth reading, but after reading it, I still can't be sure whether the Keynesian beauty contest can stabilize.

So, what is the Cairns pageant contest? When will it be stable and when will it not be stable? How does it work in cryptocurrency?


Cairns Beauty Contest


The Cairns pageant contest describes a game that motivates players to take action based on predicting other players' behavior (other players are doing the same thing). Keynes wrote in his 1936 book The General Theory of Employment, Interest, and Money:

…Professional investment is like a competition in a newspaper . The person who participates in the competition must choose the best looking face from the 100 photos. If the contestant ’s choice is closest to the competition The overall average preference, then the contestant wins the award. The result is that each contestant will not choose the face he thinks is the best, but will choose the face that he thinks the other contestants are the best. All the contestants have the same idea. This is not a question of picking the best people according to their preferences, or even a question that everyone thinks is the best person. We have reached the third dimension, we put Ingenuity is invested in predicting what is expected from a group perspective. I believe that some people will reach the fourth, fifth or even higher dimensions. "

Sometimes player behavior is described as a game in n dimensions, where:

In the zero dimension, the player randomly chooses;

In the first dimension, players pick the best people in their minds;

In the second dimension, players pick the best people they think others are in the mind;

In the third dimension, the players pick the best-looking people in the minds of others who they think other people think;

… move toward a higher dimension

The concept of the “Keynesian Beauty Contest” is usually market-related, especially in speculative markets, as its market participants try to speculate on the ideas of other participants. One-dimensional traders buy stocks that they think are undervalued. Two-dimensional market traders buy stocks that others think are undervalued. According to this logic, they continue to move toward higher levels. (Blue Fox Note: If a person reaches 3D, 4D or even 5D, the insight of the market can be imagined.)

This has led to the market being vulnerable to speculative bubbles because the market is unable to anchor “fundamental value”. I mentioned in the "narrative bubble cycle":

The narrative-driven speculative bubble environment has three characteristics:

1. There is no reliable or relevant historical data to form an estimate;

2. Have the conditions to attract retail investors, usually poorly regulated;

3. In a investment environment with a lot of opportunities, a relatively strong narrative can attract people's attention.

This is very consistent with what we see in cryptocurrency. Because of the lack of proven cryptographic asset valuation models, narratives can drive investment decisions. (Blue Fox Note: The narrative here is similar to the "storytelling" we often see in cryptocurrency projects.)

Market participants are unable to reach a consensus on the valuation method of assets because of the lack of reliable or relevant historical data for valuation. As a result, investors are playing a "Keynesian beauty contest" and are trying to predict each other's ideas.

As a result, the market is highly volatile and accompanied by a fragile market structure, as we have observed in the cryptocurrency market, there have been sharp rises and falls and corrections. So, will the Keynesian beauty pageant be stable in the end?


Nash Equilibrium


In experimental economics, the Cairns beauty pageant often experimentes in the form of a digital guessing game:

1. At least three people participate in the digital guessing game;

2. Participants can guess a number between 0 and 100, making it closest to 2/3 of the average of all people, which is 66%, the closest to win.

The maximum number of players who "self-profit" will choose 66, because if everyone else chooses 100, the winning number will be 66. Therefore, everyone predicts that others will choose a number of 66 or lower. Then, the second highest number predicted by others is 66% of 66, which is 43. This experiment has been done many times and the answer is around 20.

However, if the same player plays multiple times, the final number will reach a balance of 0, because the player will not believe that other players will choose a larger number than themselves.

In 2004, Kocher and Sutter conducted a "time is money" theme study. If you spend more time between multiple rounds of guessing games, the easier it is to achieve equilibrium.

This is an example of a trend towards stability in the Keynesian beauty pageant. It is also called "Nash Equilibrium", that is, participants do not change their behavior while knowing other people's equilibrium behavior. The current state is the best choice for everyone.

This game shows that when there is a Nash equilibrium, the Keynesian beauty pageant will eventually stabilize.

Stocks also form a Nash equilibrium around their "fundamental value." Koning cited an example of Amazon stocks stabilizing.

Why do Amazon stocks tend to be stable and Bitcoin will have the same trajectory? When Amazon's stock went public in 1997, it had no earnings . […] Amazon's stock price stabilization is not driven by a larger market capitalization or a growing volume. From a deeper perspective, the fundamentals have undergone qualitative changes . The company's business is becoming more mature and its profits have become more stable and predictable. The price of the stock also changes , because this is a reflection of its fundamentals.

In other words, because of the market's consensus on “fundamental value,” this creates a Nash equilibrium. There are valuation methods, such as multiple valuation of earnings and discounted cash flow valuation.

Is there a Nash equilibrium for the price of Bitcoin ?


Unlike the digital guessing game, there is no Nash equilibrium in the price of bitcoin. Bitcoin does not have a valuation method that everyone agrees with, and may not necessarily exist in the future.

At any point in time, some people may attack it as a rat poison, while others believe that it will become a global reserve currency. Even if most people think that it will become the global reserve currency, it is impossible to assign a balanced value to it. The best thing people can do is to anchor value to known assets, such as gold or money.

If there are enough people agreeing that the bitcoin price should equal an anchor (or multiple of the anchor), this will achieve some sort of equilibrium. For example, if the vast majority of people agree that Bitcoin should be as valuable as gold, then each bitcoin should be worth $380,000. However, this view is invalid unless

Everyone thinks that everyone else believes in this anchor.

This is not a Nash equilibrium. Recall that Nash Equilibrium has the following requirements:

1. Everyone knows the equilibrium behavior of others;

2. Everyone will not change their behavior.

These requirements are not met because gold is only one of many possible equilibrium behaviors, and market participants who are tempting will constantly try to operate a balance that is beneficial to them. There is equilibrium at any given point in time, which is reflected in the spot price, but no one knows what other people's equilibrium behavior is, and everyone is willing to change their behavior in the new information given the equilibrium behavior of others.

If you accept this logic, there is no Nash equilibrium for Bitcoin, so there is no reason to achieve stability.

But this logic also shows that all liquid assets do not have a true Nash equilibrium. Tesla seems to have “fundamental value”, but some believe that its value is seriously overestimated, while others believe its value is seriously underestimated. They are not evaluating company value in the same way. It's completely different from a clear balance of digital guessing games. Real-world assets have multiple levels of strength.

It's useful to think about the problem with Graham's famous saying: "In the short run, the market is a voting machine, but in the long run, it is a weighing machine."

Changing from a voting machine to a weighing machine means that it is shifting toward equilibrium. But this equilibrium is not always a single equilibrium, and all equilibriums are adjusted according to their popularity and intensity (or, "Do Nash Equilibrium" – the relative dominance of equilibrium).


A feasible path to achieve bitcoin stability

The stability of Bitcoin depends on the design of its “weighing machine”. According to the popularity and intensity of the equilibrium behavior, the weighing machine adjusts each of its equalization behaviors (such as anchoring gold, or thinks its value is zero) and returns to the net weight. (price).

Stability will come from the relative stagnation in the "weighing machine" design. E.g:

1. The amount of money flowing in and out of the market (inflow and outflow of legal currency);

2. The deviation in the equilibrium composition (ie the narrative);

3. A change in the intensity of a single equilibrium.

When Bitcoin is used all over the world, and everyone agrees to value it in a way (such as MV = PQ), then maximum stability will come. In fact, this is consistent with the supporters of the “Bitcoin Bubble Theory”. Once the “super-bitification” phase is reached, Bitcoin assets will stabilize near very large numbers.

It can be easily seen that the current price is a Keynesian beauty pageant without Nash Equilibrium. It can also be seen how a future will be stabilized by everyone using Bitcoin. But how to move from today to the future is not so easy to see clearly.

Look forward to the "narrative bubble cycle" repeating itself until people find a narrative that resonates. Whether Bitcoin is the world's reserve currency, or worthless, or in the middle, there is still no answer.


Risk Warning: All articles in Blue Fox Notes do not constitute investment recommendations . Investment is risky . Investment should consider individual risk tolerance . It is recommended to conduct in-depth inspections of the project and carefully make your own investment decisions.

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