The Hodler’s Game — Game Theory applied to Bitcoin’s pricing

muhuuh
muhuuh
Feb 17 · 7 min read
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The Prisoner’s Dilemna: A famous application of Game Theory (Picture)

Introduction

The Hodler’s Game model is meant to offer a different perspective about two of the currently most discussed topics in the bitcoin community: Is the S2F Model accurate and is the halving priced in. Many opinions have already been stated within the community, but most from a technical/IT/statistics point of view (or just out of gut feelings). This model will add an economics point of view to the discussion. Overall it will investigate two questions: Will we continue to see similar price volatility and price cycles, and if yes, why?

An asset needs to meet several attributes to be considered money, for example: durable, divisible, portable, uniform, scarce and some more. Many digital assets easily meet many of these attributes, except for “scarcity”, as the same digital asset can be infinitely copied. Bitcoin is considered the first truly scarce digital asset, some even consider it one of the scarcest resources on earth, as its supply is irreversibly fixed and 100% known — and scarcity is one of the very few factors that makes something valuable.

The Stock to flow ratio is meant to measure scarcity. It divides the existing stockpiles/reserves of the specific asset by its yearly supply (or growth rate). Therefore, the higher the stock to flow ratio, the lower the price elasticity of supply. A supply with a low-price elasticity is very “inflexible” to demand volatility, which has an amplified effect on the assets price. Economist have found that the S2F ratio has a strong correlation to assets’ prices and introduced Bitcoin’s S2F ratio (Saifedean Ammous — The Bitcoin Standard). Following this observation, PlanB developed a model based on Bitcoin’s S2F ratio to predict future price developments (PlanB, 2019). The S2F model demonstrates that, up until today, Bitcoin price can very accurately be modeled by this model and that Bitcoin’s price will continue to increase step wise after each halving, following S2F ratio’s pattern (Figure 1).

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Figure 1: S2F Ration by Plan B (2019)

Hodler’s Game Model

Based on observations, the Hodler’s game model assumes that two different types of people participate in the market: Hodlers and Opportunists. Hodlers are long-term investors who already (almost) hold as many Bitcoins as they feel comfortable with (most have reached their maximum risk/financial exposure). Opportunists, on the other hand, are newcomers and/or traders with a short/middle term investment horizon.

Hodlers tend to accumulate during low volatility periods and to sell during incurring price spikes, while Opportunists take the other side of the trade and kick-start the volatility when they enter the market (Figure 2).

Figure 2: Liveliness (Glassnode.com, 2020) & (Tamas Blummer).
Figure 2: Liveliness (Glassnode.com, 2020) & (Tamas Blummer).
Figure 2: Liveliness is defined as the ratio of the sum of Coin Days Destroyed and the sum of all coin days ever created. Liveliness increases as long-term holder liquidate positions and decreases while they accumulate to HODL.” Hodlers are selling their holding when the price increases, re-buy them during downturns and accumulate in low volatility phases. (Glassnode.com, 2020) & (Tamas Blummer)

In the Hodler’s game model, both participants have been attributed strategies that they typically use in different market cycles, corresponding to the behavior described above. Depending on the strategy of the opponent, the player’s potential pay-out (utility) will differ for each of his strategies. These pay-outs are attributed subjectively based on observation and experience. In a Game Theory set up, participants behave as to maximize their pay-outs (red circled). The situation when both players’ best response strategy matches (two red circles in the same matrix intersection) is called a Nash Equilibrium.

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Figure 3: Phase I — Hodlers vs Hodlers, Phase II — Hodlers vs Opportunists, Phase III — Hodlers vs Opportunists

The model shows that, during the re-accumulation phase, Hodlers will retain a more or less constant positive buying pressure by either buying or hodling. The reason for it, is that they have almost reached their maximum bearable exposure and would rather see the price increase without further increasing their own exposure. This constant and rather light buying pressure slows down the previous “crash”, stabilizes and slowly increases the price again (flat U-shape) (Phase I). The halving, by cutting Bitcoin’s supply by half, in combination with the constant buying pressure, will continue to slowly increase price and volatility because Holders won’t change their strategy because of that event. The increasing price/volatility soaks in new/more opportunists in an upwards vicious circle, while Hodlers start to sell (Phase II). The dominant strategy for Opportunists is here to “Buy”: no matter what the opponents does, buying will offer them the highest payouts, while“Selling“ is the weakly dominant strategy for Hodlers. This dynamics goes on up until the point the price crashes back as not enough opportunists continue entering the market (Phase III). Bitcoin is still considered a very risky market and the majority of people are still “afraid” of it. Therefore, the pool of potential buyers ready to enter the market (opportunists) quickly dries out. At this point, Hodlers buy back their holdings as “Buying” is now their weakly dominant strategy (along with “Hodl” as an option), while “Selling” is the dominant strategy for Opportunists. The exiting of Opportunists leaves at the end a majority of Hodlers left in the market, which naturally leads to a “Buy-Hodl” equilibrium → re-accumulation (Phase I).

The predicted behavior by the Hodler’s Game Model, the Nash equilibrium in which no player has a profitable deviation, matches with the behavior observed under real conditions. By definition, this fact implies that the participants behavior is rational and predictable, as it is the result of rational strategic decision-making equilibria. The described rationality and predictability by the Hodler’s game model has several implications.

First implication

The first implication is that similar price cycles (re-accumulation periods followed by spikes) will continue to occur in future, a prediction that is in line with that of the S2F Model. Additionally, every major opportunist entry/exit period was accompanied by massive volatility, a period during which the respective S2F ratios were major outliers in the S2F Model.

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Figure 4: The 5% highest volatility days (positive and negative) are gathered around 3 major periods.

Therefore, it seems likely that the price will continue to exceed the “normal” predicted price by the S2F Model during the next opportunist entry periods, if conditions remain constant.

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Figure 5: The highest volatility days’ S2F ratios coincide with the most extremes S2F Model’s outliers

Second implication

The second implication is that future price cycles rely on opportunists converting to hodlers after each cycle. If the cycles were constituted only of flat re-accumulation phases with periodic spikes, the average price would remain rather flat (like “ECG” diagrams). So how does it increase “step-wise”, as demonstrated by the S2F Model? After each cycle, some opportunists convert to being hodlers, which increases the pool of long-term market participants. These participants, hodlers, are responsible for holding up the price at higher levels during the following re-accumulation phase: the next “step” in the S2F Model.

Third implication

The third, and most interesting implication, is that Bitcoin’s halving is not priced in, the reality is much more nuanced. Hodlers are aware of future halvings and have an idea how much Bitcoin “should” be worth. However, it is not priced accordingly, as hodlers lack the necessary resources to do so: “I wish I had 1/6.15/21/100 bitcoins, unfortunately I can’t afford to buy as many”. The total aggregated value of resources willing to seriously evaluate and invest long-term in Bitcoin are dwarfed by the value they estimate Bitcoin has. This fact hinders the market to price Bitcoin correspondingly to the value its participants estimate it has. Thus, paradoxically, the fact that Bitcoin’s price continues to rise over time, is simply partly due to the lack of resources at each point of time. Opportunists, who were first attracted by growing volatility and who remain in the market for the long term after the halving, are responsible for the significant long-term price increases. Therefore, one can say that halvings are helping the market to price Bitcoin more “efficiently” by attracting additional resources into Bitcoin’s pricing.

Consequently, one can assume that Bitcoin will have the possibility to be “correctly” valued, as soon as the resources available to value it, exceeds the value hodlers attribute to it. When this condition is met, we can assume that future halvings will be priced in, thus breaking the S2F Model (stepwise sharp increases will be smoothed). A factor to accelerate this process is the opportunists’ learning curve (and that of the general public), as it will influence how fast the critical valuation will be reached. Obviously, Hodlers realizing they overvalued Bitcoin (unrealistic expectations, regulations, etc) or the pool of potential opportunists drying out, will also break the S2F Model and Bitcoin’s continuous cyclical price increase.

The Hodler’s Game model shows that Bitcoin’s price, which is deemed by many to be “irrational”, is in fact the result of rational behavior. This rationality offers a certain predictability as to how future price cycles will look like. One important condition for it to hold true, is the market participant dynamics to stay constant: Opportunists entering the market in waves with a small portion staying for the long term with Hodlers supporting the price level during longer time periods.

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muhuuh

Written by

muhuuh

Bitcoin. Working on models to understand market dynamics (AI). Studied economics at world leading business schools.

Coinmonks

Coinmonks

Coinmonks is a non-profit Crypto educational publication. Follow us on Twitter @coinmonks Our other project — https://coincodecap.com

muhuuh

Written by

muhuuh

Bitcoin. Working on models to understand market dynamics (AI). Studied economics at world leading business schools.

Coinmonks

Coinmonks

Coinmonks is a non-profit Crypto educational publication. Follow us on Twitter @coinmonks Our other project — https://coincodecap.com

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