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Bitcoin system dynamics

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Bitcoin system dynamics

Exogenous variables are highlighted in gray in the figures. Bitcoin is abbreviated as BTC. The creation of bitcoins is modelled as shown in Fig. This diagram represents the mechanism of controlled supply devised by Satoshi Nakamoto. This creation rate is given by the product of two factors: how many blocks are mined per day, and how much subsidy in BTC is granted for each mined block.

This part of the model does not include any dynamic loop. No feedback is present, and with respect of the dynamic hypothesis current under investigation, the only connections to the higher layer of the model are through the variables BTC Subsidy per Mined Block and Target Block Creation Rate, which are used to compute the Revenues from Subsidy.

The addition of hash rate to the bitcoin network is modeled as shown in Fig. The negative feedback loop is the manifestation of the effect of the efficient-market hypothesis set forth earlier. The Hash Rate at time zero is set to 0. The Price of Energy is assumed to be constant over the studied time period at 0. The Energy Efficiency of State of the Art Mining Hardware is modeled as a constant level in different epochs of mining.

Subtracting the cost from the revenues of mining, the Mining Profit is calculated. This determines the amount of Hash Rate Shortfall, that is how much hashing power could be added before the marginal cost of adding more will exceed the benefit a situation of zero-profit that is the goal of the negative feedback loop :.

At last, the key factor involved in this loop is introduced: the Hash Rate Adjustment Time. This accounts for the fact that the system does not react instantaneously to a shortfall in hash rate, for instance, because the supply chain of mining hardware is notoriously limited in its throughput. This parameter is the only one that is acted upon for the correlation of the model results by comparing the calculated hash rate with the historical time series.

The results and discussion are divided into three sections about model correlation, insights about the past, and speculations about the future. Table 2 maps the number of days of the simulation to calendar dates and relevant events, to help with the interpretation of the results.

A sanity check of the model is performed by comparing the height of the blockchain calculated by the model with the actual historical time series Fig. The comparison is satisfactory, showing that the Coin Creation part of the model works as expected. The correlation of the model with historical data series has been performed by tuning the value of the Hash Rate Adjustment Time manually, and through the automated optimization routines, until reaching a satisfactory matching between the calculated and the historical time series of the hash rate.

By using a single value for the Hash Rate Adjustment Time throughout the whole time series, an optimal result can be found at days, but a poor correlation is obtained, particularly in the last three years Fig. The situation can be significantly improved by allowing for the possibility that the delay time of the feedback loop changes at some point i. The optimal fit occurs for a delay time of days from time 0 to 3, and only days from time 3, to 4, Fig.

The rest of the results in this paper are relative to this second scenario. In general, the correlation can be considered good enough to gain some insights from this model, especially considering its simplicity, with the following provisos:. Model improvements are needed to use it for this period. For example, the diffusion of new technologies could be modeled to allow for a gradual implementation of the newer generation of mining hardware, particularly in the early days, rather than as a step function.

This could reduce the tendency of the model to overestimate the hash rate in the early days, and it would also avoid discontinuities in the hash rate as for time 2, in Fig. Also, a better estimate of the Price of Energy of the miners in the early days, which as certainly higher on average than 0.

The model reasonably captures the main dynamics of the system from time 1, on, which is in the epoch of ASIC miners; however, some dynamics are not represented by the model e.

In summary, there are several opportunities to extend and improve this model by identifying and implementing these additional loops. Yet, this simple model is sufficiently complex to gain relevant insights about the system while avoiding the risk of over-fitting the data. Having established a reasonable correlation between the model and the reality, the analysis of the simulation results gives further insights on the past evolution of bitcoin mining and the related market dynamics:.

In other words, even if mining was a great deal financially speaking, procuring as much hashing power as it would financially make sense from a pure present-day profit consideration, was never possible. The long delay time of hash rate addition is also in line with the lived experience that mining hardware has always been a relatively scarce resource, and further invalidates some efficient-market hypothesis models which would overestimate hash rate growth.

The jump to a much lower delay time of the feedback loop that occurred around mid, from 1, to days, is also aligned with some factual evidence. This ratio matches quite well with the ratio between the two delays time, which is 5. Until late , there was always a positive shortfall of hashing power in the network, with the biggest spike matching the time of highest bitcoin price and transaction fees.

Compare Fig. The profit from mining, expressed in the simplistic terms of this paper as same-day revenues minus operational costs accounting for the cost of energy, was always positive, until the last few months.

The latter point, in particular, calls for some thinking about the future and the reaction of the system to the forthcoming halving event, in about a month from the time of writing. Using a model correlated with past data to attempt to predict the future is always a tricky endeavor. This is true for this model as well for two reasons. First, because it is a simple model with only one feedback loop it may not capture all the dynamics of the system.

Second, because the model correlation is performed with past data that were almost always relative to a growing network hash rate, and there is no guarantee that the same dynamics work when the market would turn in a different direction. With this necessary premise, the temptation to apply the model to a hypothetical future is irresistible.

This scenario is interesting because the current profit from mining, net of the cost of energy, is nearly zero Fig. Therefore, it is interesting to see that this equilibrium might be perturbed by the forthcoming halving of the subsidy. Specifically, we have extended the model operation from day 4, to 7, with the following assumption:.

All these assumptions are of course arbitrary, and one could play with any different set of assumption. To put it another way, the constraint of reduction of coinbase reward is expected to dominate over technological leaps in hashing efficiency. The results show a quick switch to negative-profit for block mining at the next two halving events, and particularly at the next one, when the mining subsidy will be cut in half for the third time, from Correspondingly, the Hash Rate Shortfall becomes negative, to indicate that the network has an excess of hash rate, which makes the cost of mining higher than the revenues that it generates.

The feedback loop of the model, based on the efficient-market hypothesis set forth at the beginning of the paper, operates by reducing the hash power of the network until the net profit from mining will tend again to zero. The difference from the past is that, for the first time, the hash rate would tend to its equilibrium state from the bottom instead of the top.

In the current model, the adjustment time of the net inflow hash rate is the same, regardless of the sign i. However, it is likely that the removal of hash rate will take place with a much shorter adjustment time, because it is much easier to switch off a mining hardware or use it for another purpose e. This could be implemented by considering different inflow and outflow of hash rate from the Hash Rate stock currently modeled as a single net flow, see Fig.

This effect is not considered in the model, but it can be added in the future if the network hash rate will indeed start to drop. That is, has the bitcoin reached the situation where the cost of mining is higher than the revenues from mining? Possibly, as the projection of the future evolution of the hash rate in Fig. If that will be the case, a most interesting question will be: where will all that excess hashing power be invested, and how this might change the landscape of the bitcoin and other cryptocurrencies?

May such a staggeringly large amount of hashing power that could potentially flee from the bitcoin network in the long-term be a threat to the security of the network or other SHA secured coins such as BCH and BSV , if ever it would suddenly come back?

Of course, a number of events may allow for a smooth transition between the current and the next reward era, such as significant improvements in the energy efficiency of the mining hardware, access to yet cheaper energy, or substantial inflation of bitcoin price and transaction fees.

Some of these changes e. But one thing seems true: the effect of the forthcoming halving might be different and have deeper consequences than the previous, so it is worth making sure that the bitcoin, as a dynamical system, is prepared for this transition.

Finally, it is worth considering what could be an alternative model of coin supply that would not have incurred this hypothetical peak of hash rate. Such a mechanism, among others, ensures a slower overall rate of coinbase reduction, changing the system dynamics especially in the longer term. XMR, LTC , a System Dynamics model could tell us more about how other choices of currency issuance will affect the hash rate and future security of the system. We have shown that aspects of bitcoin mining can be modeled as a dynamical system using system dynamics.

Starting with a dynamical hypothesis based on an efficient-markets hypothesis applied to the mining of blocks, we have shown how the recent evolution of the bitcoin network has rate can be explained by a negative feedback dynamic loop that zeroes on mining profit with a delay time. By extending the simulation into the future to cover the next two reward eras, under the assumption of constant bitcoin price and revenues from transaction fees approximately at the level of April , we have shown how there is a possibility that the next halving event lead to a transition to an unprofitable mining regime with an excess of network hash rate.

Finally, this model shows that system dynamics methods and tools can be effective to model the bitcoin and could be applied to other existing or new proposed cryptocurrencies as well to understand the behavior of the complex sociotechnical systems that are created from the application of blockchain technology to electronic money and other applications enabled by shared ledger. It is worth noting the relative success that the model enjoys with historical data, especially considering that there is no way to verify how many people are mining nor what hardware is available to them.

Despite a decade of practice, the theory behind public proof-of-work ledgers remains in its infancy. This dynamic hypothesis further assumes an efficient market with perfect information.

As long as the mining profit is positive, more hashing power is added to the network until the marginal cost of adding more hashing power exceeds its expected return. Conversely, when the mining profit becomes negative, hash rate is subtracted from the network. The increase and decrease of hash rate happens with a certain time constant, represented with a delay factor i. In a first approximation, this delay is assumed to be the same for both the increase and decrease of hashing rate, although the latter is likely to be smaller than the former.

This hypothesis is a coarse simplification of reality, and therefore can only provide a partial answer to the question of what drives the bitcoin network hash rate. Specifically, it assumes that all miners work for the immediate profit of mining, and it does not consider that some most?

Nevertheless, it is plausible that the perspective of a present-time gain, at any time, is the dominant mechanism underlying the decision of a miner whether or not to invest in additional mining hardware, or mine bitcoin instead of another more rewarding cryptocurrency. Furthermore, the same hypothesis is applied throughout the entire life of the bitcoin, from the early days January till now April It is obvious that the dynamics driving the mining of the bitcoin in the early days were not the same of today.

At the beginning, a true market barely existed, and mining was performed by enthusiastic individuals with modest investment in hardware infrastructure. Hence, the model is expected to correlated with historic data better in the late years than in the early years.

The model of this paper has been created with Vensim Ventana Systems, Inc. Certain variables of the system are treated as exogenous variables, meaning that neither their value is determined by the state of other variables of the system, nor they take part in feedback loops. The latter is based on our synthesis of a multitude of internet sources that are too many to be mentioned here from Wikipedia to old pages of other websites and forums about the energy efficiency of mining hardware. The model correlation is performed by comparing selected model outputs with the historical time series:.

The first two are used only as a model sanity check, whereas the last one is used for model correlation. The correlation of the model has been performed both manually and using the optimization capabilities of Vensim DSS.

The model structure is discussed in detail in the following sections. The following conventions are used: variable names are capitalized, and constant names are all capital. Exogenous variables are highlighted in gray in the figures. Bitcoin is abbreviated as BTC. The creation of bitcoins is modelled as shown in Fig.

This diagram represents the mechanism of controlled supply devised by Satoshi Nakamoto. This creation rate is given by the product of two factors: how many blocks are mined per day, and how much subsidy in BTC is granted for each mined block. This part of the model does not include any dynamic loop. No feedback is present, and with respect of the dynamic hypothesis current under investigation, the only connections to the higher layer of the model are through the variables BTC Subsidy per Mined Block and Target Block Creation Rate, which are used to compute the Revenues from Subsidy.

The addition of hash rate to the bitcoin network is modeled as shown in Fig. The negative feedback loop is the manifestation of the effect of the efficient-market hypothesis set forth earlier. The Hash Rate at time zero is set to 0. The Price of Energy is assumed to be constant over the studied time period at 0. The Energy Efficiency of State of the Art Mining Hardware is modeled as a constant level in different epochs of mining. Subtracting the cost from the revenues of mining, the Mining Profit is calculated.

This determines the amount of Hash Rate Shortfall, that is how much hashing power could be added before the marginal cost of adding more will exceed the benefit a situation of zero-profit that is the goal of the negative feedback loop :.

At last, the key factor involved in this loop is introduced: the Hash Rate Adjustment Time. This accounts for the fact that the system does not react instantaneously to a shortfall in hash rate, for instance, because the supply chain of mining hardware is notoriously limited in its throughput. This parameter is the only one that is acted upon for the correlation of the model results by comparing the calculated hash rate with the historical time series.

The results and discussion are divided into three sections about model correlation, insights about the past, and speculations about the future. Table 2 maps the number of days of the simulation to calendar dates and relevant events, to help with the interpretation of the results.

A sanity check of the model is performed by comparing the height of the blockchain calculated by the model with the actual historical time series Fig. The comparison is satisfactory, showing that the Coin Creation part of the model works as expected. The correlation of the model with historical data series has been performed by tuning the value of the Hash Rate Adjustment Time manually, and through the automated optimization routines, until reaching a satisfactory matching between the calculated and the historical time series of the hash rate.

By using a single value for the Hash Rate Adjustment Time throughout the whole time series, an optimal result can be found at days, but a poor correlation is obtained, particularly in the last three years Fig. The situation can be significantly improved by allowing for the possibility that the delay time of the feedback loop changes at some point i. The optimal fit occurs for a delay time of days from time 0 to 3, and only days from time 3, to 4, Fig. The rest of the results in this paper are relative to this second scenario.

In general, the correlation can be considered good enough to gain some insights from this model, especially considering its simplicity, with the following provisos:. Model improvements are needed to use it for this period. For example, the diffusion of new technologies could be modeled to allow for a gradual implementation of the newer generation of mining hardware, particularly in the early days, rather than as a step function.

This could reduce the tendency of the model to overestimate the hash rate in the early days, and it would also avoid discontinuities in the hash rate as for time 2, in Fig. Also, a better estimate of the Price of Energy of the miners in the early days, which as certainly higher on average than 0. The model reasonably captures the main dynamics of the system from time 1, on, which is in the epoch of ASIC miners; however, some dynamics are not represented by the model e.

In summary, there are several opportunities to extend and improve this model by identifying and implementing these additional loops. Yet, this simple model is sufficiently complex to gain relevant insights about the system while avoiding the risk of over-fitting the data. Having established a reasonable correlation between the model and the reality, the analysis of the simulation results gives further insights on the past evolution of bitcoin mining and the related market dynamics:.

In other words, even if mining was a great deal financially speaking, procuring as much hashing power as it would financially make sense from a pure present-day profit consideration, was never possible. The long delay time of hash rate addition is also in line with the lived experience that mining hardware has always been a relatively scarce resource, and further invalidates some efficient-market hypothesis models which would overestimate hash rate growth.

The jump to a much lower delay time of the feedback loop that occurred around mid, from 1, to days, is also aligned with some factual evidence. This ratio matches quite well with the ratio between the two delays time, which is 5. Until late , there was always a positive shortfall of hashing power in the network, with the biggest spike matching the time of highest bitcoin price and transaction fees.

Compare Fig. The profit from mining, expressed in the simplistic terms of this paper as same-day revenues minus operational costs accounting for the cost of energy, was always positive, until the last few months. The latter point, in particular, calls for some thinking about the future and the reaction of the system to the forthcoming halving event, in about a month from the time of writing.

Using a model correlated with past data to attempt to predict the future is always a tricky endeavor. This is true for this model as well for two reasons.

First, because it is a simple model with only one feedback loop it may not capture all the dynamics of the system. Second, because the model correlation is performed with past data that were almost always relative to a growing network hash rate, and there is no guarantee that the same dynamics work when the market would turn in a different direction.

With this necessary premise, the temptation to apply the model to a hypothetical future is irresistible. This scenario is interesting because the current profit from mining, net of the cost of energy, is nearly zero Fig.

Therefore, it is interesting to see that this equilibrium might be perturbed by the forthcoming halving of the subsidy. Specifically, we have extended the model operation from day 4, to 7, with the following assumption:. All these assumptions are of course arbitrary, and one could play with any different set of assumption.

To put it another way, the constraint of reduction of coinbase reward is expected to dominate over technological leaps in hashing efficiency. The results show a quick switch to negative-profit for block mining at the next two halving events, and particularly at the next one, when the mining subsidy will be cut in half for the third time, from Correspondingly, the Hash Rate Shortfall becomes negative, to indicate that the network has an excess of hash rate, which makes the cost of mining higher than the revenues that it generates.

The feedback loop of the model, based on the efficient-market hypothesis set forth at the beginning of the paper, operates by reducing the hash power of the network until the net profit from mining will tend again to zero. The difference from the past is that, for the first time, the hash rate would tend to its equilibrium state from the bottom instead of the top.

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