The Blockchain was generated starting since January 3, by the inventor of the Bitcoin system himself, Satoshi Nakamoto. The whole system is set up to yield just 21 million Bitcoins by , and over time the process of mining will become less and less profitable. The main source of remuneration for the miners in the future will be the fees on transactions, and not the mining process itself. In this work, we propose an agent-based artificial cryptocurrency market model with the aim to study and analyze the mining process and the Bitcoin market from September 1, , the approximate date when miners started to buy mining hardware to mine Bitcoins, to September 30, The model described is built on a previous work of the authors [ 2 ], which modeled the Bitcoin market under a purely financial perspective, while in this work, we fully consider also the economics of mining.
The proposed model simulates the mining process and the Bitcoin transactions, by implementing a mechanism for the formation of the Bitcoin price, and specific behaviors for each typology of trader who mines, buys, or sells Bitcoins. To our knowledge, this is the first model based on the heterogeneous agents approach that studies the generation of Bitcoins, the hashing capability, the power consumption, and the mining hardware and electrical energy expenditures of the Bitcoin network.
The paper is organized as follows. In Section Related Work we discuss other works related to this paper, in Section Mining Process we describe briefly the mining process and we give an overview of the mining hardware and of its evolution over time. In Section The Model we present the proposed model in detail.
Section Simulation Results presents the values given to several parameters of the model and reports the results of the simulations, including statistical analysis of Bitcoin real prices and simulated Bitcoin price, and sensitivity analysis of the model to some key parameters. The conclusions of the paper are reported in the last Section. Finally, Appendices A, B, C, and D, in S1 Appendix , deal with the calibration to some parameters of the model, while Appendix E, in S1 Appendix , deals with the sensitivity of the model to some model parameters.
The study and analysis of the cryptocurrency market is a relatively new field. In the latest years, several papers appeared on this topic, given its potential interest and the many issues related to it. Several papers focus on the de-anonymization of Bitcoin users by introducing clustering heuristics to form a user network see for instance the works [ 3 — 5 ] ; others focus on the promise, perils, risks and issues of digital currencies, [ 6 — 10 ]; others focus on the technical issues about protocols and security, [ 11 , 12 ].
However, very few works were made to model the cryptocurrencies market. Among these, we can cite the works by Luther [ 13 ], who studied why some cryptocurrencies failed to gain widespread acceptance using a simple agent model; by Bornholdt and Steppen [ 14 ], who proposed a model based on a Moran process to study the cryptocurrencies able to emerge; by Garcia et al.
In this paper we propose a complex agent-based artificial cryptocurrency market model in order to reproduce the economy of the mining process, the Bitcoin transactions and the main stylized facts of the Bitcoin price series, following the well known agent-based approach. For reviews about agent-based modelling of the financial markets see the works [ 19 , 20 ] and [ 21 ]. The proposed model simulates the Bitcoin market, studying the impact on the market of three different trader types: Random traders, Chartists and Miners.
Random traders trade randomly and are constrained only by their financial resources as in work [ 22 ]. They issue buy or sell orders with the same probability and represent people who are in the market for business or investing, but are not speculators. Chartists represent speculators.
They usually issue buy orders when the price is increasing and sell orders when the price is decreasing. Miners are in the Bitcoin market aiming to generate wealth by gaining Bitcoins and are modeled with specific strategies for mining, trading, investing in, and divesting mining hardware. Note that in our model no trader uses rules to form expectations on prices or on gains, contrarily to the works by Chiarella et al.
In addition, no trader imitates the expectations of the most successful traders as in the work by Tedeschi et al. The proposed model implements a mechanism for the formation of the Bitcoin price based on an order book. In particular, the definition of price follows the approach introduced by Raberto et al.
As regards the limit order book, it is constituted by two queues of orders in each instant—sell orders and buy orders. At each simulation step, various new orders are inserted into the respective queues. As soon as a new order enters the book, the first buy order and the first sell order of the lists are inspected to verify if they match. If they match, a transaction occurs. This in contrast with the approach adopted by Chiarella et al.
The proposed model is, to our knowledge, the first model that aims to study the Bitcoin market and in general a cryptocurrency market— as a whole, including the economics of mining. It was validated by performing several statistical analyses in order to study the stylized facts of Bitcoin price and returns, following the approaches used by Chiarella et al. Today, every few minutes thousands of people send and receive Bitcoins through the peer-to-peer electronic cash system created by Satoshi Nakamoto.
All transactions are public and stored in a distributed database called Blockchain, which is used to confirm transactions and prevent the double-spending problem. There is no way of knowing how this sequence will look before calculating it, and the introduction of a minor change in the initial data causes a drastic change in the resulting Hash.
The goal is to find a Hash having a given number of leading zero bits. This number can be varied to change the difficulty of the problem. Producing a single hash is computationally very easy. Consequently, in order to regulate the generation of Bitcoins, the Bitcoin protocol makes this task more and more difficult over time. If the hash does not match the required format, a new nonce is generated and the Hash calculation starts again [ 1 ].
Non-specialized hardware comparison
Countless attempts may be necessary before finding a nonce able to generate a correct Hash the size of the nonce is only 32 bits, so in practice it is necessary to vary also other information inside the block to be able to get a hash with the required number of leading zeros, which at the time of writing is about The computational complexity of the process necessary to find the proof-of-work is adjusted over time in such a way that the number of blocks found each day is more or less constant approximately blocks in two weeks, one every 10 minutes.
In the beginning, each generated block corresponded to the creation of 50 Bitcoins, this number being halved each four years, after , blocks additions. So, the miners have a reward equal to 50 Bitcoins if the created blocks belong to the first , blocks of the Blockchain, 25 Bitcoins if the created blocks range from the ,st to the ,th block in the Blockchain, Over time, mining Bitcoin is getting more and more complex, due to the increasing number of miners, and the increasing power of their hardware.
We have witnessed the succession of four generations of hardware, i. To face the increasing costs, miners are pooling together to share resources. Like him, the early miners mined Bitcoin running the software on their personal computers. Each era announces the use of a specific typology of mining hardware. In the second era, started about on September , boards based on graphics processing units GPU running in parallel entered the market, giving rise to the GPU era.
Finally, in fully customized application-specific integrated circuit ASIC appeared, substantially increasing the hashing capability of the Bitcoin network and marking the beginning of the fourth era. Over time, the different mining hardware available was characterized by an increasing hash rate, a decreasing power consumption per hash, and increasing costs. The goal of our work is to model the economy of the mining process, so we neglected the first era, when Bitcoins had no monetary value, and miners used the power available on their PCs, at almost no cost.
We simulated only the remaining three generations of mining hardware.
We gathered information about the products that entered the market in each era to model these three generations of hardware, in particular with the aim to compute:. The average hash rate and the average power consumption were computed averaging the real market data at specific times and constructing two fitting curves. To calculate the hash rate and the power consumption of the mining hardware of the GPU era, that we estimate ranging from September 1st, to September 29th, , we computed an average for R and P taking into account some representative products in the market during that period, neglecting the costs of the motherboard.
In that era, motherboards with more than one Peripheral Component Interconnect Express PCIe slot started to enter the market, allowing to install multiple video cards in only one system, by using adapters, and to mine criptocurrency, thanks to the power of the GPUs. In Table 1 , we describe the features of some GPUs in the market in that period.
We call the fitting curves R t and P t , respectively.
We used a general exponential model to fit the curve of the hash rate, R t obtained by using Eq 1 :. The fitting curve of the power consumption P t is also a general exponential model:. Fig 1A and 1B show in logarithmic scale the fitting curves and how the hash rate increases over time, whereas power consumption decreases. We used blockchain.
In particular, we observed the time trend of the Bitcoin price in the market, the total number of Bitcoins, the total hash rate of the Bitcoin network and the total number of Bitcoin transactions. The proposed model presents an agent-based artificial cryptocurrency market in which agents mine, buy or sell Bitcoins. We modeled the Bitcoin market starting from September 1st, , because one of our goals is to study the economy of the mining process. It was only around this date that miners started to buy mining hardware to mine Bitcoins, denoting a business interest in mining.
Previously, they typically just used the power available on their personal computers. Miners belong to mining pools. This means that at each time t they always have a positive probability to mine at least a fraction of Bitcoin.
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Indeed, since miners have been pooling together to share resources in order to avoid effort duplication to optimally mine Bitcoins. A consequence of this fact is that gains are smoothly distributed amongst Miners. Since then, the difficulty of the problem of mining increased exponentially, and nowadays it would be almost unthinkable to mine without participating in a pool.
In the next subsections we describe the model simulating the mining, the Bitcoin market and the related mechanism of Bitcoin price formation in detail. Agents, or traders, are divided into three populations: Miners, Random traders and Chartists.
Every i -th trader enters the market at a given time step, t i E. Such a trader can be either a Miner, a Random trader or a Chartist. They represent the persons present in the market, mining and trading Bitcoins, before the period considered in the simulation. These traders represent people interested in entering the market, investing their money in it.
Modeling and Simulation of the Economics of Mining in the Bitcoin Market
The wealth distribution of traders follows a Zipf law [ 32 ]. Also, the wealth distribution in crypto cash of the traders in the market at initial time follows a Zipf law. More details on the trader wealth endowment are illustrated in Appendix A , in S1 Appendix. In that appendix, we report also some results that show that the heterogeneity in the fiat and crypto cash of the traders emerges endogenously also when traders start from the same initial wealth. Miners are in the Bitcoin market aiming to generate wealth by gaining Bitcoins. Core i5 is a brand name of a series of fourth-generation x64 microprocessors developed by Intel and brought to market in October In addition, over time all Miners can improve their hashing capability by buying new mining hardware investing both their fiat and crypto cash.
AMD HD 6970M vs ATI Mobility HD 5870
At each time t , their values are given by using the fitting curves described in subsection Modelling the Mining Hardware Performances ;. It is equal to a random variable characterized by a lognormal distribution with average 0. It is equal to 0.