In January 3, 2009, Satoshi Nakamoto gave rise to the "Bitcoin Block Chain" creating the first block of the chain hashing on his computers central processing unit (CPU). Since then, the hash calculations to mine Bitcoin have been getting more and more complex, and consequently the mining hardware evolved to adapt to this increasing difficulty. Three generations of mining hardware have followed the CPU's generation. They are GPU's, FPGA's and ASIC's generations. This work presents an agent based artificial market model of the Bitcoin mining process and of the Bitcoin transactions. The goal of this work is to model the economy of the mining process, starting from GPU's generation, the first with economic significance. The model reproduces some "stylized facts" found in real time price series and some core aspects of the mining business. In particular, the computational experiments performed are able to reproduce the unit root property, the fat tail phenomenon and the volatility clustering of Bitcoin price series. In addition, under proper assumptions, they are able to reproduce the price peak at the end of November 2013, its next fall in April 2014, the generation of Bitcoins, the hashing capability, the power consumption, and the mining hardware and electrical energy expenses of the Bitcoin network. The study and analysis of the cryptocurrency market is a relatively new field. In the last years, several papers appeared on this topic given its potential interest and the many issues related to it (see for instance the works [3, 5, 7, 24, 28, 29, 39, 53] ). However, very few works were made to model the cryptocurrencies market. We can cite the works by Luther [37] , who studied why some cryptocurrencies failed to gain widespread acceptance using a simple agent model; by Bornholdt et al. [6], who proposed a model based on Moran process to study the cryptocurrencies able to emerge; by Garcia et al. [27], who studied the role of social interactions in the creation of price bubbles; by Kristoufek [31] who analysed the main drivers of the Bitcoin price; and by Kaminsky et al. [30] who related the Bitcoin market with its sentiment analysis on social networks. In this paper we propose a complex agent-based model in order to reproduce the economy of the mining process and the main stylized facts of the Bitcoin price series. Our model is inspired by business, economic and financial agent-based models that depict how organizations, or in general the economy of a country, create, deliver, and capture value. As regards the business models, Amini et al. [2] presented a agent-based model with the aim to analyze the impact of alternative production and sales policies on the diffusion of a new product; Cocco et al. [12, 13, 14] proposed agent-based models to simulate the software market and analyze the business processes and policies adopted by proprietary software firms and Open Source software firms; Li et al. [35] researched the dominant players behavior in supply chains and the relationship between the selling prices and purchasing prices in supply chains by using a multi-agent simulation model; Rohitratana et al. [51] studied the pricing schemes of the market of the Software as-a-Service and on the market of the proprietary or traditional software; finally, Xiaoming et al. [56] studied how a firm maximizes its profit by determining the production and sales policies for a new product during the lifetime of the product. Concerning economic models, in [11] the authors presented one of the most significant agent-based model developed to date in order to study the European economy. In particular, they show how monetary policies, i.e, credit money supplied by commercial banks as loans to firms, influence the economy of a country. In [21, 23] agent based keynesian models are presented in order to investigate the properties of macro economic dynamics and the impact of public polices on supply, demand and the fundamentals of the economy, and to study the interactions between income distribution and monetary and fiscal policies. As regards artificial financial market models, they reproduce the real functioning of markets, trying to explain the main stylised facts observed in financial markets, such as the fat-tailed distribution of returns, the volatility clustering, and the unit-root property. For a review, see works [8] and [9]. Raberto et al. [47] and Cincotti et al. [10] proposed the Genoa Artificial Stock Mar-
In REF the same authors proposed an agent-based artificial cryptocurrency market in order to model the economy of the mining process.
Modeling and Simulation of the Economics of Mining in the Bitcoin Market
PLoS ONE
PLoS ONE
Economics Computer Science Medicine