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We present an analysis of the Proof-of-Work consensus algorithm, used on the Bitcoin blockchain, using a Mean Field Game framework. Using a master equation, we provide an equilibrium characterization of the total computational power devoted…
The resource-consuming mining of blocks on a blockchain equipped with a proof of work consensus protocol bears the risk of ruin, namely when the operational costs for the mining exceed the received rewards. In this paper we investigate to…
In the context of the `selfish-mine' strategy proposed by Eyal and Sirer, we study the effect of propagation delay on the evolution of the Bitcoin blockchain. First, we use a simplified Markov model that tracks the contrasting states of…
We analyze Bitcoin mining from the perspective of a game and propose an optimal mining model that maximizes profits of pools and miners. The model is a two-stage Stackelberg game in which each stage forms a sub-game. In stage I, pools are…
Proof-of-work blockchains must implement a difficulty adjustment algorithm (DAA) in order to maintain a consistent inter-arrival time between blocks. Conventional DAAs are essentially feedback controllers, and as such, they are inherently…
Proof of Work (PoW) has extensively served as the foundation of blockchain's security, consistency, and tamper-resistance. However, long has it been criticized for its tremendous and inefficient utilization of computational power and…
The world economy is experiencing the novel adoption of distributed currencies that are free from the control of central banks. Distributed currencies suffer from extreme volatility, and this can lead to catastrophic implications during…
We present and validate a novel mathematical model of the blockchain mining process and use it to conduct an economic evaluation of the double-spend attack, which is fundamental to all blockchain systems. Our analysis focuses on the value…
The energy sustainability of blockchains, whose consensus protocol rests on the Proof-of-Work, nourishes a heated debate. The underlying issue lies in a highly energy-consuming process, defined as mining, required to validate crypto-asset…
Background: During the last years, there has been a lot of discussion and estimations on the energy consumption of Bitcoin miners. However, most of the studies are focused on estimating energy consumption, not in exploring the factors that…
The security of Bitcoin protocols is deeply dependent on the incentives provided to miners, which come from a combination of block rewards and transaction fees. As Bitcoin experiences more halving events, the protocol reward converges to…
As the pioneer of blockchain technology, Bitcoin is the most popular cryptocurrency to date. Given its dramatic price spikes (and crashes) along with the never-ending news from SEC regulations to security breaches, there seems to be a lack…
Bitcoin uses blockchain technology and proof-of-work (PoW) mechanism where nodes spend computing resources and earn rewards in return for spending these resources. This incentive system has caused power to be significantly biased towards a…
Large proof of work (PoW) networks allow anyone to earn rewards by running computation-intensive hash puzzles for profit, yet they typically consume electricity comparable to that of medium-sized countries. Repurposing computing resources…
A model is proposed for Bitcoin prices that takes into account market attention. Market attention, modeled by a mean-reverting Cox-Ingersoll-Ross processes, affects the volatility of Bitcoin returns, with some delay. The model is affine and…
We study efficiency in a proof-of-work blockchain with non-zero latencies, focusing in particular on the (inequality in) individual miners' efficiencies. Prior work attributed differences in miners' efficiencies mostly to attacks, but we…
Modern Portfolio Theory (MPT) prescribes how to maximise the return of an asset portfolio for a given level of risk. The optimal trade-off between return and variance defines the efficient frontier. Whether actual cryptoasset portfolios…
A key challenge for Bitcoin cryptocurrency holders, such as startups using ICOs to raise funding, is managing their FX risk. Specifically, a misinformed decision to convert Bitcoin to fiat currency could, by itself, cost USD millions. In…
It is interesting but difficult and challenging to study Ethereum with multiple mining pools. One of the main difficulties comes from not only how to represent such a general tree with multiple block branches (or sub-chains) related to the…
The protocol for cryptocurrencies can be divided into three parts, namely consensus, wallet, and networking overlay. The aim of the consensus part is to bring trustless rational peer-to-peer nodes to an agreement to the current status of…