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Bitcoin mining is a wasteful and resource-intensive process. To add a block of transactions to the blockchain, miners spend a considerable amount of energy. The Bitcoin protocol, named 'proof of work' (PoW), resembles a lottery and the…

This paper studies a fundamental problem regarding the security of blockchain on how the existence of multiple misbehaving pools influences the profitability of selfish mining. Each selfish miner maintains a private chain and makes it…

The rewards a blockchain miner earns vary with time. Most of the time is spent mining without receiving any rewards, and only occasionally the miner wins a block and earns a reward. Mining pools smoothen the stochastic flow of rewards, and…

Blockchain consensus is a state whereby each node in a network agrees on the current state of the blockchain. Existing protocols achieve consensus via a contest or voting procedure to select one node as a dictator to propose new blocks.…

Evolutionary game dynamics on networks typically consider the competition among simple strategies such as cooperation and defection in the Prisoner's Dilemma and summarize the effect of population structure as network reciprocity. However,…

As a key enabler of Web3, Ethereum has long faced scalability challenges. The recent EIP-4844 upgrade aims to alleviate the scalability issue by introducing the ''blob'', a new data structure for Layer-2 rollups that enables off-chain…

Proof of Stake (PoS) protocols rely on voting mechanisms to reach consensus on the current state. If an enhanced majority of staking nodes, also called validators, agree on a proposed block, then this block is appended to the blockchain.…

Blockchains rely on economic incentives to ensure secure and decentralised operation, making incentive compatibility a core design concern. However, protocols are rarely deployed in isolation. Applications interact with the underlying…

In this paper, we review the undercutting attacks in the transaction-fee-based regime of proof-of-work (PoW) blockchains with the longest chain fork-choice rule. Next, we focus on the problem of fluctuations in mining revenue and the mining…

Mining is the important part of the blockchain used the proof of work (PoW) on its consensus, looking for the matching block through testing a number of hash calculations. In order to attract more hash computing power, the miner who finds…

We propose a mean field game model to study the question of how centralization of reward and computational power occur in Bitcoin-like cryptocurrencies. Miners compete against each other for mining rewards by increasing their computational…

As the core technology behind Bitcoin, Blockchain's decentralized, tamper-proof, and traceable features make it the preferred platform for organizational innovation. In current Bitcoin, block reward is halved every four years, and…

Following the publication of Bitcoin's arguably most famous attack, selfish mining, various works have introduced mechanisms to enhance blockchain systems' game theoretic resilience. Some reward mechanisms, like FruitChains, have been shown…

A soft control of the network activity through varying reward in a proof-of-work (PoW) cryptocurrency is reported. Rewards are the necessity to incent the contributors activities (i.e., mining) in order to maintain the PoW network. Contrary…

Blockchain systems run consensus rules as code to agree on the state of the distributed ledger and secure the network. Changing these rules can be risky and challenging. In addition, it can often be controversial and take much effort to…

The study of the evolution of cooperative behaviours --which provide benefits to others-- and altruism --which provides benefits to others at a cost to oneself-- has been on the core of the evolutionary game theoretical framework since its…

Selfish mining is a well known vulnerability in blockchains exploited by miners to steal block rewards. In this paper, we explore a new form of selfish mining attack that guarantees high rewards with low cost. We show the feasibility of…

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 develop a dynamic model of the Bitcoin market where users set fees themselves and miners decide whether to operate and whom to validate based on those fees. Our analysis reveals how, in equilibrium, users adjust their bids in response to…

Blockchain protocols incentivize participation through monetary rewards, assuming rational actors behave honestly to maximize their gains. However, attackers may attempt to harm others even at personal cost. These denial of profit attacks…