A game theoretic analysis of resource mining in blockchain

Blockchain and cryptocurrency are a hot topic in today’s digital world. In this paper, we create a game theoretic model in continuous time. We consider a dynamic game model of the bitcoin market, where miners or players use mining systems to mine bitcoin by investing electricity into the mining system. Although this work is motivated by BTC, the work presented can be applicable to other mining systems similar to BTC. We propose three concepts of dynamic game theoretic solutions to the model: Social optimum, Nash equilibrium and myopic Nash equilibrium. Using the model that a player represents a single “miner” or a “mining pool”, we develop novel and interesting results for the cryptocurrency world

A game theoretic analysis of resource mining in blockchain

Blockchain and cryptocurrency are a hot topic in today’s digital world. In this paper, we create a game theoretic model in continuous time. We consider a dynamic game model of the bitcoin market, where miners or players use mining systems to mine bitcoin by investing electricity into the mining system. Although this work is motivated by BTC, the work presented can be applicable to other mining systems similar to BTC. We propose three concepts of dynamic game theoretic solutions to the model: Social optimum, Nash equilibrium and myopic Nash equilibrium. Using the model that a player represents a single “miner” or a “mining pool”, we develop novel and interesting results for the cryptocurrency world

Be Selfish and Avoid Dilemmas: Fork After Withholding (FAW) Attacks on Bitcoin

In the Bitcoin system, participants are rewarded for solving cryptographic puzzles. In order to receive more consistent rewards over time, some participants organize mining pools and split the rewards from the pool in proportion to each participant's contribution. However, several attacks threaten the ability to participate in pools. The block withholding (BWH) attack makes the pool reward system unfair by letting malicious participants receive unearned wages while only pretending to contribute work. When two pools launch BWH attacks against each other, they encounter the miner's dilemma: in a Nash equilibrium, the revenue of both pools is diminished. In another attack called selfish mining, an attacker can unfairly earn extra rewards by deliberately generating forks. In this paper, we propose a novel attack called a fork after withholding (FAW) attack. FAW is not just another attack. The reward for an FAW attacker is always equal to or greater than that for a BWH attacker, and it is usable up to four times more often per pool than in BWH attack. When considering multiple pools - the current state of the Bitcoin network - the extra reward for an FAW attack is about 56% more than that for a BWH attack. Furthermore, when two pools execute FAW attacks on each other, the miner's dilemma may not hold: under certain circumstances, the larger pool can consistently win. More importantly, an FAW attack, while using intentional forks, does not suffer from practicality issues, unlike selfish mining. We also discuss partial countermeasures against the FAW attack, but finding a cheap and efficient countermeasure remains an open problem. As a result, we expect to see FAW attacks among mining pools.Comment: This paper is an extended version of a paper accepted to ACM CCS 201

The Miner's Dilemma

An open distributed system can be secured by requiring participants to present proof of work and rewarding them for participation. The Bitcoin digital currency introduced this mechanism, which is adopted by almost all contemporary digital currencies and related services. A natural process leads participants of such systems to form pools, where members aggregate their power and share the rewards. Experience with Bitcoin shows that the largest pools are often open, allowing anyone to join. It has long been known that a member can sabotage an open pool by seemingly joining it but never sharing its proofs of work. The pool shares its revenue with the attacker, and so each of its participants earns less. We define and analyze a game where pools use some of their participants to infiltrate other pools and perform such an attack. With any number of pools, no-pool-attacks is not a Nash equilibrium. With two pools, or any number of identical pools, there exists an equilibrium that constitutes a tragedy of the commons where the pools attack one another and all earn less than they would have if none had attacked. For two pools, the decision whether or not to attack is the miner's dilemma, an instance of the iterative prisoner's dilemma. The game is played daily by the active Bitcoin pools, which apparently choose not to attack. If this balance breaks, the revenue of open pools might diminish, making them unattractive to participants

Cryptocurrency Mining Games with Economic Discount and Decreasing Rewards

In the consensus protocols used in most cryptocurrencies, participants called miners must find valid blocks of transactions and append them to a shared tree-like data structure. Ideally, the rules of the protocol should ensure that miners maximize their gains if they follow a default strategy, which consists on appending blocks only to the longest branch of the tree, called the blockchain. Our goal is to understand under which circumstances are miners encouraged to follow the default strategy. Unfortunately, most of the existing models work with simplified payoff functions, without considering the possibility that rewards decrease over time because of the game rules (like in Bitcoin), nor integrating the fact that a miner naturally prefers to be paid earlier than later (the economic concept of discount). In order to integrate these factors, we consider a more general model where issues such as economic discount and decreasing rewards can be set as parameters of an infinite stochastic game. In this model, we study the limit situation in which a miner does not receive a full reward for a block if it stops being in the blockchain. We show that if rewards are not decreasing, then miners do not have incentives to create new branches, no matter how high their computational power is. On the other hand, when working with decreasing rewards similar to those in Bitcoin, we show that miners have an incentive to create such branches. Nevertheless, this incentive only occurs when a miner controls a proportion of the computational power which is close to half of the computational power of the entire network

Blockchain Mining Games with Pay Forward

We study the strategic implications that arise from adding one extra option to the miners participating in the bitcoin protocol. We propose that when adding a block, miners also have the ability to pay forward an amount to be collected by the first miner who successfully extends their branch, giving them the power to influence the incentives for mining. We formulate a stochastic game for the study of such incentives and show that with this added option, smaller miners can guarantee that the best response of even substantially more powerful miners is to follow the expected behavior intended by the protocol designer