A Survey on Consensus Mechanisms and Mining Strategy Management in Blockchain Networks <s> B. Resource Investment and Transaction Selection for Mining under Nakamoto Protocols <s> Besides attracting a billion dollar economy, Bitcoin revolutionized the field of digital currencies and influenced many adjacent areas. This also induced significant scientific interest. In this survey, we unroll and structure the manyfold results and research directions. We start by introducing the Bitcoin protocol and its building blocks. From there we continue to explore the design space by discussing existing contributions and results. In the process, we deduce the fundamental structures and insights at the core of the Bitcoin protocol and its applications. As we show and discuss, many key ideas are likewise applicable in various other fields, so that their impact reaches far beyond Bitcoin itself. <s> BIB001 </s> A Survey on Consensus Mechanisms and Mining Strategy Management in Blockchain Networks <s> B. Resource Investment and Transaction Selection for Mining under Nakamoto Protocols <s> When processing transactions in a block, a miner increases his reward but also decreases his probability to earn any reward because the time needed for his block to reach consensus depends on its size. We show that this leads to a game situation between miners. We analytically solve this game for two miners. Then, we show that miners do not play a Nash equilibrium in the current Bitcoin mining environment, instead, they should not process any transaction. Finally, we show that the situation where no transaction is ever processed would stop being a Nash equilibrium if the transaction fee was multiplied or, equivalently, the fixed reward divided by a factor of about 12. <s> BIB002 </s> A Survey on Consensus Mechanisms and Mining Strategy Management in Blockchain Networks <s> B. Resource Investment and Transaction Selection for Mining under Nakamoto Protocols <s> This paper presents a simple game theoretic framework, assuming complete information, to model Bitcoin mining activity. It does so by formalizing the activity as an all-pay contest: a competition where participants contend with each other to win a prize by investing in computational power, and victory is probabilistic. With at least two active miners, the unique pure strategy Nash equilibrium of the game suggests the following interesting insights on the motivation for being a miner: while the optimal amount of energy consumption depends also on the reward for solving the puzzle, as long as the reward is positive the decision to be an active miner depends only on the mining costs. Moreover, the intrinsic structure of the mining activity seems to prevent the formation of a monopoly, because in an equilibrium with two miners, both of them will have positive expected profits for any level of the opponent’s costs. A monopoly could only form if the rate of return on investment were higher outside bitcoin. <s> BIB003 </s> A Survey on Consensus Mechanisms and Mining Strategy Management in Blockchain Networks <s> B. Resource Investment and Transaction Selection for Mining under Nakamoto Protocols <s> Blockchain technologies are gaining massive momentum in the last few years. Blockchains are distributed ledgers that enable parties who do not fully trust each other to maintain a set of global states. The parties agree on the existence, values and histories of the states. As the technology landscape is expanding rapidly, it is both important and challenging to have a firm grasp of what the core technologies have to offer, especially with respect to their data processing capabilities. In this paper, we first survey the state of the art, focusing on private blockchains (in which parties are authenticated). We analyze both in-production and research systems in four dimensions: distributed ledger, cryptography, consensus protocol and smart contract. We then present BLOCKBENCH, a benchmarking framework for understanding performance of private blockchains against data processing workloads. We conduct a comprehensive evaluation of three major blockchain systems based on BLOCKBENCH, namely Ethereum, Parity and Hyperledger Fabric. The results demonstrate several trade-offs in the design space, as well as big performance gaps between blockchain and database systems. Drawing from design principles of database systems, we discuss several research directions for bringing blockchain performance closer to the realm of databases. <s> BIB004 </s> A Survey on Consensus Mechanisms and Mining Strategy Management in Blockchain Networks <s> B. Resource Investment and Transaction Selection for Mining under Nakamoto Protocols <s> With the exponential rise in the number of devices, the Internet of Things (IoT) is geared toward edge-centric computing to offer high bandwidth, low latency, and improved connectivity. In contrast, legacy cloud-centric platforms offer deteriorated bandwidth and connectivity that affect the quality of service. Edge-centric Internet of Things-based technologies, such as fog and mist computing, offer distributed and decentralized solutions to resolve the drawbacks of cloud-centric models. However, to foster distributed edge-centric models, a decentralized consensus system is necessary to incentivize all participants to share their edge resources. This paper is motivated by the shortage of comprehensive reviews on decentralized consensus systems for edge-centric Internet of Things that elucidates myriad of consensus facets, such as data structure, scalable consensus ledgers, and transaction models. Decentralized consensus systems adopt either blockchain or blockchainless directed acyclic graph technologies, which serve as immutable public ledgers for transactions. This paper scrutinizes the pros and cons of state-of-the-art decentralized consensus systems. With an extensive literature review and categorization based on existing decentralized consensus systems, we propose a thematic taxonomy. The pivotal features and characteristics associated with existing decentralized consensus systems are analyzed via a comprehensive qualitative investigation. The commonalities and variances among these systems are analyzed using key criteria derived from the presented literature. Finally, several open research issues on decentralized consensus for edge-centric IoT are presented, which should be highlighted regarding centralization risk and deficiencies in blockchain/blockchainless solutions. <s> BIB005 </s> A Survey on Consensus Mechanisms and Mining Strategy Management in Blockchain Networks <s> B. Resource Investment and Transaction Selection for Mining under Nakamoto Protocols <s> In proof-of-work-based blockchain networks, the block miners participate in a crypto-puzzle solving competition to win the reward of publishing (i.e., mining) new blocks. Due to the remarkable difficulty of the crypto-puzzle, individual miners tend to join mining pools to secure stable profits. We study the dynamics of mining pool selection in a blockchain network, where mining pools may choose arbitrary block mining strategies. We identify the hash rate for puzzle-solving and the block propagation delay as two major factors determining the mining competition results. We then model the strategy evolution of individual miners as an evolutionary game. We provide the theoretical analysis of evolutionary stability in the pool selection dynamics for a two-pool case. Numerical simulations support our theoretical findings as well as demonstrate the stability in the evolution of miners’ strategies in a general case. <s> BIB006 </s> A Survey on Consensus Mechanisms and Mining Strategy Management in Blockchain Networks <s> B. Resource Investment and Transaction Selection for Mining under Nakamoto Protocols <s> Blockchain, an emerging decentralized security system, has been applied in many applications, such as bitcoin, smart grid, and Internet-of-Things. However, running the mining process may cost too much energy consumption and computing resource usage on handheld devices, which restricts the use of blockchain in mobile environments. In this paper, we consider deploying edge computing service to support the mobile blockchain. We propose an auction-based edge computing resource market of the edge computing service provider. Since there is competition among miners, the allocative externalities (positive and negative) are taken into account in the model. In our auction mechanism, we maximize the social welfare while guaranteeing the truthfulness, individual rationality and computational efficiency. Based on blockchain mining experiment results, we define a hash power function that characterizes the probability of successfully mining a block. Through extensive simulations, we evaluate the performance of our auction mechanism which shows that our edge computing resources market model can efficiently solve the social welfare maximization problem for the edge computing service provider. <s> BIB007 </s> A Survey on Consensus Mechanisms and Mining Strategy Management in Blockchain Networks <s> B. Resource Investment and Transaction Selection for Mining under Nakamoto Protocols <s> Public blockchain networks using proof of work (PoW)-based consensus protocols are considered as a promising platform for decentralized resource management with financial incentive mechanisms. In order to maintain a secured, universal state of the blockchain, PoW-based consensus protocols financially incentivize the nodes in the network to compete for the privilege of block generation through cryptographic puzzle solving. For rational consensus nodes, i.e., miners with limited local computational resources, offloading the computation load for PoW to the cloud/fog providers (CFPs) becomes a viable option. In this paper, we study the interaction between the CFPs and the miners in a PoW-based blockchain network using a game theoretic approach. In particular, we propose a lightweight infrastructure of the PoW-based blockchains, where the computation-intensive part of the consensus process is offloaded to the cloud/fog. We formulate the computation resource management in the blockchain consensus process as a two-stage Stackelberg game, where the profit of the CFP and the utilities of the individual miners are jointly optimized. In the first stage of the game, the CFP sets the price of offered computing resource. In the second stage, the miners decide on the amount of service to purchase accordingly. We apply backward induction to analyze the subgame perfect equilibria in each stage for both uniform and discriminatory pricing schemes. For uniform pricing where the same price applies to all miners, the uniqueness of the Stackelberg equilibrium is validated by identifying the best response strategies of the miners. For discriminatory pricing where the different prices are applied, the uniqueness of the Stackelberg equilibrium is proved by capitalizing on the variational inequality theory. Further, the real experimental results are employed to justify our proposed model. <s> BIB008
According to BIB004 , an honest consensus node has to invest in the mining resources, e.g., hashrates, disk space, etc, to win the puzzle solution competition under Nakamoto consensus protocols. Intuitively, the more resources a miner casts into the network, the higher chance the miner has to win the puzzle competition and obtain the mining reward. However, the success is not guaranteed because this also depends on the mining resources of other miners. Since mining resources are usually expensive, how to properly invest in the mining resources to maximize the profit is a big concern of the miners. The study in BIB003 abstracts the mining investment in the Bitcoin network as the energy consumption cost. It is assumed that N active miners in the network are competing in the "allpay contest" for block-mining rewards. The cost of presenting a unit mining resource by each miner may be different, e.g., with different electricity prices in different areas. The miners determine how much to invest in mining resources (hashrates) such that the expected profit is maximized. This forms a noncooperative game among the miners. Analysis of the game's unique Nash equilibrium in BIB003 shows that the decision of a miner to participate in the mining process or not solely depends on its individual mining cost, as long as the block reward is positive. Meanwhile, the structure of the formulated mining game prevents the emergence of a monopolistic mining activity. Namely, it is guaranteed that at least two miners will remain active in the game with positive expected profits. By (6) and (7), even if a miner succeeds in the puzzle solution competition, it is still possible for the proposed block to get orphaned due to the propagation delay. For ease of exposition, we can assume that all transactions in a block set the same amount of transactions fee F . Let R denote the fixed reward for block generation and m denote the number of transactions in the block. Then, the revenue to mine this block is R + mF . Apparently, a rational miner expects to include as many as possible transactions in a block to maximize the received reward. However, due to the risk of block orphaning, a miner also has to carefully balance the tradeoff between the mining reward and the risk of block orphaning. In  , the author proposes a mining profit model by assuming the propagation delay of a block to follow a Poisson distribution. Thus, the orphaning probability can be approximated by BIB005 . Let η denote the monetary cost per hash query and ψ denote the probability for the miner being the leader (see also BIB001 ). Then, for an average block arrival duration T and block propagation time τ , a miner's profit can be modeled as follows: The profit model in  is capable of reflecting the impact of miners' strategies in both resource investment and transaction selection. Therefore, this model is especially appropriate for game-theoretic formulation of mining resource management problems. Recently, (12) and its variation have been adopted to construct the payoff function of miners by a series of studies, which propose to use different game-based models, e.g., evolutionary game BIB006 , hierarchical game BIB008 and auctions BIB007 , to capture the rational behaviors of individual miners in different network setups. In BIB002 , an alternative model of winning probability is proposed to explicitly capture the influence of the adversary miners' strategy of block-size selection. We denote s i as block size of miner i in a blockchain network and w i as its computational power. Then, the block winning probability of miner i can be expressed by BIB002 : where t is the time when all miners start mining a new block and τ (s i ) is the time needed for a block with size s i to reach consensus. In  , the first and second terms represent the probability for miner i to first solve the puzzle based on its block, for this block to be the first one reaching the consensus across the network, respectively.  implies that the strategy of mining a large block may have positive externalities to other miners in the network. By analyzing the Nash equilibrium of the non-cooperative mining game with two miners, the author of BIB002 shows an interesting result, namely, the miner with higher computational power will prefer blocks of larger sizes. Meanwhile, the author also discusses the scenarios in which the Nash equilibrium is a breaking point, i.e., miners adopt the strategy of including no transaction in their proposed blocks. The studies in  and BIB002 essentially assume that the mining process is synchronized and all miners honestly follow the rules of block/transaction propagation in Nakamoto protocols. However, such assumptions may not be met in practical scenarios. Thus, related strategies may not be the miners' best response and further investigation is needed on this topic.