Understanding the strategic behavior of miners in a blockchain is of great importance for its proper operation. A common model for mining games considers an infinite time horizon, with players optimizing asymptotic average objectives. Implicitly, this assumes that the asymptotic behaviors are realized at human-scale times, otherwise invalidating current models. We study the mining game utilizing Markov Decision Processes. Our approach allows us to describe the asymptotic behavior of the game in terms of the stationary distribution of the induced Markov chain. We focus on a model with two players under immediate release, assuming two different objectives: the (asymptotic) average reward per turn and the (asymptotic) percentage of obtained blocks.
Using tools from Markov chain analysis, we show the existence of a strategy achieving slow mixing times, exponential in the policy parameters. This result emphasizes the imperative need to understand convergence rates in mining games, validating the standard models. Towards this end, we provide upper bounds for the mixing time of certain meaningful classes of strategies. This result yields criteria for establishing that long-term averaged functions are coherent as payoff functions. Moreover, by studying hitting times, we provide a criterion to validate the common simplification of considering finite states models. For both considered objectives functions, we provide explicit formulae depending on the stationary distribution of the underlying Markov chain. In particular, this shows that both mentioned objectives are not equivalent. Finally, we perform a market share case study in a particular regime of the game. More precisely, we show that an strategic player with a sufficiently large processing power can impose negative revenue on honest players.
To participate in the distributed consensus of permissionless blockchains, prospective nodes -- or miners -- provide proof of designated, costly resources. However, in contrast to the intended decentralization, current data on blockchain mining unveils increased concentration of these resources in a few major entities, typically mining pools. To study strategic considerations in this setting, we employ the concept of Oceanic Games, Milnor and Shapley (1978). Oceanic Games have been used to analyze decision making in corporate settings with small numbers of dominant players (shareholders) and l…
It is an important decision-making problem for a miner in the blockchain networks if he/she participates in the mining so that he/she earns a reward by creating a new block earlier than other miners. We formulate this decision-making problem as a noncooperative game, because the probability of creating a block depends not only on one's own available computational resources, but also those of other miners. Through theoretical and numerical analyses, we show a hysteresis phenomenon of Nash equilibria depending on the reward and a jump phenomenon of miner decisions by a slight change in reward. W…
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 …
To maintain blockchain-based services with ensuring its security, it is an important issue how to decide a mining reward so that the number of miners participating in the mining increases. We propose a dynamical model of decision-making for miners using an evolutionary game approach and analyze the stability of equilibrium points of the proposed model. The proposed model is described by the 1st-order differential equation. So, it is simple but its theoretical analysis gives an insight into the characteristics of the decision-making. Through the analysis of the equilibrium points, we show the t…
In blockchain networks adopting the proof-of-work schemes, the monetary incentive is introduced by the Nakamoto consensus protocol to guide the behaviors of the full nodes (i.e., block miners) in the process of maintaining the consensus about the blockchain state. The block miners have to devote their computation power measured in hash rate in a crypto-puzzle solving competition to win the reward of publishing (a.k.a., mining) new blocks. Due to the exponentially increasing difficulty of the crypto-puzzle, individual block miners tends to join mining pools, i.e., the coalitions of miners, in o…
Towards Secure Decentralized Applications and Consensus Protocols in Blockchains (on Selfish Mining, Undercutting Attacks, DAG-Based Blockchains, E-Voting, Cryptocurrency Wallets, Secure-Logging, and CBDC)
Blockchain systems often employ proof-of-work consensus protocols to validate and add transactions into hashchains. These protocols stimulate competition among miners in solving cryptopuzzles (e.g. SHA-256 hash computation in Bitcoin) in exchange for a monetary reward. Here, we model mining as an all-pay auction, where miners' computational efforts are interpreted as bids, and the allocation function is the probability of solving the cryptopuzzle in a single attempt with unit (normalized) computational capability. Such an allocation function captures how blockchain systems control the difficul…
Temporary fork is a fundamental phenomenon in many blockchains with proof of work, and the analysis of temporary fork has recently drawn great attention. Different from existing efforts that focus on the blockchain system factors such as block size, network propagation delay or block generation speed, in this paper we explore a new key dimension of computing power from the miners' perspective. Specifically, we first propose a detailed mathematical model to characterize the impact of computing power competition of the mining pools on the temporary fork. We also derive closed-form formula of the…
In a PoW-based blockchain network, mining pools (the solo miner could be regarded as a mining pool containing one miner) compete to successfully mine blocks to pursue rewards. Generally, the rewards include the fixed block subsidies and time-varying transaction fees. The transaction fees are offered by the senders whose transactions are packaged into blocks and is increasing with the block size. However, the larger size of a block brings the longer latency, resulting in a smaller probability of successfully mining. Therefore, finding the optimal block size to trade off these two factors is a c…
We study the strategic considerations of miners participating in the bitcoin's protocol. We formulate and study the stochastic game that underlies these strategic considerations. The miners collectively build a tree of blocks, and they are paid when they create a node (mine a block) which will end up in the path of the tree that is adopted by all. Since the miners can hide newly mined nodes, they play a game with incomplete information. Here we consider two simplified forms of this game in which the miners have complete information. In the simplest game the miners release every mined block imm…
The pool-hopping attack casts down the expected profits of both the mining pool and honest miners in Blockchain. The mainstream countermeasures, namely PPS (pay-per-share) and PPLNS (pay-per-last-N-share), can hedge pool hopping, but pose a risk to the pool as well as the cost to miners. In this study, we apply the zero-determinant (ZD) theory to design a novel pooled mining which offers an incentive mechanism for motivating non-memorial and memorial evolutionary miners not to switch in pools strategically. In short, our hopping-proof pooled mining has three unique features: 1) fee-free. No fe…
A blockchain, such as Bitcoin, is an append-only, secure, transparent, distributed ledger. A fair blockchain is expected to have healthy metrics; high honest mining power, low processing latency, i.e., low wait times for transactions and stable price of consumption, i.e., the minimum transaction fee required to have a transaction processed. As Bitcoin matures, the influx of transactions increases and the block rewards become insignificant. We show that under these conditions, it becomes hard to maintain the health of the blockchain. In Bitcoin, under these mature operating conditions (MOC), th…
The selfish mining attack, arguably the most famous game-theoretic attack in blockchain, indicates that the Bitcoin protocol is not incentive-compatible. Most subsequent works mainly focus on strengthening the selfish mining strategy, thus enabling a single strategic agent more likely to deviate. In sharp contrast, little attention has been paid to the resistant behavior against the selfish mining attack, let alone further equilibrium analysis for miners and mining pools in the blockchain as a multi-agent system. In this paper, first, we propose a strategy called insightful mining to counterac…
The decentralized cryptocurrency Bitcoin has experienced great success but also encountered many challenges. One of the challenges has been the long confirmation time. Another challenge is the lack of incentives at certain steps of the protocol, raising concerns for transaction withholding, selfish mining, etc. To address these challenges, we propose Solida, a decentralized blockchain protocol based on reconfigurable Byzantine consensus augmented by proof-of-work. Solida improves on Bitcoin in confirmation time, and provides safety and liveness assuming the adversary control less than (roughly…
Mining in the blockchain requires high computing power to solve the hash puzzle for example proof-of-work puzzle. It takes high cost to achieve the calculation of this problem in devices of IOT, especially the mobile devices of IOT. It consequently restricts the application of blockchain in mobile environment. However, edge computing can be utilized to solve the problem for insufficient computing power of mobile devices in IOT. Edge servers can recruit many mobile devices to contribute computing power together to mining and share the reward of mining with these recruited mobile devices. In thi…
This paper proposes a conceptual framework for the analysis of reward sharing schemes in mining pools, such as those associated with Bitcoin. The framework is centered around the reported shares in a pool instead of agents and results in two new fairness criteria, absolute and relative redistribution. These criteria impose that the addition of a share to the pool affects all previous shares in the same way, either in absolute amount or in relative ratio. We characterize two large classes of economically viable reward sharing schemes corresponding to each of these fairness criteria in turn. We …
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 (posi…
We study a game-theoretic model of blockchain mining economies and show that griefing, a practice according to which participants harm other participants at some lesser cost to themselves, is a prevalent threat at its Nash equilibria. The proof relies on a generalization of evolutionary stability to non-homogeneous populations via griefing factors (ratios that measure network losses relative to deviator's own losses) which leads to a formal theoretical argument for the dissipation of resources, consolidation of power and high entry barriers that are currently observed in practice. A critical a…
Survey on Strategic Mining in Blockchain: A Reinforcement Learning Approach
Zhongguancun Laboratory（中关村实验室）；Peking University（北京大学）；Beihang University（北京航空航天大学）；Hangzhou International Innovation Institute of Beihang University（北京航空航天大学杭州国际创新研究院）
Indiana University-Purdue University Indianapolis（印第安纳大学-普渡大学印第安纳波利斯分校）；Bowling Green State University（鲍灵格林州立大学）；Shandong University（山东大学）
Blockchain-based federated learning (BCFL) has recently gained tremendous attention because of its advantages such as decentralization and privacy protection of raw data. However, there has been few research focusing on the allocation of resources for clients in BCFL. In the BCFL framework where the FL clients and the blockchain miners are the same devices, clients broadcast the trained model updates to the blockchain network and then perform mining to generate new blocks. Since each client has a limited amount of computing resources, the problem of allocating computing resources into training…
Many of today's crypto currencies use blockchains as decentralized ledgers and secure them with proof of work. In case of a fork of the chain, Bitcoin's rule for achieving consensus is selecting the longest chain and discarding the other chain as stale. It has been demonstrated that this consensus rule has a weakness against selfish mining in which the selfish miner exploits the variance in block generation by partially withholding blocks. In Ethereum, however, under certain conditions stale blocks don't have to be discarded but can be referenced from the main chain as uncle blocks yielding a …
In the past decades, the blockchain technology has attracted tremendous attention from both academia and industry. The popularity of blockchain networks was originated from a crypto-currency to serve as a decentralized and tamperproof transaction data ledger. Nowadays, blockchain as the key framework in the decentralized public data-ledger, has been applied to a wide range of scenarios far beyond crypto-currencies, such as Internet of Things (IoT), healthcare, and insurance. This survey aims to fill the gap between the large number of studies on blockchain network, where game theory emerges as…
Transaction fees represent a major incentive in many blockchain systems as a way to incentivize processing transactions. Unfortunately, they also introduce an enormous amount of incentive asymmetry compared to alternatives like fixed block rewards. We analyze some of the incentive compatibility issues that arise from transaction fees, which relate to the bids that users submit, the allocation rules that miners use to choose which transactions to include, and where they choose to mine in the context of longest-chain consensus. We start by surveying a variety of mining attacks including undercut…
