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 immediately, but are strategic on which blocks to mine. In the second more complicated game, when a block is mined it is announced immediately, but it may not be released so that other miners cannot continue mining from it. A miner not only decides which blocks to mine, but also when to release blocks to other miners. In both games, we show that when the computational power of each miner is relatively small, their best response matches the expected behavior of the bitcoin designer. However, when the computational power of a miner is large, he deviates from the expected behavior, and other Nash equilibria arise.
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)
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 playe…
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…
Open-access blockchains based on proof-of-work protocols have gained tremendous popularity for their capabilities of providing decentralized tamper-proof ledgers and platforms for data-driven autonomous organization. Nevertheless, the proof-of-work based consensus protocols are vulnerable to cyber-attacks such as double-spending. In this paper, we propose a novel approach of cyber risk management for blockchain-based service. In particular, we adopt the cyber-insurance as an economic tool for neutralizing cyber risks due to attacks in blockchain networks. We consider a blockchain service marke…
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…
Despite the popularity and practical applicability of blockchains, there is very limited work on the theoretical foundation of blockchains: The lack of rigorous theory and analysis behind the curtain of blockchains has severely staggered its broader applications. This paper attempts to lay out a theoretical foundation for a specific type of blockchains---the ones requiring basic authenticity from the participants, also called \textit{permissioned blockchain}. We formulate permissioned blockchain systems and operations into a game-theoretical problem by incorporating constraints implied by the …
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…
This paper deals with the design of the secure blockchain network framework to prevent damages from an attacker. The decentralized network design called the Blockchain Governance Game is a new hybrid theoretical model and it provides the stochastic game framework to find best strategies towards preparation for preventing a network malfunction by an attacker. Analytically tractable results are obtained by using the fluctuation theory and the mixed strategy game theory. These results enable to predict the moment for operations and deliver the optimal portion of backup nodes to protect the blockc…
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…
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 …
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…
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…
This paper deals with design of the alternative secure Blockchain network framework to prevent damages from an attacker. The concept of the strategic alliance of the management is applied on the top of the recent developed stochastic game framework. This new enhanced hybrid theoretical model has been developed based on the combination of the conventional game theory, the fluctuation theory and the Blockchain Governance Game to find best strategies towards preparation for preventing a network malfunction from an attacker by making the strategic alliance with other genuine miners. Analytically t…
This position paper presents a synthesis viewpoint of blockchains from two orthogonal perspectives: fault-tolerant distributed systems and game theory. Specifically, we formulate a new game-theoretical problem in the context of blockchains and sketch a closed-form Nash equilibrium to the problem.
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）
With the development of decentralized consensus protocols, permissionless blockchains have been envisioned as a promising enabler for the general-purpose transaction-driven, autonomous systems. However, most of the prevalent blockchain networks are built upon the consensus protocols under the crypto-puzzle framework known as proof-of-work. Such protocols face the inherent problem of transaction-processing bottleneck, as the networks achieve the decentralized consensus for transaction confirmation at the cost of very high latency. In this paper, we study the problem of consensus formation in a …
The blockchain concept forms the backbone of a new wave technology that promises to be deployed extensively in a wide variety of industrial and societal applications. Governments, financial institutions, banks, industrial supply chains, service companies, and even educational institutions and hospitals are investing in a substantial manner in the hope of improving business efficiency and operational robustness through deployment of blockchain technology. This thesis work is concerned with designing trustworthy business-to-business (B2B) market platforms drawing upon blockchain technology and g…
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…
This research contributes to the security design of an advanced smart drone swarm network based on a variant of the Blockchain Governance Game (BGG), which is the theoretical game model to predict the moments of security actions before attacks, and the Strategic Alliance for Blockchain Governance Game (SABGG), which is one of the BGG variants which has been adapted to construct the best strategies to take preliminary actions based on strategic alliance for protecting smart drones in a blockchain-based swarm network. Smart drones are artificial intelligence (AI)-enabled drones which are capable…
This paper deals with the design of the secure network in an Enhanced Internet of Vehicles by using the Blockchain Governance Game (BGG). The BGG is a system model of a stochastic game to find best strategies towards preparation of preventing a network malfunction by an attacker and the paper applies this game model into the connected vehicle security. Analytically tractable results for decision-making parameters enable to predict the moment for safety operations and to deliver the optimal combination of the number of reserved nodes with the acceptance probability of backup nodes to protect a …
Blockchains have witnessed widespread adoption in the past decade in various fields. The growing demand makes their scalability and sustainability challenges more evident than ever. As a result, more and more blockchains have begun to adopt proof-of-stake (PoS) consensus protocols to address those challenges. One of the fundamental characteristics of any blockchain technology is its crypto-economics and incentives. Lately, each PoS blockchain has designed a unique reward mechanism, yet, many of them are prone to free-rider and nothing-at-stake problems. To better understand the ad-hoc design o…
Cooperation is fundamental for human prosperity. Blockchain, as a trust machine, is a cooperative institution in cyberspace that supports cooperation through distributed trust with consensus protocols. While studies in computer science focus on fault tolerance problems with consensus algorithms, economic research utilizes incentive designs to analyze agent behaviors. To achieve cooperation on blockchains, emerging interdisciplinary research introduces rationality and game-theoretical solution concepts to study the equilibrium outcomes of various consensus protocols. However, existing studies d…
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 the leaders who assign a computing power to be consumed by miners. In stage II, miners decide of their power consumption and distribution. They find themselves in a social dilemma in which they must choose between mining in solo, therefore prioritizing their individual preferences, and participating in a pool for the collective interest. The model relies on a…
Blockchain has recently been applied in many applications such as bitcoin, smart grid, and Internet of Things (IoT) as a public ledger of transactions. However, the use of blockchain in mobile environments is still limited because the mining process consumes too much computing and energy resources on mobile devices. Edge computing offered by the Edge Computing Service Provider can be adopted as a viable solution for offloading the mining tasks from the mobile devices, i.e., miners, in the mobile blockchain environment. However, a mechanism needs to be designed for edge resource allocation to m…
Low transaction throughput and poor scalability are significant issues in public blockchain consensus protocols such as Bitcoins. Recent research efforts in this direction have proposed shard-based consensus protocols where the key idea is to split the transactions among multiple committees (or shards), which then process these shards or set of transactions in parallel. Such a parallel processing of disjoint sets of transactions or shards by multiple committees significantly improves the overall scalability and transaction throughout of the system. However, one significant research gap is a la…
Pool block withholding attack is performed among mining pools in digital cryptocurrencies, such as Bitcoin. Instead of mining honestly, pools can be incentivized to infiltrate their own miners into other pools. These infiltrators report partial solutions but withhold full solutions, share block rewards but make no contribution to block mining. The block withholding attack among mining pools can be modeled as a non-cooperative game called "the miner's dilemm", which reduces effective mining power in the system and leads to potential systemic instability in the blockchain. However, existing lite…
In this paper we analyze from the game theory point of view Byzantine Fault Tolerant blockchains when processes exhibit rational or Byzantine behavior. Our work is the first to model the Byzantine-consensus based blockchains as a committee coordination game. Our first contribution is to offer a game-theoretical methodology to analyse equilibrium interactions between Byzantine and rational committee members in Byzantine Fault Tolerant blockchains. Byzantine processes seek to inflict maximum damage to the system, while rational processes best-respond to maximise their expected net gains. Our sec…
Bilevel programming problems are often found in practice. In this paper, we handle one such bilevel application problem from the domain of environmental economics. The problem is a Stakelberg game with multiple objectives at the upper level, and a single objective at the lower level. The leader in this case is the regulating authority, and it tries to maximize its total tax revenue over multiple periods while trying to minimize the environmental damages caused by a mining company. The follower is the mining company whose sole objective is to maximize its total profit over multiple periods unde…
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…
This work lies in the fusion of experimental economics and data mining. It continues author's previous work on mining behaviour rules of human subjects from experimental data, where game-theoretic predictions partially fail to work. Game-theoretic predictions aka equilibria only tend to success with experienced subjects on specific games, what is rarely given. Apart from game theory, contemporary experimental economics offers a number of alternative models. In relevant literature, these models are always biased by psychological and near-psychological theories and are claimed to be proven by th…
