The growth of the Bitcoin network during the first decade of its operation to a global scale system is a singular event in the deployment of Information Technology systems. Can this approach serve as a wider paradigm for Information Technology services beyond the use case of digital currencies? We investigate this question by introducing the concept of resource based systems and their four fundamental characteristics: (i) resource-based operation, (ii) tokenomics, (iii) decentralized service provision, and (iv) rewards sharing. We explore these characteristics, identify design goals and challenges and investigate some crucial game theoretic aspects of reward sharing that can be decisive for their effective operation.
Jin Xing Lim, Barnabé Monnot, Shaowei Lin, Georgios Piliouras
Formalization of mathematics is the process of digitizing mathematical knowledge, which allows for formal proof verification as well as efficient semantic searches. Given the large and ever-increasing gap between the set of formalized and unformalized mathematical knowledge, there is a clear need to encourage more computer scientists and mathematicians to solve and formalize mathematical problems together. With blockchain technology, we are able to decentralize this process, provide time-stamped verification of authorship and encourage collaboration through implementation of incentive mechanisms via smart contracts. Currently, the formalization of mathematics is done through the use of proof assistants, which can be used to verify programs and protocols as well. Furthermore, with the advancement in artificial intelligence (AI), particularly machine learning, we can apply automated AI reasoning tools in these proof assistants and (at least partially) automate the process of synthesizing proofs. In our paper, we demonstrate a blockchain-based system for collaborative formalization of mathematics and programs incorporating both human labour as well as automated AI tools. We explain how Token-Curated Registries (TCR) and smart contracts are used to ensure appropriate documents are recorded and encourage collaboration through implementation of incentive mechanisms respectively. Using an illustrative example, we show how formalized proofs of different sorting algorithms can be produced collaboratively in our proposed blockchain system.
In blockchains such as Bitcoin and Ethereum, users compete in a transaction fee auction to get their transactions confirmed in the next block. A line of recent works set forth the desiderata for a "dream" transaction fee mechanism (TFM), and explored whether such a mechanism existed. A dream TFM should satisfy 1) user incentive compatibility (UIC), i.e., truthful bidding should be a user's dominant strategy; 2) miner incentive compatibility (MIC), i.e., the miner's dominant strategy is to faithfully implement the prescribed mechanism; and 3) miner-user side contract proofness (SCP), i.e., no coalition of the miner and one or more user(s) can increase their joint utility by deviating from the honest behavior. The weakest form of SCP is called 1-SCP, where we only aim to provide resilience against the collusion of the miner and a single user. Sadly, despite the various attempts, to the best of knowledge, no existing mechanism can satisfy all three properties in all situations. Since the TFM departs from classical mechanism design in modeling and assumptions, to date, our understanding of the design space is relatively little. In this paper, we further unravel the mathematical structure of transaction fee mechanism design by proving the following results: - Can we have a dream TFM? - Rethinking the incentive compatibility notions. - Do the new design elements make a difference?
Blockchain systems need to solve consensus despite the presence of rational users and failures. The notion of $(k,t)$-robustness has shown instrumental to list problems that cannot be solved if $k$ players are rational and $t$ players are Byzantine or act arbitrarily. What is less clear is whether one can solve such problems if the faults are benign. In this paper, we bridge the gap between games that are robust against Byzantine players and games that are robust against crash players. Our first result is an impossibility result: We show that no $(k,t)$-robust consensus protocol can solve consensus in the crash model if $k+2t\geq n$ unless there is a particular punishment strategy, called the $(k,t)$-baiting strategy. This reveals the need to introduce baiting as the act of rewarding a colluding node when betraying its coalition, to make blockchains more secure. Our second result is an equivalence relation between crash fault tolerant games and Byzantine fault tolerant games, which raises an interesting research question on the power of baiting to solve consensus. To this end, we show, on the one hand, that a $(k,t)$-robust consensus protocol becomes $(k+t,t)$-robust in the crash model. We show, on the other hand, that the existence of a $(k,t)$-robust consensus protocol in the crash model that does not make use of a baiting strategy implies the existence of a $(k-t,t)$-robust consensus protocol in the Byzantine model, with the help of cryptography.
Propagating information to more people through their friends is becoming an increasingly important technology used in domains such as blockchain, advertising, and social media. To incentivize people to broadcast the information, the designer may use a monetary rewarding scheme, which specifies who gets how much, to compensate for the propagation. Several properties are desirable for the rewarding scheme, such as budget feasible, individually rational, incentive compatible, and Sybil-proof. In this work, we design a free market with lotteries, where every participant can decide by herself how much of the reward she wants to withhold before propagating to others. We show that in the free market, the participants have a strong incentive to maximally propagate the information and all the above properties are satisfied automatically.
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 complex and crucial problem for the mining pools. In this paper, we model a repeated mining competition dynamics in blockchain system as an evolutionary game to study the interactions among mining pools. In this game, each pool has two strategies: to follow the default size $\bar{B}$, i.e., the upper bound of a block size, or not follow. Because of the bounded rationality, each mining pool pursues its evolutionary stable block size (ESS) according to the mining pools' computing power and other factors by continuous learning and adjustments during the whole mining process. A study framework is built for the general evolutionary game, based on which we then theoretically explore the existence and stability of the ESSs for a case of two mining pools. Numerical experiments with real Bitcoin data are conducted to show the evolutionary decisions of mining pools and to demonstrate the theoretical findings in this paper.
Ethereum Improvement Proposal (EIP) 1559 was recently implemented to transform Ethereum's transaction fee market. EIP-1559 utilizes an algorithmic update rule with a constant learning rate to estimate a base fee. The base fee reflects prevailing network conditions and hence provides a more reliable oracle for current gas prices. Using on-chain data from the period after its launch, we evaluate the impact of EIP-1559 on the user experience and market performance. Our empirical findings suggest that although EIP-1559 achieves its goals on average, short-term behavior is marked by intense, chaotic oscillations in block sizes (as predicted by our recent theoretical dynamical system analysis [1]) and slow adjustments during periods of demand bursts (e.g., NFT drops). Both phenomena lead to unwanted inter-block variability in mining rewards. To address this issue, we propose an alternative base fee adjustment rule in which the learning rate varies according to an additive increase, multiplicative decrease (AIMD) update scheme. Our simulations show that the latter robustly outperforms the EIP-1559 protocol under various demand scenarios. These results provide evidence that variable learning rate mechanisms may constitute a promising alternative to the default EIP-1559-based format and contribute to the ongoing discussion on the design of more efficient transaction fee markets.
Ceren Kocaoğullar, Arthur Gervais, Benjamin Livshits
While quantitative automation related to trading crypto-assets such as ERC-20 tokens has become relatively commonplace, with services such as 3Commas and Shrimpy offering user-friendly web-driven services for even the average crypto trader, we have not yet seen the emergence of on-chain trading as a phenomenon. We hypothesize that just like decentralized exchanges (DEXes) that by now are by some measures more popular than traditional exchanges, process in the space of decentralized finance (DeFi) may enable attractive online trading automation options. In this paper we present ChainBot, an approach for creating algorithmic trading bots with the help of blockchain technology. We show how to partition the computation into on- and off-chain components in a way that provides a measure of end-to-end integrity, while preserving the algorithmic "secret sauce". Our system is enabled with a careful use of algorithm partitioning, zero-knowledge proofs and smart contracts. We also show that with layer-2 (L2) technologies, trades can be kept private, which means that algorithmic parameters are difficult to recover by a chain observer. Our approach offers more transparent access to liquidity and better censorship-resistance compared to traditional off-chain trading approaches. We develop a sample ChainBot and train it on historical data, resulting in returns that are up to 2.4x the buy-and-hold strategy, which we use as our baseline. Our measurements show that across 1000 runs, the end-to-end average execution time for our system is 48.4 seconds. We demonstrate that the frequency of trading does not significantly affect the rate of return and Sharpe ratio, which indicates that we do not have to trade at every block, thereby significantly saving in terms of gas fees. In our implementation, a user who invests \$1,000 would earn \$105, and spend \$3 on gas; assuming a user pool of 1,000 subscribers.
Sophie Rain, Georgia Avarikioti, Laura Kovács, Matteo Maffei
Off-chain protocols constitute one of the most promising approaches to solve the inherent scalability issue of blockchain technologies. The core idea is to let parties transact on-chain only once to establish a channel between them, leveraging later on the resulting channel paths to perform arbitrarily many peer-to-peer transactions off-chain. While significant progress has been made in terms of proof techniques for off-chain protocols, existing approaches do not capture the game-theoretic incentives at the core of their design, which led to overlooking significant attack vectors like the Wormhole attack in the past. In this work we take a first step towards a principled game-theoretic security analysis of off-chain protocols by introducing the first game-theoretic model that is expressive enough to reason about their security. We advocate the use of Extensive Form Games (EFGs) and introduce two instances of EFGs to capture security properties of the closing and the routing of the Lightning Network. Specifically, we model the closing protocol, which relies on punishment mechanisms to disincentivize parties to upload old channel states on-chain. Moreover, we model the routing protocol, thereby formally characterizing the Wormhole attack, a vulnerability that undermines the fee-based incentive mechanism underlying the Lightning Network.
JUBILEE is a securely computed mechanism for debt relief and forgiveness in a frictionless manner without involving trusted third parties, leading to more harmonious debt settlements by incentivising the parties to truthfully reveal their private information. JUBILEE improves over all previous methods: - individually rational, incentive-compatible, truthful/strategy-proof, ex-post efficient, optimal mechanism for debt relief and forgiveness with private information - by the novel introduction of secure computation techniques to debt relief, the "blessing of the debtor" is hereby granted for the first time: debt settlements with higher expected profits and a higher probability of success than without using secure computation A simple and practical implementation is included for "The Secure Spreadsheet". Another implementation is realised using Raziel smart contracts on a blockchain with Pravuil consensus.
Proof-of-Stake (PoS) blockchain systems, especially those that allow stakeholders to organize themselves in “stake-pools”, have emerged as a compelling paradigm for the deployment of large scale distributed ledgers. A stake-pool operates a node that engages in the PoS protocol and potentially represents a large number of smaller stakeholders. While such pooled PoS operation is attractive from various angles, it also exhibits a significant shortcoming that, so far and to the best of our knowledge, has not been sufficiently understood or investigated. Pooled PoS operation, to be effective and not lead to sub-optimal dictatorial or cartel-like configurations, should enable the stakeholders to revoke and re-delegate their stake in a way that is aligned with their incentives. However, given that stake-pool operators are exactly those entities who determine what transactions are to be recorded in the ledger, they are quite likely to form a cartel and censor any transaction they want, such as those that attempt to adjust the current stake-pool lineup. In this way, a power grab takes place, where the stake-pool cartel perpetuates its control over the PoS system. We first model and observe formally the emergence of the above problem in pooled PoS systems. Then, we describe an anti-censorship mechanism that takes advantage of the underlying cryptographic functions of the ledger and the nature of peer-to-peer networks to diffuse information without suppression. Specifically, the mechanism exploits digital signatures which can endorse messages that are censored and bind them to delegation transactions, as well as the ability of the underlying ledger to produce unpredictable randomness which can be used to randomly “audit” the suitability of a stake-pool by forcibly expiring it. Upon such expiration, members can evaluate their membership taking into account what information is available, including information potentially not recorded in the ledger but diffused in the peer-to-peer network. We provide a thorough game-theoretic analysis of this mechanism discovering various types of Nash equilibria which demonstrate that the “revolution”, i.e., the strategic decision of pool members to withdraw support from a censoring cartel as well as the pool operators to step down, can be incentivized, under suitable and plausible conditions in the utility functions of the involved participants.
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 pool protocol based on a simulated game in which the miners compete for the reward won by the pool. The solutions for the stage I sub-game and the simulated protocol game are unique and stable Nash equilibriums while the stage II sub-game leads to a stable cooperative equilibrium only when miners choose their strategies according to certain criteria. We conclude that the cooperative optimal mining model has the potential to favor Bitcoin decentralization and stability. Mainly, the social dilemma faced by miners together with the balance of incentives ensure a certain distribution of the network computing power between pools and solo miners, while equilibriums in the game solutions provide stability to the system.
Alejandro Jofré, Angel Pardo, David Salas, Victor Verdugo · 5 authors
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.
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 further show that the intersection of these classes brings about a generalization of the well-known proportional scheme, which also leads to a new characterization of the proportional scheme as a corollary.
Proof-of-Stake blockchains based on a longest-chain consensus protocol are an attractive energy-friendly alternative to the Proof-of-Work paradigm. However, formal barriers to "getting the incentives right" were recently discovered, driven by the desire to use the blockchain itself as a source of pseudorandomness \cite{brown2019formal}. We consider instead a longest-chain Proof-of-Stake protocol with perfect, trusted, external randomness (e.g. a randomness beacon). We produce two main results. First, we show that a strategic miner can strictly outperform an honest miner with just $32.5\%$ of the total stake. Note that a miner of this size {\em cannot} outperform an honest miner in the Proof-of-Work model. This establishes that even with access to a perfect randomness beacon, incentives in Proof-of-Work and Proof-of-Stake longest-chain protocols are fundamentally different. Second, we prove that a strategic miner cannot outperform an honest miner with $30.8\%$ of the total stake. This means that, while not quite as secure as the Proof-of-Work regime, desirable incentive properties of Proof-of-Work longest-chain protocols can be approximately recovered via Proof-of-Stake with a perfect randomness beacon. The space of possible strategies in a Proof-of-Stake mining game is {\em significantly} richer than in a Proof-of-Work game. Our main technical contribution is a characterization of potentially optimal strategies for a strategic miner, and in particular, a proof that the corresponding infinite-state MDP admits an optimal strategy that is positive recurrent.
Payment channel is a protocol which allows cryptocurrency users to route multiple transactions through network without committing them to the main blockchain network (mainnet). This ability makes them the most prominent solution to blockchains' scalability problem. Each modification of payment channels requires a transaction on the mainnet and therefore, big transaction fees. In this paper, we assume that a set of payment transactions are given (batch or online) and we study the problem of scheduling modificiations on payment channels to route all of the transactions with minimum modification cost. We investigate two cost models for aforementioned problem: the step cost function in which every channel modification has a constant cost and the linear cost function in which modification costs are proportional to the amount of change. For the step cost function model, we prove impossibility results for both batch and online case. Moreover, some heuristic methods for the batch case are presented and compared. For the linear cost we propose a polynomial time algorithm using linear programming for the batch case.
Rongfei Zeng, Chao Zeng, Xingwei Wang, Bo Li · 5 authors
Federated learning utilizes various resources provided by participants to collaboratively train a global model, which potentially address the data privacy issue of machine learning. In such promising paradigm, the performance will be deteriorated without sufficient training data and other resources in the learning process. Thus, it is quite crucial to inspire more participants to contribute their valuable resources with some payments for federated learning. In this paper, we present a comprehensive survey of incentive schemes for federate learning. Specifically, we identify the incentive problem in federated learning and then provide a taxonomy for various schemes. Subsequently, we summarize the existing incentive mechanisms in terms of the main techniques, such as Stackelberg game, auction, contract theory, Shapley value, reinforcement learning, blockchain. By reviewing and comparing some impressive results, we figure out three directions for the future study.
Mohsen Rahnamaei, Saeid Tousi Saeidi, Siavash Khorsandi, Mehdi Shajari
Many companies use identity information for different goals. There are a lot of marketplaces for identity information. These markets have some practical issues such as privacy, mutual trust and fairing exchange. The management of identity information is one of the most important applications for blockchain, for which researchers have proposed a large number of models. In the present paper, an attempt has been made to solve the problems that mentioned earlier to exchange identity information on the blockchain. By using the game theory we propose a fair model of selling authorized identity information in an environment that include untrusted parties. Moreover, we employ ZK-SNARK to protect users' privacy. Also, we use proxy re-encryption to record these informations in IPFS.
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 assumption in this type of analysis is that miners' decisions have significant influence in aggregate network outcomes (such as network hashrate). However, as networks grow larger, the miner's interaction more closely resembles a distributed production economy or Fisher market and its stability properties change. In this case, we derive a proportional response (PR) update protocol which converges to market equilibria at which griefing is irrelevant. Convergence holds for a wide range of miners risk profiles and various degrees of resource mobility between blockchains with different mining technologies. Our empirical findings in a case study with four mineable cryptocurrencies suggest that risk diversification, restricted mobility of resources (as enforced by different mining technologies) and network growth, all are contributing factors to the stability of the inherently volatile blockchain ecosystem.
Demand for blockchains such as Bitcoin and Ethereum is far larger than supply, necessitating a mechanism that selects a subset of transactions to include "on-chain" from the pool of all pending transactions. This paper investigates the problem of designing a blockchain transaction fee mechanism through the lens of mechanism design. We introduce two new forms of incentive-compatibility that capture some of the idiosyncrasies of the blockchain setting, one (MMIC) that protects against deviations by profit-maximizing miners and one (OCA-proofness) that protects against off-chain collusion between miners and users. This study is immediately applicable to a recent (August 5, 2021) and major change to Ethereum's transaction fee mechanism, based on a proposal called "EIP-1559." Historically, Ethereum's transaction fee mechanism was a first-price (pay-as-bid) auction. EIP-1559 suggested making several tightly coupled changes, including the introduction of variable-size blocks, a history-dependent reserve price, and the burning of a significant portion of the transaction fees. We prove that this new mechanism earns an impressive report card: it satisfies the MMIC and OCA-proofness conditions, and is also dominant-strategy incentive compatible (DSIC) except when there is a sudden demand spike. We also introduce an alternative design, the "tipless mechanism," which offers an incomparable slate of incentive-compatibility guarantees -- it is MMIC and DSIC, and OCA-proof unless in the midst of a demand spike.
We suggest a framework to determine optimal trading fees for constant function market makers (CFMMs) in order to maximize liquidity provider returns. In a setting of multiple competing liquidity pools, we show that no race to the bottom occurs, but instead pure Nash equilibria of optimal fees exist. We theoretically prove the existence of these equilibria for pools using the constant product trade function used in popular CFMMs like Uniswap. We also numerically compute the equilibria for a number of examples and discuss the effects the equilibrium fees have on capital allocation among pools. Finally, we use our framework to compute optimal fees for real world pools using past trade data.
It is impossible to solve the Byzantine consensus problem in an open network of $n$ participants if only $2n/3$ or less of them are correct. As blockchains need to solve consensus, one might think that blockchains need more than $2n/3$ correct participants. But it is yet unknown whether consensus can be solved when less than $2n/3$ participants are correct and $k$ participants are rational players, which misbehave if they can gain the loot. Trading correct participants for rational players may not seem helpful to solve consensus since rational players can misbehave whereas correct participants, by definition, cannot. In this paper, we show that consensus is actually solvable in this model, even with less than $2n/3$ correct participants. The key idea is a baiting strategy that lets rational players pretend to misbehave in joining a coalition but rewards them to betray this coalition before the loot gets stolen. We propose TRAP, a protocol that builds upon recent advances in the theory of accountability to solve consensus as soon as $n>\max\bigl(\frac{3}{2}k+3t,2(k+t)\bigr)$: by assuming that private keys cannot be forged, this protocol is an equilibrium where no coalition of $k$ rational players can coordinate to increase their expected utility regardless of the arbitrary behavior of up to $t$ Byzantine players. Finally, we show that a baiting strategy is necessary and sufficient to solve this, so-called rational agreement problem. First, we show that it is impossible to solve this rational agreement problem without implementing a baiting strategy. Second, the existence of TRAP demonstrates the sufficiency of the baiting strategy. Our TRAP protocol finds applications in blockchains to prevent players from disagreeing, that could otherwise lead to "double spending".
EIP-1559 is a new proposed pricing mechanism for the Ethereum protocol developed to bring stability to fluctuating gas prices. To properly understand this as a stochastic process, it is necessary to develop the mathematical foundations to understand under what conditions the base fee gas price outcomes behave as a stationary process, and when it does not. Understanding these mathematical fundamentals is critical to properly engineering a stable system.
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 transcritical bifurcations and hysteresis phenomena of the equilibrium points. We also design a controller that determines the mining reward based on the number of participating miners to stabilize the state that all miners participate in the mining. Numerical simulation shows that there is a trade-off in the choice of the design parameters.