Dimitris Karakostas, Aggelos Kiayias, Thomas Zacharias
We analyze bribing attacks in Proof-of-Stake distributed ledgers from a game theoretic perspective. In bribing attacks, an adversary offers participants a reward in exchange for instructing them how to behave, with the goal of attacking the protocol's properties. Specifically, our work focuses on adversaries that target blockchain safety. We consider two types of bribing, depending on how the bribes are awarded: i) guided bribing, where the bribe is given as long as the bribed party behaves as instructed; ii) effective bribing, where bribes are conditional on the attack's success, w.r.t. well-defined metrics. We analyze each type of attack in a game theoretic setting and identify relevant equilibria. In guided bribing, we show that the protocol is not an equilibrium and then describe good equilibria, where the attack is unsuccessful, and a negative one, where all parties are bribed such that the attack succeeds. In effective bribing, we show that both the protocol and the "all bribed" setting are equilibria. Using the identified equilibria, we then compute bounds on the Prices of Stability and Anarchy. Our results indicate that additional mitigations are needed for guided bribing, so our analysis concludes with incentive-based mitigation techniques, namely slashing and dilution. Here, we present two positive results, that both render the protocol an equilibrium and achieve maximal welfare for all parties, and a negative result, wherein an attack becomes more plausible if it severely affects the ledger's token's market price.
Abstract Decentralized applications (DApps) built on blockchain platforms such as Ethereum and coded in languages such as Solidity, have recently gained attention for their potential to disrupt traditional centralized systems. Despite their rapid adoption, limited research has been conducted to understand the underlying code structure of these applications. In particular, each DApp is composed of multiple smart contracts, each containing a number of functions that can be called to trigger a specific event, e.g., a token transfer. In this paper, we reconstruct and analyse the network of contracts and functions calls within the DApp, which is helpful to unveil vulnerabilities that can be exploited by malicious attackers. We show how decentralization is architecturally implemented, identifying common development patterns and anomalies that could influence the system’s robustness and efficiency. We find a consistent network structure characterized by modular, self-sufficient contracts and a complex web of function interactions, indicating common coding practices across the blockchain community. Critically, a small number of key functions within each DApp play a central role in maintaining network connectivity, making them potential targets for cyber attacks and highlighting the need for robust security measures.
Daniel Mawunyo Doe, Jing Li, Dusit Niyato, Yuqing Hu · 8 authors
In this paper, we address key challenges in Proof-of-Stake (PoS) blockchains, with a particular focus on Ethereum 2.0. We introduce an innovative mechanism that combines Tullock contests and signaling games to optimize weight assignments based on security deposits from heterogeneous nodes. While Tullock contests motivate participants to allocate resources for potential rewards, signaling games enable efficient information transfer, thereby enriching decision-making. This approach enhances network security, efficiency, and resilience by incentivizing resource investment and facilitating effective information exchange. Our framework significantly outperforms existing methods, achieving a 45.43% increase in blockchain utility and a 47.92% rise in node utility. Additionally, it yields marked improvements in user participation rates (26.89 − 32.21%) and service coverage (24 − 29.54%), and also proves to be resilient against attacks from selfish nodes.
Blockchain and other decentralized databases, known as distributed ledgers, are designed to store information online where all trusted network members can update the data with transparency. The dynamics of ledger's development can be mathematically represented by a directed acyclic graph (DAG). One essential property of a properly functioning shared ledger is that all network members holding a copy of the ledger agree on a sequence of information added to the ledger, which is referred to as consensus and is known to be related to a structural property of DAG called one-endedness. In this paper, we consider a model of distributed ledger with sequential stochastic arrivals that mimic attachment rules from the IOTA cryptocurrency. We first prove that the number of leaves in the random DAG is bounded by a constant infinitely often through the identification of a suitable martingale, and then prove that a sequence of specific events happens infinitely often. Combining those results we establish that, as time goes to infinity, the IOTA DAG is almost surely one-ended.
We provide a game-theoretic analysis of the problem of front-running attacks. We use it to distinguish attacks from legitimate competition among honest users for having their transactions included earlier in the block. We also use it to introduce an intuitive notion of the severity of front-running attacks. We then study a simple commit-reveal protocol and discuss its properties. This protocol has costs because it requires two messages and imposes a delay. However, we show that it prevents the most severe front-running attacks while preserving legitimate competition between users, guaranteeing that the earliest transaction in a block belongs to the honest user who values it the most. When the protocol does not fully eliminate attacks, it nonetheless benefits honest users because it reduces competition among attackers (and overall expenditure by attackers). This paper was accepted by Joshua Gans, business strategy. Funding: The authors gratefully acknowledge the financial support of the Ethereum Foundation [Grant FY22-0840].
Distributed ledger technologies provide a mechanism to achieve ordering among transactions that are scattered on multiple participants with no prerequisite trust relations. This mechanism is essentially based on the idea of new transactions referencing older ones in a chain structure. Recently, directed acyclic graph (DAG)-type distributed ledgers that are based on DAGs were proposed to increase the system scalability through sacrificing the total order of transactions. In this paper, we develop a mathematical model to study the process that governs the addition of new transactions to the DAG-type distributed ledger. We propose a simple model for DAG-type distributed ledgers that are obtained from a recursive young-age preferential attachment scheme (i.e., new connections are made preferably to transactions that have not been in the system for very long). We determine the asymptotic degree structure of the resulting graph and show that a forward component of linear size arises if the edge density is chosen sufficiently large in relation to the “young-age preference” that tunes how quickly old transactions become unattractive. Funding: The research of C. Mönch is supported by the Deutsche Forschungsgemeinschaft [Grant 443916008].
Relay Mining presents a scalable solution employing probabilistic mechanisms, crypto-economic incentives, and new cryptographic primitives to estimate and prove the volume of Remote Procedure Calls (RPCs) made from a client to a server. Distributed ledgers are designed to secure permissionless state transitions (writes), highlighting a gap for incentivizing full non-validating nodes to service non-transactional (read) RPCs. This leads applications to have a dependency on altruistic or centralized off-chain Node RPC Providers. We present a solution that enables multiple RPC providers to service requests from independent applications on a permissionless network. We leverage digital signatures, commit-and-reveal schemes, and Sparse Merkle Sum Tries (SMSTs) to prove the amount of work done. This is enabled through the introduction of a novel ClosestMerkleProof proof-of-inclusion scheme. A native cryptocurrency on a distributed ledger is used to rate limit applications and disincentivize over-usage. Building upon established research in token bucket algorithms and distributed rate-limiting penalty models, our approach harnesses a feedback loop control mechanism to adjust the difficulty of mining relay rewards, dynamically scaling with network usage growth. By leveraging crypto-economic incentives, we reduce coordination overhead costs and introduce a mechanism for providing RPC services that are both geopolitically and geographically distributed. We use common formulations from rate limiting research to demonstrate how this solution in the Web3 ecosystem translates to distributed verifiable multi-tenant rate limiting in Web2.
We introduce semitopology, a generalisation of point-set topology that removes the restriction that intersections of open sets need necessarily be open. The intuition is that points represent participants in a decentralised system, and open sets represent collections of participants that collectively have the authority to collaborate to update their local state; we call this an actionable coalition. Examples of actionable coalition include: majority stakes in proof-of-stake blockchains; communicating peers in peer-to-peer networks; and even pedestrians working together to not bump into one another in the street. Where actionable coalitions exist, they have in common that: collaborations are local (updating the states of the participants in the coalition, but not immediately those of the whole system); collaborations are voluntary (up to and including breaking rules); participants may be heterogeneous in their computing power or in their goals (not all pedestrians want to go to the same place); participants can choose with whom to collaborate; and they are not assumed subject to permission or synchronisation by a central authority. We develop a topology-flavoured mathematics that goes some way to explaining how and why these complex decentralised systems can exhibit order, and gives us new ways to understand existing practical implementations.
Automated Market Makers (AMMs) have cemented themselves as an integral part of the decentralized finance (DeFi) space. AMMs are a type of exchange that allows users to trade assets without the need for a centralized exchange. They form the foundation for numerous decentralized exchanges (DEXs), which help facilitate the quick and efficient exchange of on-chain tokens. All present-day popular DEXs are static protocols, with fixed parameters controlling the fee and the curvature - they suffer from invariance and cannot adapt to quickly changing market conditions. This characteristic may cause traders to stay away during high slippage conditions brought about by intractable market movements. We propose a Reinforcement Learning (RL) framework to optimize the fees collected on an AMM protocol. In particular, we develop a Q-Learning Agent for Market Making Protocols (QLAMMP) that learns the optimal fee rates and leverage coefficients for a given AMM protocol and maximizes the expected fee collected under a range of different market conditions. We show that QLAMMP is consistently able to outperform its static counterparts under all the simulated test conditions.
Abstract Are managers necessary for organizations? Could organizations function without them? To answer, we must separate between two questions: are top managers necessary? And are middle managers necessary? I argue that larger organizations are prone to need someone to have oversight of the wholeness and to take responsibility for its design and development. Given the dedication and time commitment needed to fulfill that role, it is virtually impossible to have a larger organization without any top management. However, a large organization with top management and frontline employees—but no managerial layers in between—is already a much more realistic possibility. It typically requires having autonomous, self-managing teams empowered to make all the necessary decisions related to their own work, accompanied by certain structural solutions (often enhanced by ICT) solving key information- and coordination-related tasks that are traditionally taken care of by middle managers. Often specific coach roles also emerge. In principle, if working substitutes are found to all tasks traditionally taken care of by middle managers, an organization can be functional and successful without any managerial layers. I examine a few successful examples of such organizations, Buurtzorg and Reaktor, while also highlighting key boundary conditions for when, where, and how self-managing organizations can succeed. I conclude by distinguishing between structure and hierarchy, arguing that while self-managing organizations are characterized by high levels of decentralization, their functionality is ensured through having enough structure, thus combining low hierarchy with adequate structure to find the most functional form of organizing in a particular context.
Pietro Ferraro, Andreas Penzkofer, Christopher King, Robert Shorten
In this article, we present a feedback approach to the design of an attack mitigation policy for directed acyclic graph (DAG)-based distributed ledgers. We develop a model to analyze the behavior of the ledger under the so-calledTips Inflation Attack, which endangers the liveness of transactions, and we design a control strategy to counteract this attack strategy. The efficacy of this approach is showcased through a theoretical analysis, in the form of two theorems about the stability properties of the ledger with and without the controller, and extensive Monte Carlo simulations of an agent-based model of the distributed ledger.
Matthias Lohr, Kenneth Skiba, Marco Konersmann, Jan Jürjens · 5 authors
Existing fair exchange protocols usually neglect consideration of cost when assessing their fairness. However, in an environment with non-negligible transaction cost, e.g., public blockchains, high or unexpected transaction cost might be an obstacle for wide-spread adoption of fair exchange protocols in business applications. For example, as of 2021-12-17, the initialization of the FairSwap protocol on the Ethereum blockchain requires the selling party to pay a fee of approx. 349.20 USD per exchange. We address this issue by defining cost fairness, which can be used to assess two-party exchange protocols including implied transaction cost. We show that in an environment with non-negligible transaction cost where one party has to initialize the exchange protocol and the other party can leave the exchange at any time cost fairness cannot be achieved.
We study a scenario where an adjudication task (e.g., the resolution of a binary dispute) is outsourced to a set of agents who are appointed as jurors. This scenario is particularly relevant in a Web3 environment, where no verification of the adjudication outcome is possible, and the appointed agents are, in principle, indifferent to the final verdict. We consider simple adjudication mechanisms that use (1) majority voting to decide the final verdict and (2) a payment function to reward the agents with the majority vote and possibly punish the ones in the minority. Agents interact with such a mechanism strategically: they exert some effort to understand how to properly judge the dispute and cast a yes/no vote that depends on this understanding and on information they have about the rest of the votes. Eventually, they vote so that their utility (i.e., their payment from the mechanism minus the cost due to their effort) is maximized. Under reasonable assumptions about how an agent's effort is related to her understanding of the dispute, we show that appropriate payment functions can be used to recover the correct adjudication outcome with high probability. Our findings follow from a detailed analysis of the induced strategic game and make use of both theoretical arguments and simulation experiments.
Dimitris Karakostas, Aggelos Kiayias, Thomas Zacharias
We study Nash-dynamics in the context of blockchain protocols. We introduce a formal model, within which one can assess whether the Nash dynamics can lead utility-maximizing participants to defect from the "honest" protocol operation, towards variations that exhibit one or more undesirable infractions, such as abstaining from participation and producing conflicting protocol histories. Blockchain protocols that do not lead to such infraction states are said to be compliant. Armed with this model, we evaluate the compliance of various Proof-of-Work (PoW) and Proof-of-Stake (PoS) protocol families, with respect to different utility functions and reward schemes, leading to the following results: i) PoS ledgers under resource-proportional rewards can be compliant if costs are negligible, but non-compliant if costs are significant; ii) PoW and PoS under block-proportional rewards exhibit different compliance behavior, depending on the lossiness of the network; iii) PoS ledgers can be compliant w.r.t. one infraction, i.e., producing conflicting messages, but non-compliant (and non-equilibria) w.r.t. abstaining or an attack we call selfish signing; iv) taking externalities, such as exchange rate fluctuations, into account, we quantify the benefit of economic penalties, in the context of PoS protocols, in disincentivizing particular infractions.
We introduce the SPRIG (Smart Proofs via Recursive Information Gathering) protocol. SPRIG allows agents to propose, question, and defend mathematical proofs in a decentralized fashion. A structure of stakes and bounties aims at producing debates in good faith and if those persist, they must go down to machine-level details, where they can be settled automatically. This combination of economic incentives and an oracle is designed to promote succinct and informative proofs. SPRIG can run autonomously as a smart contract on a blockchain platform, and hence it does not rely on a central trusted institution. We translate SPRIG into a general game-theoretic model and prove that the protocol satisfies two desirable properties: no spamming and monotonicity. We then characterize analytically the equilibrium of a simple two-player specification of the model: this provides important insights into the impact of the protocol’s parameters on the probabilities that it induces type I/II errors. We conclude by discussing the main attacks SPRIG’s designers will need to take into account.
We propose and study a new class of polynomial voting rules for a general decentralized decision/consensus system, and more specifically for the proof-of-stake protocol. The main idea, inspired by the Penrose square-root law and the more recent quadratic voting rule, is to differentiate a voter’s voting power and the voter’s share (fraction of the total in the system). We show that, whereas voter shares form a martingale process that converges to a Dirichlet distribution, their voting powers follow a supermartingale process that decays to zero over time. This prevents any voter from controlling the voting process and, thus, enhances security. For both limiting results, we also provide explicit rates of convergence. When the initial total volume of votes (or stakes) is large, we show a phase transition in share stability (or the lack thereof), corresponding to the voter’s initial share relative to the total. We also study the scenario in which trading (of votes/stakes) among the voters is allowed and quantify the level of risk sensitivity (or risk aversion) in three categories, corresponding to the voter’s utility being a supermartingale, a submartingale, and a martingale. For each category, we identify the voter’s best strategy in terms of participation and trading. Funding: W. Tang gratefully acknowledges financial support through the National Science Foundation [Grants DMS-2113779 and DMS-2206038] and through a start-up grant at Columbia University. D. D. Yao’s work is part of a Columbia–City University/Hong Kong collaborative project that is supported by InnoHK Initiative, the Government of Hong Kong Special Administrative Region, and the Laboratory for AI-Powered Financial Technologies.
A decentralized blockchain is a distributed ledger that is often used as a platform for exchanging goods and services. This ledger is maintained by a network of nodes that obeys a set of rules, called a consensus protocol, which helps to resolve inconsistencies among local copies of a blockchain. In this paper, we build a mathematical framework for the consensus protocol designer, specifying (a) the measurement of a resource which nodes strategically invest in and compete for to win the right to build new blocks in the blockchain; and (b) a payoff function for such efforts. Thus, the equilibrium of an associated stochastic differential game can be implemented by selecting nodes in proportion to this specified resource and penalizing dishonest nodes by its loss. This associated, induced game can be further analyzed using mean field games. The problem can be broken down into two coupled PDEs, where an individual node's optimal control path is solved using a Hamilton-Jacobi-Bellman equation, and where the evolution of states distribution is characterized by a Fokker-Planck equation. We develop numerical methods to compute the mean field equilibrium for both steady states at the infinite time horizon and evolutionary dynamics. As an example, we show how the mean field equilibrium can be applied to the Bitcoin blockchain mechanism design. We demonstrate that a blockchain can be viewed as a mechanism that operates in a decentralized setup and propagates properties of the mean field equilibrium over time, such as the underlying security of the blockchain.
The recently proposed Uniswap v3 replaces the fungible liquidity provider token (LP token) into non-fungible ones, making the design for liquidity mining more difficult. In this paper, we propose a flexible liquidity mining scheme that realizes the overall liquidity distribution through the fine control of local rewards. From the liquidity provider's point of view, the liquidity provision strategy forms a multiplayer zero-sum game. We analyze the Nash Equilibrium and the corresponding strategy, approximately, deploying the liquidity proportional to the reward distribution, in some special cases and use it to guide the general situations. Based on the strategic response above, such a scheme allows the mining rewards provider to optimize the distribution of liquidity for the purpose such as low slippage and price stabilization.
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 of reward mechanisms, in this paper, we develop a reward mechanism framework that could apply to many PoS blockchains. We formulate the block validation game wherein the rewards are distributed for validating the blocks correctly. Using evolutionary game theory, we analyze how the participants' behaviour could potentially evolve with the reward mechanism. Also, penalties are found to play a central role in maintaining the integrity of blockchains.
This study aims to solve the credit problems in the supply chain commodity and currency circulation links from the perspective of the ledger, while the game model method has been adopted. The research firstly reviews the relationship between distributed ledger technology and the essential functions of currency. Then, by constructing two-agent single-period and multi-period game models in the entire supply chain, the researchers analysed the incentive mechanism and equilibrium solution of distributed nodes of Central Bank Digital Currency (CBDC). The results of this study include the incentive mechanism and optimization of distributed nodes based on licensed distributed ledger technology, which is an important issue that CBDC faces when performing currency functions. The implications of this study mainly cover the limitations of the underlying technology of the public chain and its reward mechanism in the supply chain management and provide support for the rationality of the CBDC issuance mechanism based on state-owned commercial banks, which provides a reference for the CBDC practice. The main value of the research not only serves the decision-making department of the CBDC issuance but also provides ideas on the operation mode of digital currency for the field of digital currency research.