Abstract This paper introduces semi-competitive differential game logic $$\textsf {dG}\mathcal {L}_{sc}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>dG</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>sc</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , which enables verification of safety-critical applications that involve interactions between two agents. In $$\textsf {dG}\mathcal {L}_{sc}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>dG</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>sc</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , these interactions are specified as games on hybrid systems with two players that may collaborate with each other when helpful and may compete when necessary. The players in the hybrid games of $$\textsf {dG}\mathcal {L}_{sc}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>dG</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>sc</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> have individual goals that may overlap, leading to nonzero-sum games. This makes $$\textsf {dG}\mathcal {L}_{sc}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>dG</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>sc</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> especially well-suited for verifying situations where players, e.g., share safety objectives but otherwise pursue different goals, so that zero-sum assumptions lead to overly conservative results. Additionally, $$\textsf {dG}\mathcal {L}_{sc}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>dG</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>sc</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> solves the subtlety that even though each player may benefit from knowledge of the other player’s goals, e.g., concerning shared safety objectives, unsafe situations might still occur if every player were to mutually assume the other player would act to avoid unsafety. The syntax and semantics, as well as a sound and relatively complete proof calculus are presented for $$\textsf {dG}\mathcal {L}_{sc}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>dG</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>sc</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . The relationship between $$\textsf {dG}\mathcal {L}_{sc}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>dG</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>sc</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and zero-sum differential game logic $$\textsf {dG}\mathcal {L}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>dG</mml:mi> <mml:mi>L</mml:mi> </mml:mrow> </mml:math> is discussed and the purpose of $$\textsf {dG}\mathcal {L}_{sc}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>dG</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>sc</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> illustrated in a canonical example.
The field of quantitative finance is constantly seeking new tools to exploit the complexities of the financial markets. With classical computers having limitations, the burgeoning field of quantum computing offers immense computational capabilities. Though Belief Networks have been useful in quantitative finance, their towering computational demands on classical systems limit their efficacy. On the other hand, Bitcoin’s popularity has increased in the last few years due to its unique features, such as decentralization and blockchain. Being relatively new Bitcoin’s market possesses huge potential. Price of the Bitcoin depends upon various economic and market factors, also possesses quite high volatility making traders worried while dealing with it. This project tries explore the potential of quantum computing technologies and Belief networks for developing new long-short Bitcoin trading strategy by leveraging the strengths of both paradigms.
With complete-information bilateral bargaining in network settings, holdup is eliminated when contracts across the network are agreed atomically (all or none) via a smart contract. Applications include over-the-counter trading, syndicated lending, multi-tranche securitizations, third-party financed purchases, and bookbuilding. Under a novel extensive-form bargaining protocol, any firm can give a “greenlight” to the terms of a contract proposed to that firm, which automatically converts those terms into a binding contract if the terms proposed to all other firms also receive greenlights. In any Perfect Bayesian Equilibrium with Markov strategies, firms immediately agree on socially efficient contracts that equalize expected gains across firms.
The consensus problem in distributed ledger systems has two distinct dimensions that existing protocols systematically conflate. The first is the Byzantine fault-tolerance question: can a network reach agreement in the presence of arbitrary failures? The second — less formalised but no less fundamental — is the anti-cartel question: can the incentive structure of the consensus mechanism structurally resist the formation of cartels that reconstitute centralised authority under a nominally decentralised banner? Bitcoin's proof-of-work has produced a system where a small number of industrial mining pools control the majority of hash power. BitCell is a proposal that takes the anti-cartel question seriously as an engineering problem rather than an economic folk theorem. BitCell replaces hash-grinding and stake-weighting with cellular automaton tournaments as the computational substrate for block proposal rights. In each round, miners commit to a pattern in a bounded Conway's Game of Life grid, are verifiably randomly paired via a VRF-based pairing mechanism, and compete in a deterministic single-elimination tournament whose outcome depends on strategic pattern design rather than raw computational expenditure or capital size. Victory rights are not transferable and are not enhanced by pooling strategies: a cartel of sub-majority miners cannot coordinate to construct a jointly optimal pattern that dominates unilateral honest play, because the tournament's pairwise structure, hidden identities (via ring signatures), non-shareable rewards, and reputation-gated eligibility remove each of the primary economic motivations that make mining pools attractive. Under a simple Bayesian model of miner incentives, collusive strategies for sub-majority cartels yield strictly lower expected payoffs than unilateral honest participation. Tournament eligibility and reward weighting are governed by an Evidence-Based Subjective Logic (EBSL) reputation layer. All state transitions are proven using succinct zero-knowledge proofs, enabling a ZKVM-backed smart contract layer with native privacy. BitCell makes three primary contributions: (i) a proof-of-computation consensus mechanism whose computational task is verifiable, bounded, non-parallelisable by pooling, and intellectually non-trivial; (ii) a game-theoretic proof that the combination of pairwise tournaments, anonymised pairing, non-transferable victory rights, and reputation gating renders cartel coordination strictly dominated in a Bayesian Nash equilibrium; and (iii) a native ZKVM execution environment for privacy-preserving smart contracts.
We study a game-theoretic model for pool formation in Proof of Stake blockchain protocols. In such systems, stakeholders can form pools as a means of obtaining regular rewards from participation in ledger maintenance, with the power of each pool being dependent on its collective stake. The question we are interested in is the design of mechanisms, i.e., "reward sharing schemes," that suitably split rewards among pool members and achieve favorable properties in the resulting pool configuration. With this in mind, we initiate a non-cooperative game-theoretic analysis of the well known Shapley value scheme from cooperative game theory into the context of blockchains. In particular, we focus on the oceanic model of games, proposed by Milnor and Shapley (1978), which is suitable for populations where a small set of large players coexists with a big mass of rather small, negligible players. This provides an appropriate level of abstraction for pool formation processes that occur among the stakeholders of a blockchain. We provide comparisons between the Shapley mechanism and the more standard proportional scheme, in terms of attained decentralization, via a Price of Stability analysis and in terms of susceptibility to Sybil attacks, i.e., the strategic splitting of a players' stake with the intention of participating in multiple pools for increased profit. Interestingly, while the widely deployed proportional scheme appears to have certain advantages, the Shapley value scheme, which rewards higher the most pivotal players, emerges as a competitive alternative, by being able to bypass some of the downsides of proportional sharing in terms of Sybil attack susceptibility, while also not being far from optimal guarantees w.r.t. decentralization. Finally, we also complement our study with some variations of proportional sharing, where the profit is split in proportion to a superadditive or a subadditive function of the stake, showing that our results for the Shapley value scheme are maintained in comparison to these functions as well.
Yixuan Fan, Ziyi Zhou, Zhixiang Qiao, Yao Sun · 5 authors
Decentralized autonomous organizations (DAOs), originating from Ethereum, are pioneering entities in the world of Web 3, driven by the decentralization philosophy. In DAO systems, voting mechanisms are essential for decision-making. Their design is crucial for both community development and individual interest protection. While research has explored critical aspects such as decentralization, security, and effectiveness, there is a noticeable absence in analyzing the efficiency of DAO voting mechanisms. To address this, we focus on three key efficiency factors in DAO voting: voter turnout, processing time, and accuracy. Specifically, we identify high voter participation, shorter voting periods, and an approximately neutral approval rate as the primary factors for an efficient DAO voting process. Using a stochastic process model for DAO voting, we explore the interrelationship between these factors. We observe a trade-off between a shorter voting period and an approval rate closer to neutrality, and we also find a positive relationship between increased voter participation and achieving an appropriate approval rate. Finally, in simulations, we examine four common DAO voting mechanisms to determine their most efficient ranges.
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].
Yackolley Amoussou-Guenou, Bruno Biais, Maria Potop-Butucaru, Sara Tucci-Piergiovanni
Abstract We study consensus in a protocol capturing in a simplified manner the major features of the majority of Proof of Stake blockchains. A committee is formed; one member proposes a block; and the others can check its validity and vote for it. Blocks with a majority of votes are produced. When an invalid block is produced, the stakes of the members who voted for it are “slashed.” Profit-maximizing members interact with adversaries seeking to disrupt consensus. When slashing is limited, free-riding and moral-hazard lead to invalid blocks in equilibrium. We propose a protocol modification producing only valid blocks in equilibrium. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.
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].
Asset digitization is an important part of digital society. However, there are many problems in existing centralized asset trading platforms, for example, the platform has the dominant power in the transaction process and holds a large amount of user data, which is detrimental to users’ interests. To solve these problems, we propose a distributed asset trading mechanism based on automated negotiation. Firstly, we propose a distributed asset trading framework based on the consortium blockchain, which provides trust guarantees for trading through the access control of the consortium blockchain, represents the ownership of assets through non-fungible tokens (NFT), and reduces the blockchain burden by moving the negotiation process off the blockchain through the state channel technology. Then, to reduce the negotiation cost and improve the negotiation results, we propose a bilateral automated multi-issue negotiation model for asset trading. The experimental results show that the negotiation model performs well in terms of success rate and negotiation time, and can achieve win-win agreements.
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.