This paper presents a comprehensive refutation of the so-called "blockchain trilemma," a widely cited but formally ungrounded claim asserting an inherent trade-off between decentralisation, security, and scalability in blockchain protocols. Through formal analysis, empirical evidence, and detailed critique of both methodology and terminology, we demonstrate that the trilemma rests on semantic equivocation, misuse of distributed systems theory, and a failure to define operational metrics. Particular focus is placed on the conflation of topological network analogies with protocol-level architecture, the mischaracterisation of Bitcoin's design--including the role of miners, SPV clients, and header-based verification--and the failure to ground claims in complexity-theoretic or adversarial models. By reconstructing Bitcoin as a deterministic, stateless distribution protocol governed by evidentiary trust, we show that scalability is not a trade-off but an engineering outcome. The paper concludes by identifying systemic issues in academic discourse and peer review that have allowed such fallacies to persist, and offers formal criteria for evaluating future claims in blockchain research.
Rugsafe introduces a comprehensive protocol aimed at mitigating the risks of rug pulls in the cryptocurrency ecosystem. By utilizing cryptographic security measures and economic incentives, the protocol provides a secure multichain system for recovering assets and transforming rugged tokens into opportunities and rewards. Foundational to Rugsafe are specialized vaults where rugged tokens can be securely deposited, and anticoin tokens are issued as receipts. These anticoins are designed to be inversely pegged to the price movement of the underlying rugged token. Users can utilize these anticoins within the ecosystem or choose to burn them, further securing the protocol and earning additional rewards. The supply of the native Rugsafe token is dynamically adjusted based on the volume, value, and activity of rugged tokens, ensuring stability and resilience. By depositing rugged tokens into a vault on several chains, and by burning anticoins, users receive incentives on the RugSafe chain. This protocol's vaults are designed to work in heterogenous blockchain ecosystems, offering a practical and effective solution to one of the most significant challenges in the cryptocurrency market.
We consider a revenue-optimizing auctioneer in single-dimensional environments with matroid feasibility constraints. Akbarpour and Li (2020) argue that any revenue-optimal, truthful, and credible mechanism requires unbounded communication. Recent works (Ferreira and Weinberg, 2020; Essaidi et al., 2022; Chitra et al., 2024) circumvent their impossibility for the single-item setting through the use of cryptographic commitments and blockchains. We extend their results to matroid feasibility constraints. At a high level, the two-round Deferred-Revelation Auction (DRA) discussed by Ferreira and Weinberg (2020) and Chitra et al., (2024) requires each bidder to submit a deposit, which is slashed upon presenting verifiable evidence indicating a deviation from the behaviour prescribed by the mechanism. We prove that the DRA satisfies truthfulness, credibility and revenue-optimality for all matroid environments when bidders' values are drawn from $α$-strongly regular distributions for $α> 0$. Further, we argue that the DRA is not credible for any feasibility constraint beyond matroids and for any smaller deposits than suggested by previous literature even in single-item environments. Finally, we modify the Ascending Deferred-Revelation Auction (ADRA) for single-item settings proposed by Essaidi et al., (2022) for arbitrary bidder value distributions. We implement a deferred-revelation variant of the deferred-acceptance auction for matroids due to Bikhchandani et al., (2011), which requires the same bounded communication as the ADRA.
The CAP theorem asserts a trilemma between consistency, availability, and partition tolerance. This paper introduces a rigorous automata-theoretic and economically grounded framework that reframes the CAP trade-off as a constraint optimization problem. We model distributed systems as partition-aware state machines and embed economic incentive layers to stabilize consensus behavior across adversarially partitioned networks. By incorporating game-theoretic mechanisms into the global transition semantics, we define provable bounds on convergence, liveness, and correctness. Our results demonstrate that availability and consistency can be simultaneously preserved within bounded epsilon margins, effectively extending the classical CAP limits through formal economic control.
The blockchain oracle problem, which refers to the challenge of injecting reliable external data into decentralized systems, remains a fundamental limitation to the development of trustless applications. While recent years have seen a proliferation of architectural, cryptographic, and economic strategies to mitigate this issue, no one has yet fully resolved the fundamental question of how a blockchain can gain knowledge about the off-chain world. In this position paper, we critically assess the role artificial intelligence (AI) can play in tackling the oracle problem. Drawing from both academic literature and practitioner implementations, we examine how AI techniques such as anomaly detection, language-based fact extraction, dynamic reputation modeling, and adversarial resistance can enhance oracle systems. We observe that while AI introduces powerful tools for improving data quality, source selection, and system resilience, it cannot eliminate the reliance on unverifiable off-chain inputs. Therefore, this study supports the idea that AI should be understood as a complementary layer of inference and filtering within a broader oracle design, not a substitute for trust assumptions.
Censorship resilience is a fundamental assumption underlying the security of blockchain protocols. Additionally, the analysis of blockchain security from an economic and game theoretic perspective has been growing in popularity in recent years. In this work, we present a surprising rational censorship attack on blockchain censorship resilience when we adopt the analysis of blockchain security from a game theoretic lens and assume all users are rational. In our attack, a colluding group with sufficient voting power censors the remainder nodes such that the group alone can gain all the rewards from maintaining the blockchain. We show that if nodes are rational, coordinating this attack just requires a public read and write blackboard and we formally model the attack using a game theoretic framework. Furthermore, we note that to ensure the success of the attack, nodes need to know the total true voting power held by the colluding group. We prove that the strategy to join the rational censorship attack and also for nodes to honestly declare their power is a subgame perfect equilibrium in the corresponding extensive form game induced by our attack. Finally, we discuss the implications of the attack on blockchain users and protocol designers as well as some potential countermeasures.
We consider the problem of a game theorist analyzing a game that uses cryptographic protocols. Ideally, a theorist abstracts protocols as ideal, implementation-independent primitives, letting conclusions in the "ideal world" carry over to the "real world." This is crucial, since the game theorist cannot--and should not be expected to--handle full cryptographic complexity. In today's landscape, the rise of distributed ledgers makes a shared language between cryptography and game theory increasingly necessary. The security of cryptographic protocols hinges on two types of assumptions: state-of-the-world (e.g., "factoring is hard") and behavioral (e.g., "honest majority"). We observe that for protocols relying on behavioral assumptions (e.g., ledgers), our goal is unattainable in full generality. For state-of-the-world assumptions, we show that standard solution concepts, e.g., ($ε$-)Nash equilibria, are not robust to transfer from the ideal to the real world. We propose a new solution concept: the pseudo-Nash equilibrium. Informally, a profile $s=(s_1,\dots,s_n)$ is a pseudo-Nash equilibrium if, for any player $i$ and deviation $s'_i$ with higher expected utility, $i$'s utility from $s_i$ is (computationally) indistinguishable from that of $s'_i$. Pseudo-Nash is simpler and more accessible to game theorists than prior notions addressing the mismatch between (asymptotic) cryptography and game theory. We prove that Nash equilibria in games with ideal, unbreakable cryptography correspond to pseudo-Nash equilibria when ideal cryptography is instantiated with real protocols (under state-of-the-world assumptions). Our translation is conceptually simpler and more general: it avoids tuning or restricting utility functions in the ideal game to fit quirks of cryptographic implementations. Thus, pseudo-Nash lets us study game-theoretic and cryptographic aspects separately and seamlessly.
This paper develops a formal game-theoretic model to examine how protocol mutability disrupts cooperative mining behaviour in blockchain systems. Using a repeated game framework with stochastic rule shocks, we show that even minor uncertainty in institutional rules increases time preference and induces strategic deviation. Fixed-rule environments support long-term investment and stable equilibrium strategies; in contrast, mutable protocols lead to short-termism, higher discounting, and collapse of coordinated engagement. Simulation results identify instability zones in the parameter space where rational mining gives way to extractive or arbitrage conduct. These findings support an Austrian economic interpretation: calculability requires rule stability. Institutional noise undermines the informational basis for productive action. We conclude that protocol design must be treated as a constitutional economic constraint, not a discretionary variable, if sustainable cooperation is to emerge in decentralised systems.
This paper integrates Austrian capital theory with repeated game theory to examine strategic miner behaviour under different institutional conditions in blockchain systems. It shows that when protocol rules are mutable, effective time preference rises, undermining rational long-term planning and cooperative equilibria. Using formal game-theoretic analysis and Austrian economic principles, the paper demonstrates how mutable protocols shift miner incentives from productive investment to political rent-seeking and influence games. The original Bitcoin protocol is interpreted as an institutional anchor: a fixed rule-set enabling calculability and low time preference. Drawing on the work of Bohm-Bawerk, Mises, and Hayek, the argument is made that protocol immutability is essential for restoring strategic coherence, entrepreneurial confidence, and sustainable network equilibrium.
This paper presents a formal analysis of the Lightning Network as a monetary system structurally diverging from Bitcoin's base-layer settlement model. We demonstrate that under increasing transaction demand, BTC transaction fees rise superlinearly due to throughput constraints, while Lightning Network routing costs approach a bounded asymptote. Using mathematical modeling, game-theoretic proofs, and complexity analysis, we show that Lightning enables indefinite off-chain operation via the emergence of liquidity hub oligopolies. These hubs exhibit properties of unregulated financial intermediaries, including rent extraction, opacity, and systemic fragility. Strategic agent models show that channel closure becomes economically infeasible, and routing problems approach hardness limits in P-Space complexity. We conclude that Lightning does not merely extend Bitcoin, but constitutes a synthetic financial system with shadowbank characteristics, lacking reserve discipline, transparency, or enforceable settlement guarantees.
Lending protocols are one of the main applications of Decentralized Finance (DeFi), enabling crypto-assets loan markets with a total value estimated in the tens of billions of dollars. Unlike traditional lending systems, these protocols operate without relying on trusted authorities or off-chain enforcement mechanisms. To achieve key economic goals such as stability of the loan market, they devise instead trustless on-chain mechanisms, such as rewarding liquidators who repay the loans of under-collateralized borrowers by awarding them part of the borrower's collateral. The complexity of these incentive mechanisms, combined with their entanglement in low-level implementation details, makes it challenging to precisely assess the structural and economic properties of lending protocols, as well as to analyze user strategies and attacks. Crucially, since participation is open to anyone, any weaknesses in the incentive mechanism may give rise to unintended emergent behaviours, or even enable adversarial strategies aimed at making profits to the detriment of legit users, or at undermining the stability of the protocol. In this work, we propose a formal model of lending protocols that captures the essential features of mainstream platforms, enabling us to identify and prove key properties related to their economic and strategic dynamics.
Aggelos Kiayias, Elias Koutsoupias, Giorgos Panagiotakos, Kyriaki Zioga
Blockchain transactions consume diverse resources, foremost among them storage, but also computation, communication, and others. Efficiently charging for these resources is crucial for effective system resource allocation and long-term economic viability. The prevailing approach, one-dimensional pricing, sets a single price for a linear combination of resources. However, this often leads to under-utilization when resource capacities are limited. Multi-dimensional pricing, which independently prices each resource, offers an alternative but presents challenges in price discovery. This work focuses on the welfare achieved by these two schemes. We prove that multi-dimensional pricing is superior under stable blockchain conditions. Conversely, we show that one-dimensional pricing outperforms its multi-dimensional counterpart in transient states, exhibiting faster convergence and greater computational tractability. These results highlight a critical trade-off: while multi-dimensional pricing offers efficiency gains at equilibrium, its implementation incurs costs associated with system transitions. Our findings underscore the necessity for a deeper understanding of these transient effects before widespread adoption. Finally, we propose mechanisms that aim to mitigate some of these issues, paving the way for future research.
We propose \textit{OpenAlpha}, a community-led strategy validation framework for decentralised capital management on a host blockchain network, which integrates game-theoretic validation, adversarial auditing, and market-based belief aggregation. This work formulates treasury deployment as a capital optimisation problem under verification costs and strategic misreporting, and operationalises it through a decision waterfall that sequences intention declaration, strategy proposal, prediction-market validation, dispute resolution, and capital allocation. Each phase of this framework's validation process embeds economic incentives to align proposer, verifier, and auditor behaviour, producing confidence scores that may feed into a capital allocation rule. While OpenAlpha is designed for capital strategy assessment, its validation mechanisms are composable and extend naturally to evaluating external decentralised applications (DApps), enabling on-chain scrutiny of DApp performance, reliability, and integration risk. This architecture allows for adaptive, trust-minimised capital deployment without reliance on centralised governance or static audits.
This paper presents a mathematically rigorous formal analysis of Simplified Payment Verification (SPV) clients, as specified in Section 8 of the original Bitcoin white paper, versus non-mining full nodes operated by home users. It defines security as resistance to divergence from global consensus and models transaction acceptance, enforcement capability, and divergence probability under adversarial conditions. The results demonstrate that SPV clients, despite omitting script verification, are cryptographically sufficient under honest-majority assumptions and topologically less vulnerable to attack than structurally passive, non-enforcing full nodes. The paper introduces new axioms on behavioral divergence and communication topology, proving that home-based full nodes increase systemic entropy without contributing to consensus integrity. Using a series of formally defined lemmas, propositions, and Monte Carlo simulation results, it is shown that SPV clients represent the rational equilibrium strategy for non-mining participants. This challenges the prevailing narrative that home validators enhance network security, providing formal and operational justifications for the sufficiency of SPV models.
Decentralized exchanges (DEXs) are crucial to de-centralized finance (DeFi) as they enable trading without intermediaries. However, they face challenges like impermanent loss (IL), where liquidity providers (LPs) see their assets’ value change un-favorably within a liquidity pool compared to outside it. To tackle these issues, we propose dynamic fee mechanisms over traditional fixed-fee structures used in automated market makers (AMM). Our solution includes asymmetric fees via block-adaptive, deal-adaptive, and the "ideal but unattainable" oracle-based fee algorithm, utilizing all data available to arbitrageurs to mitigate IL. We developed a simulation-based framework to compare these fee algorithms systematically. This framework replicates trading on a DEX, considering both informed and uninformed users and a psychological relative loss factor. Results show that adaptive algorithms outperform fixed-fee baselines in reducing IL while maintaining trading activity among uninformed users. Additionally, insights from oracle-based performance underscore the potential of dynamic fee strategies to lower IL, boost LP profitability, and enhance overall market efficiency.
Blockchain protocols incentivize participation through monetary rewards, assuming rational actors behave honestly to maximize their gains. However, attackers may attempt to harm others even at personal cost. These denial of profit attacks aim to reduce the rewards of honest participants, potentially forcing them out of the system. While existing work has largely focused on the profitability of attacks, they often neglect the potential harm inflicted on the victim, which can be significant even when the attacker gains little or nothing. This paper introduces a framework to quantify denial of profit attacks by measuring both attacker cost and victim loss. We model these attacks as a game and introduce relevant metrics to quantify these attacks. We then focus on committee-based blockchains and model vote collection as a game. We show that in the vote collection game, disincentivizing one denial of profit attack will make another attack more appealing, and therefore, attacks have to be balanced. We apply our framework to analyze real-world reward mechanisms in Ethereum and Cosmos. Our framework reveals imbalances in Cosmos that can make correct behavior suboptimal in practice. While Ethereum provides stronger protections, our framework shows that it is also not complete, and we propose alternative parameter settings to improve the balance between attacks. Our findings highlight the need for better-balanced reward designs to defend against denial of profit attacks.
Optimistic Rollups (ORUs) significantly enhance blockchain scalability but inherently suffer from the verifier's dilemma, particularly concerning validator attentiveness. Current systems lack mechanisms to proactively ensure validators are diligently monitoring L2 state transitions, creating a vulnerability where fraudulent states could be finalized. This paper introduces the Randomized Attention Test (RAT), a novel L1-based protocol designed to probabilistically challenge validators in ORUs, thereby verifying their liveness and computational readiness. Our game-theoretic analysis demonstrates that an Ideal Security Equilibrium, where all validators are attentive and proposers are honest, can be achieved with RAT. Notably, this equilibrium is attainable and stable with relatively low economic penalties (under \$1000) for non-responsive validators, a low attention test frequency (under 1\% per epoch), and a minimal operation overhead (monthly under \$30) with 10 validators. RAT thus provides a pivotal, practical mechanism to enforce validator diligence, fortifying the overall security and integrity of ORU systems with minimizing additional costs.
In online auctions, fraudulent behaviors such as shill bidding pose significant risks. This paper presents a conceptual framework that applies dynamic, behavior-based penalties to deter auction fraud using blockchain smart contracts. Unlike traditional post-auction detection methods, this approach prevents manipulation in real-time by introducing an economic disincentive system where penalty severity scales with suspicious bidding patterns. The framework employs the proposed Bid Shill Score (BSS) to evaluate nine distinct bidding behaviors, dynamically adjusting the penalty fees to make fraudulent activity financially unaffordable while providing fair competition. The system is implemented within a decentralized English auction on the Ethereum blockchain, demonstrating how smart contracts enforce transparent auction rules without trusted intermediaries. Simulations confirm the effectiveness of the proposed model: the dynamic penalty mechanism reduces the profitability of shill bidding while keeping penalties low for honest bidders. Performance evaluation shows that the system introduces only moderate gas and latency overhead, keeping transaction costs and response times within practical bounds for real-world use. The approach provides a practical method for behaviour-based fraud prevention in decentralised systems where trust cannot be assumed.
We construct an empirically founded model of a repo trade intermediated by two broker-dealers and prove multiple equilibrium and the existence of equilibrium at the joint profit maximizing volume of trade. We then present a smart contract that resolves multiple equilibrium by requiring each broker-dealer to report its client schedule and its minimum hurdle spread, and implementing a selection rule that filters out hurdle-infeasible outcomes. Whenever there exists an equilibrium that exceeds both hurdle spreads, the protocol selects the joint profit maximizing feasible trade and thereby avoids a collapse to no trade. The smart contract is a machine executed algorithm which eliminates the need for trust. Hardware and cryptography are used to prevent leakage of broker-dealer client trade schedules, and to enable privacy-protected auditing with zero-knowledge proofs of the integrity of computations. The outcome can be implemented by a myopic strategy where a broker-dealer truthfully reports its own variables without anticipating its counterparty's reports. This minimizes cognitive and computational complexity, thereby making our smart contract suitable for real-world deployment.
Proof-of-Work (PoW) consensus is traditionally analyzed under the assumption that all miners incur similar costs per unit of computational effort. In reality, costs vary due to factors such as regional electricity cost differences and access to specialized hardware. These variations in mining costs become even more pronounced in the emerging paradigm of \emph{Proof-of-Useful-Work} (PoUW), where miners can earn additional \emph{external} rewards by performing beneficial computations, such as Artificial Intelligence (AI) training and inference workloads. Continuing the work of Fiat et al., who investigate equilibrium dynamics of PoW consensus under heterogeneous cost structures due to varying energy costs, we expand their model to also consider external rewards. We develop a theoretical framework to model miner behavior in such conditions and analyze the resulting equilibrium. Our findings suggest that in some cases, miners with access to external incentives will optimize profitability by concentrating their useful tasks in a single block. We also explore the implications of external rewards for decentralization, modeling it as the Shannon entropy of computational effort distribution among participants. Empirical evidence supports many of our assumptions, indicating that AI training and inference workloads, when reused for consensus, can retain security comparable to Bitcoin while dramatically reducing computational costs and environmental waste.
This paper presents a comprehensive framework for transaction posting and pricing in Layer 2 (L2) blockchain systems, focusing on challenges stemming from fluctuating Layer 1 (L1) gas fees and the congestion issues within L2 networks. Existing methods have focused on the problem of optimal posting strategies to L1 in isolation, without simultaneously considering the L2 fee mechanism. In contrast, our work offers a unified approach that addresses the complex interplay between transaction queue dynamics, L1 cost variability, and user responses to L2 fees. We contribute by (1) formulating a dynamic model that integrates both posting and pricing strategies, capturing the interplay between L1 gas price fluctuations and L2 queue management, (2) deriving an optimal threshold-based posting policy that guides L2 sequencers in managing transactions based on queue length and current L1 conditions, and (3) establishing theoretical foundations for a dynamic L2 fee mechanism that balances cost recovery with congestion control. We validate our framework through simulations.
As markets have digitized, the number of tradable products has skyrocketed. Algorithmically constructed portfolios of these assets now dominate public and private markets, resulting in a combinatorial explosion of tradable assets. In this paper, we provide a simple means to compute market clearing prices for semi-fungible assets which have a partial ordering between them. Such assets are increasingly found in traditional markets (bonds, commodities, ETFs), private markets (private credit, compute markets), and in decentralized finance. We formulate the market clearing problem as an optimization problem over a directed acyclic graph that represents participant preferences. Subsequently, we use convex duality to efficiently estimate market clearing prices, which correspond to particular dual variables. We then describe dominant strategy incentive compatible payment and allocation rules for clearing these markets. We conclude with examples of how this framework can construct prices for a variety of algorithmically constructed, semi-fungible portfolios of practical importance.
We initiate the study of transaction fee mechanism design for blockchain protocols in which multiple block producers contribute to the production of each block. Our contributions include: - We propose an extensive-form (multi-stage) game model to reason about the game theory of multi-proposer transaction fee mechanisms. - We define the strongly BPIC property to capture the idea that all block producers should be motivated to behave as intended: for every user bid profile, following the intended allocation rule is a Nash equilibrium for block producers that Pareto dominates all other Nash equilibria. - We propose the first-price auction with equal sharing (FPA-EQ) mechanism as an attractive solution to the multi-proposer transaction fee mechanism design problem. We prove that the mechanism is strongly BPIC and guarantees at least a 63.2% fraction of the maximum-possible expected welfare at equilibrium. - We prove that the compromises made by the FPA-EQ mechanism are qualitatively necessary: no strongly BPIC mechanism with non-trivial welfare guarantees can be DSIC, and no strongly BPIC mechanism can guarantee optimal welfare at equilibrium.
Retroactive Public Goods Funding (RetroPGF) rewards blockchain projects based on proven impact rather than future promises. This paper reviews voting mechanisms for Optimism's RetroPGF, where "badgeholders" allocate rewards to valuable projects. We explore Optimism's previous schemes for RetroPGF voting, including quadratic, mean, and median voting. We present a proof-based formal analysis for vulnerabilities in these voting schemes, empirically validate these vulnerabilities using voting simulations, and offer assessments and practical recommendations for future iterations of Optimism's system based on our findings.