Jingyu Liu, Bolin Zhang, Lin William Cong, Siguang Li · 5 authors
Ethereum's Glamsterdam upgrade introduces enshrined proposer-builder separation (ePBS), replacing relay-centric PBS with direct builder bids to proposers. We study how this shift changes the block-building microstructure through a general imperfect-information two-stage auction with verifiable messages, where an early bid serves as both a price offer and a signal. PBS and ePBS are modeled as restrictions of the same block-building game: PBS fixes stopping and disclosure exogenously, while ePBS lets the proposer choose stopping and disclosure ex post. Latency heterogeneity is captured by asymmetric information updates: fast builders observe disclosed early information before rebidding, while slow builders do not. We combine exact perfect Bayesian equilibrium characterizations in tractable cases with calibrated no-regret learning in finite games. For PBS, we show that separating equilibria preserve the standard first-price-auction payoff benchmark and provide conditions for their existence. For ePBS, we demonstrate a ratchet effect: because the proposer can defer block proposal and use early bid information in the second stage, builders anticipate ex-post extraction and shade or pool early bids, generating allocation inefficiency and revenue-efficiency valleys. We interpret this ratchet distortion as a commitment failure. Under full commitment, the optimal policy collapses to the static Myerson auction and removes the ratchet channel. To realize part of this commitment advantage in a feasible mechanism, we propose a Trusted Execution Environment (TEE) sidecar that enforces limited commitment. We formulate the revenue-maximizing TEE mechanism as a bilinear optimization problem. In conservative finite benchmarks, the TEE design increases the proposer revenue relative to the first-price benchmark by approximately \(25\%\).
Blockchain applications may have preferences over the order in which transactions execute: an automated market maker may use an external feed to price its liquidity, and require that the oracle update incorporating this price execute before any swap; an exchange may want to execute cancellations of limit orders before incoming market orders; an application may run an on-chain auction by executing bids from highest to lowest, so that the first bid wins. However, the ordering of transactions is chosen by the underlying blockchain and may not be compatible with the requirements of a specific application. In this paper, I tackle this problem by introducing an algorithm called unanimity override. The intuition is that when all the applications agree on how to order two transactions, the underlying blockchain should respect this agreement; a default order - the order in which transactions appear in the block - settles the rest. The problem with this naive approach is that application unanimity may form cycles, which the algorithm must break. Cycle-breaking is also the rule's main vulnerability because an attacker can insert transactions to manufacture a cycle. Yet two guarantees hold against any attacker who sets the default order, deploys applications, and inserts transactions. All transactions that interact with a single application that expressed preferences are ordered according to that application's preferences, even when they also interact with other applications that did not express preferences. Also, gated transactions - those that cannot be outranked in the unanimity order by any transaction crafted by an attacker - always execute as the applications unanimously prefer, even when they touch many applications. The two guarantees identify the preferences the protocol can protect, and they tell applications and senders in advance which transactions will execute in the intended order.
This paper presents an open-economy macroeconomic equilibrium model for Proof-of-Stake (PoS) networks with fee-burn mechanics (EIP-1559) that formalizes the strategic interplay between a Kelly-optimizing rational institutional investor and a utility-driven retail consumer. We analyze network dynamics across two behavioral regimes. In The Unbounded Accumulation Model, the consumer purely accumulates tokens, creating an exclusive buy-side pressure that interacts with institutional portfolio rebalancing to fuel an ever-expanding speculative bubble and generate compounding excess returns for investors. Conversely, in The Utility-Consumption Model, the consumer dynamically buys and sells tokens to balance crypto wealth against real-world fiat consumption. Within this framework, we derive an explicit steady-state equilibrium price for ETH, demonstrating how token valuation anchors to a stable fundamental baseline that scales directly with network adoption while completely dissolving the institutional yield premium. Our numerical simulations show that while exogenous traditional finance (TradFi) shocks propagate through portfolio rebalancing to drive high token price volatility, network inflation remains highly stable. Furthermore, we prove that network security is insulated from institutional monopoly by counter-cyclical consumer behavior. Our findings reveal that institutional excess wealth creation in PoS ecosystems is not native to the staking protocol itself, but is strictly driven by the leveraged extraction of the retail consumer's continuous demand for transactional utility.
Proof-of-work (PoW) blockchains rely on computational expenditure to secure a ledger supporting a native cryptocurrency. In existing systems such as Bitcoin, this expenditure is intentionally useless: the computation secures consensus but produces no external economic output. An emerging alternative -- proof of useful work (PoUW) -- enables the same computation to simultaneously secure the blockchain and generate economically valuable output. However, PoUW is often criticized on economic grounds: if the work is useful, attackers might be "paid to attack," potentially weakening security. We develop a competitive-equilibrium model of a PoUW blockchain in which compute can be allocated across pure mining, pure useful work -- instantiated as machine-learning inference -- or "duplex" work that produces both with computational overheads. We provide a complete closed-form characterization of equilibrium allocations and prices as a function of the duplex overheads and a single economic parameter -- the token-inference ratio -- measuring token adoption relative to the inference market. This characterization reveals three regimes: "Bitconia," in which the economy reduces to classical PoW; "Fortessia," in which duplex replaces mining, increasing security while useful output remains unchanged; and "Duplexia," in which token rewards subsidize inference, lowering prices and expanding inference supply. Contrary to the common strawman argument, PoUW does not make attacks economically cheap: once equilibrium prices are taken into account, the economic cost of a majority attack remains tied to the block reward. Moreover, in Duplexia, block rewards act as rebates on inference prices, generating additional socially useful computation that would not arise without the blockchain -- an expansion monotonically increasing in token adoption and technological efficiency.
Many proof-of-stake protocols finance validator rewards from two sources: transaction fees and a finite reserve of tokens. This creates a dynamic hand-off problem. Early in the life of the system, fees may be too small to fund the target level of security; later, fees may become sufficient. The central question is whether the reserve provides enough runway for the protocol to remain secure until this fee-only region is reached. We study this problem in a discrete-time stochastic model of validator participation. Token price and transaction demand fluctuate over time, while validators choose participation strategically. We solve the validator entry game and derive an exact state-dependent reserve threshold, i.e., the minimal reserve stock necessary and sufficient to sustain a target security level. This threshold separates three regions: infeasibility, reserve-dependent security, and fee-only security. Security fails if the reserve first falls below the state-dependent threshold, and a successful hand-off occurs exactly if the fee-only region is reached before that failure time. We derive stress-test guarantees that convert lower confidence bands for token price and demand into reserve requirements, and obtain explicit failure-probability and expected hand-off-time bounds. Finally, we extend the model to forward-looking validators and derive the Markov participation condition that captures how current participation affects future reserve-funded rewards. The main implication is that reserve policy should not be evaluated by nominal depletion dates or steady-state reward ratios alone. A protocol can have a large nominal reserve and still be close to security failure after adverse price or demand shocks. Conversely, once demand crosses the fee-only threshold, the reserve becomes redundant for security. This paper provides a tractable equilibrium framework for stress-testing this transition.
The value of proof-of-work cryptocurrencies critically depends on miners having incentives to follow the protocol. However, the Bitcoin mining protocol proposed by Nakamoto (2008) and implemented in practice is well known not to constitute an equilibrium: Eyal and Sirer (2018) construct a profitable deviation called ``selfish mining'' which relies on strategically delaying disclosure of newly mined blocks rather than publishing them immediately. We propose inertial mining, a novel mining protocol. When miners follow inertial mining, they produce the outcome intended by Nakamoto, i.e., a single longest chain. But unlike the Bitcoin mining protocol, inertial mining constitutes an equilibrium (assuming no miner controls more than half of the mining power). Indeed, neither selfish mining nor any other deviation is profitable. Furthermore, inertial mining only changes miners' behavior in the event of off-path forks, and can be implemented in Bitcoin without any changes to its consensus mechanism or blockchain architecture.
Consider a social-choice function (SCF) is chosen to decide votes in a formal system, including votes to replace the voting method itself. Agents vote according to their ex-ante belief over what decisions are considered, and whether they prefer them to be decided by the incumbent SCF or the suggested replacement. The existing SCF then aggregates the agents' votes and arrives at a decision of whether it should itself be replaced. An SCF is self-maintaining if it can not be replaced in such fashion by any other SCF. Our focus is on the implications of self-maintenance for centralization. For this purpose, unlike [Barbera and Jackson, 2004], we do not generally restrict attention to anonymous SCFs. We also do not restrict attention to neutral SCFs, unlike [Koray, 2000]. We present results considering optimistic, pessimistic and i.i.d. approaches with respect to agent beliefs, different tie-breaking rules, and different SCF domains. To highlight two of the results, (i) for the i.i.d. unbiased case with arbitrary tie-breaking and general Boolean functions, we prove an Arrow-Style Theorem for Dynamics: We show that only a dictatorship is self-maintaining, and any other SCF has a path of changes that arrives at a dictatorship. (ii) With a pessimistic approach, tie-breaking that prefers the status quo, and WMGs, we provide a tight characterization of the self-maintaining rules, which are exactly all games with minimal winning coalitions of size at most 2. We then consider two extensions, (i) forward-looking voters, (ii) Where the voter utility depends on wisdom of the crowd effects. In both cases, less centralized SCFs become self-maintaining. All in all we provide a basic framework and body of results for centralization dynamics and stability, applicable for institution design, especially in formal De-Jure systems, such as Blockchain Decentralized Autonomous Organizations (DAOs).
Michele Fabi, Viraj Nadkarni, Leonardo Leone, Matheus V. X. Ferreira
<div> We develop an axiomatic theory for Automated Market Makers (AMMs) in local energy sharing markets and analyze the Markov Perfect Equilibrium of the resulting economy with a Mean-Field Game. In this game, heterogeneous prosumers solve a Bellman equation to optimize energy consumption, storage, and exchanges. Our axioms identify a class of mechanisms with linear, Lipschitz continuous payment functions, where prices decrease with the aggregate supply-to-demand ratio of energy. We prove that implementing batch execution and concentrated liquidity allows standard design conditions from decentralized finance-quasi-concavity, monotonicity, and homotheticity-to construct AMMs that satisfy our axioms. The resulting AMMs are budget-balanced and achieve ex-ante efficiency, contrasting with the strategy-proof, expost optimal VCG mechanism. Since the AMM implements a Potential Game, we solve its equilibrium by first computing the social planner's optimum and then decentralizing the allocation. Numerical experiments using data from the Paris administrative region suggest that the prosumer community can achieve gains from trade up to 40% relative to the grid-only benchmark. </div>
Blockchains face inherent limitations when communicating outside their own ecosystem, largely due to the Byzantine Fault Tolerant (BFT) 3f+1 security model. Trusted Execution Environments (TEEs) are a promising mitigation because they allow a single trusted broker to interface securely with external systems. This paper develops a cost-of-collusion principal-agent model for compromising a TEE in a Data Center Execution Assurance design. The model isolates the main drivers of attack profitability: a K-of-n coordination threshold, independent detection risk q, heterogeneous per-member sanctions F_i, and a short-window flow prize (omega) proportional to the value secured (beta times V). We derive closed-form deterrence thresholds and a conservative design bound (V_safe) that make collusion unprofitable under transparent parameter choices. Calibrations based on time-advantaged arbitrage indicate that plausible TEE parameters can protect on the order of one trillion dollars in value.
Transaction Fee Mechanisms (TFMs) study auction design in the Blockchain context, and emphasize robustness against miner and user collusion, moreso than traditional auction theory. \cite{chung2023foundations} introduce the notion of a mechanism being $c$-Side-Contract-Proof ($c$-SCP), i.e., robust to a collusion of the miner and $c$ users. Later work \cite{chung2024collusion,welfareIncreasingCollusion} shows a gap between the $1$-SCP and $2$-SCP classes. We show that the class of $2$-SCP mechanisms equals that of any $c$-SCP with $c\geq 2$, under a relatively minor assumption of consistent tie-breaking. In essence, this implies that any mechanism vulnerable to collusion, is also vulnerable to a small collusion.
Vaccines play a crucial role in the prevention and control of infectious diseases. However, the vaccine supply chain faces numerous challenges that hinder its efficiency. To address these challenges and enhance public health outcomes, many governments provide subsidies to support the vaccine supply chain. This study analyzes a government-subsidized, three-tier vaccine supply chain within a continuous-time differential game framework. The model incorporates dynamic system equations that account for both vaccine quality and manufacturer goodwill. The research explores the effectiveness and characteristics of different government subsidy strategies, considering factors such as price sensitivity, and provides actionable managerial insights. Key findings from the analysis and numerical simulations include the following: First, from a long-term perspective, proportional subsidies for technological investments emerge as a more strategic approach, in contrast to the short-term focus of volume-based subsidies. Second, when the public is highly sensitive to vaccine prices and individual vaccination benefits closely align with government objectives, a volume-based subsidy policy becomes preferable. Finally, the integration of blockchain technology positively impacts the vaccine supply chain, particularly by improving vaccine quality and enhancing the profitability of manufacturers in the later stages of production.
We formulate the design of a threshold signature scheme as made possible on cryptocurrency protocols like Bitcoin. The funds are secured by an m-of-n threshold signature, where at least m signatures are needed to unlock the funds. A user designs this scheme knowing that a malicious attacker can also obtain the signatures with some probability. Higher thresholds offer more security, but also risk locking the user out of his own funds. The optimal threshold balances these twin effects. Interventions like increasing the security or usability of the signatures allow for higher thresholds. We model dynamic threshold signature schemes, where the probability of a user or attacker obtaining signatures decays with time. A dynamic threshold signature scheme is optimal, and increasing security or usability allows for higher thresholds and longer time locks.
Jinghui Chen, Edward Furman, Stephano Ricci, Judeto Shanthirajah
The limitations of the traditional mean-variance (MV) efficient frontier, as introduced by Markowitz (1952), have been extensively documented in the literature. Specifically, the assumptions of normally distributed returns or quadratic investor preferences are often unrealistic in practice. Moreover, variance is not always an appropriate risk measure, particularly for heavy-tailed and highly volatile distributions, such as those observed in insurance claims and cryptocurrency markets, which may exhibit infinite variance. To address these issues, Shalit and Yitzhaki (2005) proposed a mean-Gini (MG) framework for portfolio selection, which requires only finite first moments and accommodates non-normal return distributions. However, downside risk measures - such as tail variance - are generally considered more appropriate for capturing risk managers' risk preference than symmetric measures like variance or Gini. In response, we introduce a novel portfolio optimization framework based on a downside risk metric: the tail Gini. In the first part of the paper, we develop the mean-tail Gini (MTG) efficient frontier. Under the assumption of left-tail exchangeability, we derive closed-form solutions for the optimal portfolio weights corresponding to given expected returns. In the second part, we conduct an empirical study of the mean-tail variance (MTV) and MTG frontiers using data from equity and cryptocurrency markets. By fitting the empirical data to a generalized Pareto distribution, the estimated tail indices provide evidence of infinite-variance distributions in the cryptocurrency market. Additionally, the MTG approach demonstrates superior performance over MTV strategy by mitigating the amplification distortions induced by $\mathrm{L}^2$-norm risk measures. The MTG framework helps avoid overly aggressive investment strategies, thereby reducing exposure to unforeseen losses.
Ethan Buchman, Paolo Dini, Shoaib Ahmed, Andrew Miller · 5 authors
For centuries, financial institutions have responded to liquidity challenges by forming closed, centralized clearing clubs with strict rules and membership that allow them to collaborate on using the least money to discharge the most debt. As closed clubs, much of the general public has been excluded from participation. But the vast majority of private sector actors consists of micro or small firms that are vulnerable to late payments and generally ineligible for bank loans. This low liquidity environment often results in gridlock and leads to insolvency, and it disproportionately impacts small enterprises and communities. On the other hand, blockchain communities have developed open, decentralized settlement systems, along with a proliferation of store of value assets and new lending protocols, allowing anyone to permissionlessly transact and access credit. However, these protocols remain used primarily for speculative purposes, and so far have fallen short of the large-scale positive impact on the real economy prophesied by their promoters. We address these challenges by introducing Cycles, an open, decentralized clearing, settlement, and issuance protocol. Cycles is designed to enable firms to overcome payment inefficiencies, to reduce their working capital costs, and to leverage diverse assets and liquidity sources, including cryptocurrencies, stablecoins, and lending protocols, in service of clearing more debt with less money. Cycles solves real world liquidity challenges through a privacy-preserving multilateral settlement platform based on a graph optimization algorithm. The design is based on a core insight: liquidity resides within cycles in the payment network's structure and can be accessed via settlement flows optimized to reduce debt.
In this paper, we present the Tokenized Sovereign Debt Conversion Mechanism (TSDCM), a smart-contracted instrument that, upon meeting both debt-to-GDP and GDP-growth thresholds, automates the retirement of sovereign debt. TSDCM initiates the conversion of a portion of outstanding bonds into performance-linked tokens by integrating a two-state regime-switching jump-diffusion framework into decentralized protocols. We prove finite-time activation and expected debt reduction through new propositions, establish the existence and uniqueness of the underlying stochastic processes, and introduce a main theorem that ensures a strict decline in expected debt levels. With significant tail-risk mitigation, calibration using IMF data and MATLAB Monte Carlo simulations shows a 20-25% decrease in expected debt-to-GDP ratios over a ten-year period. A transparent and incentive-aligned route to sustainable sovereign debt management is provided by TSDCM.
This study develops a conceptual simulation model for a tokenized recycling incentive system that integrates blockchain infrastructure, market-driven pricing, behavioral economics, and carbon credit mechanisms. The model aims to address the limitations of traditional recycling systems, which often rely on static government subsidies and fail to generate sustained public participation. By introducing dynamic token values linked to real-world supply and demand conditions, as well as incorporating non-monetary behavioral drivers (e.g., social norms, reputational incentives), the framework creates a dual-incentive structure that can adapt over time. The model uses Monte Carlo simulations to estimate outcomes under a range of scenarios involving operational costs, carbon pricing, token volatility, and behavioral adoption rates. Due to the absence of real-world implementations of such integrated blockchain-based recycling systems, the paper remains theoretical and simulation-based. It is intended as a prototype framework for future policy experimentation and pilot projects. The model provides insights for policymakers, urban planners, and technology developers aiming to explore decentralized and market-responsive solutions to sustainable waste management. Future work should focus on validating the model through field trials or behavioral experiments.
Blockchain-based smart contracts offer a new take on credible commitment, where players can commit to actions in reaction to actions of others. Such reaction-function games extend on strategic games with players choosing reaction functions instead of strategies. We formalize a solution concept in terms of fixed points for such games, akin to Nash equilibrium, and prove equilibrium existence. Reaction functions can mimic "trigger" strategies from folk theorems on infinitely repeated games -- but now in a one-shot setting -- for instance to support Pareto-improvements on Nash equilibrium outcomes. In some games, this can even be done through risk-free, safe reaction functions. We apply our theoretical framework to symmetric investment games, which includes two prominent classes of games, namely weakest-link and public-good games. In both cases, we highlight a particular safe and optimal reaction function. In this way, our findings highlight how blockchain-based commitment can help overcome trust and free-riding barriers.
No trade theorems examine conditions under which agents cannot agree to disagree on the value of a security which pays according to some state of nature, thus preventing any mutual agreement to trade. A large literature has examined conditions which imply no trade, such as relaxing the common prior and common knowledge assumptions, as well as allowing for agents who are boundedly rational or ambiguity averse. We contribute to this literature by examining conditions on the private information of agents that reveals, or verifies, the true value of the security. We argue that these conditions can offer insights in three different settings: insider trading, the connection of low liquidity in markets with no trade, and trading using public blockchains and oracles.
Motivated by applications such as cloud computing, gig platforms, and blockchain auctions, we study optimal selling mechanisms for dynamic markets with stochastic supply and demand. In our model, buyers with private valuations and homogeneous goods arrive stochastically and can be held in queues at a cost. The optimal mechanism pairs allocative efficiency with dynamic admission control: goods are assigned to the highest-value buyer, while entry is restricted by value thresholds that strictly increase with the queue length and decrease with available inventory. This policy smooths competitive pressure across time and is implemented in dominant strategies via auctions with dynamic reserve prices.
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.
We present the first formal treatment of \emph{yield tokenization}, a mechanism that decomposes yield-bearing assets into principal and yield components to facilitate risk transfer and price discovery in decentralized finance (DeFi). We propose a model that characterizes yield token dynamics using stochastic differential equations. We derive a no-arbitrage pricing framework for yield tokens, enabling their use in hedging future yield volatility and managing interest rate risk in decentralized lending pools. Taking DeFi lending as our focus, we show how both borrowers and lenders can use yield tokens to achieve optimal hedging outcomes and mitigate exposure to adversarial interest rate manipulation. Furthermore, we design automated market makers (AMMs) that incorporate a menu of bonding curves to aggregate liquidity from participants with heterogeneous risk preferences. This leads to an efficient and incentive-compatible mechanism for trading yield tokens and yield futures. Building on these foundations, we propose a modular \textit{fixed-rate} lending protocol that synthesizes on-chain yield token markets and lending pools, enabling robust interest rate discovery and enhancing capital efficiency. Our work provides the theoretical underpinnings for risk management and fixed-income infrastructure in DeFi, offering practical mechanisms for stable and sustainable yield markets.
We analyze the vulnerability of decentralized autonomous organizations (DAOs) to speculative exploitation via their redemption mechanisms. Studying a game-theoretic model of repeated auctions for governance shares with speculators, we characterize the conditions under which -- in equilibrium -- an exploitative exit is guaranteed to occur, occurs in expectation, or never occurs. We evaluate four redemption mechanisms and extend our model to include atomic exits, time delays, and DAO spending strategies. Our results highlight an inherent tension in DAO design: mechanisms intended to protect members from majority attacks can inadvertently create opportunities for costly speculative exploitation. We highlight governance mechanisms that can be used to prevent speculation.
This paper extends (Spear 2003) by replacing human agents with artificial intelligence (AI) entities that derive utility solely from electricity consumption. These AI agents must prepay for electricity using cryptocurrency and the verification of these transactions requires a fixed amount of electricity. As a result the agents must strategically allocate electricity resources between consumption and payment verification. This paper analyzes the equilibrium outcomes of such a system and discusses the implications of AI-driven energy markets.