We present a graph-theoretic and convex optimization framework for multi-path routing in decentralized exchange networks, together with its implementation and empirical evaluation on Ethereum mainnet. The framework models the market as a directed token multigraph whose arcs carry AMM exchange functions. Routing is decomposed into two implemented layers: candidate path generation via gas-aware marginal k-shortest-path enumeration, where edge scores embed expected execution cost directly into graph traversal with an explicit pool-simple constraint tracked during path construction, and continuous flow allocation over the selected candidates solved as a concave maximization over a simplex with a per-pool price-impact cap. Under standard concavity and monotonicity assumptions, the KKT conditions imply marginal-output equalization across active paths. The central technical contribution is an improving-path certificate: after solving the allocation on k=20 candidate paths, the KKT multiplier is used as a threshold to determine via a single shortest-path query whether any omitted pool-simple path could improve the current solution; in our implementation the certificate confirms sufficiency in the majority of epochs. Execution is protected by an on-chain slippage tolerance enforced at the smart-contract level. We evaluate the implemented engine against four production DEX aggregators on repeated WETH-USDT quote observations across six trade sizes on Ethereum mainnet: median shortfall is below 5 bps across all sizes and top-3 quote rank exceeds 57% of epochs.
Automated matching engines execute millions of orders per session, yet systematic asymmetries in latency, order size, and market access compound into persistent execution disparities that erode participant trust. We formulate provably fair order matching as a Constrained Markov Decision Process and propose CPO-FOAM (Constrained Policy Optimization with Feedback-Optimized Adaptive Margins). An inner loop computes an analytic trust-region step on the Fisher information manifold; a PID-controlled outer loop dynamically tightens safety margins, suppressing the sawtooth oscillations endemic to Lagrangian methods under non-stationary dynamics. Group fairness (demographic parity, equalized odds) enters the CMDP cost vector while individual Lipschitz fairness is enforced deterministically via spectral normalization. We prove BIBO stability and that the integral term drives steady-state violations to zero. On LOBSTER NASDAQ data across six market regimes, CPO-FOAM recovers 95.9% of unconstrained throughput at 2.5% constraint violation frequency; on crypto-asset LOB data under MEV injection it captures 98.4% of the reward envelope at 3.2% CVF. The method scales sub-linearly to M=8 constraints, settles on-chain within one Ethereum block, and yields a 2.1X reward improvement on Safety-Gymnasium, confirming domain-agnostic generalization.
The Debreu Koopmans theorem restricts separable aggregation to at most one nonconvex component. We solve this by proving that a separable, additive or multiplicative, function is star quasiconvex, those with star shaped sublevel sets about minimizers, if and only if each component is star quasiconvex. This immediately yields star quasiconvexity of separable sums of quasiconvex functions, formally bridging diversification theory with the S shaped value functions of Prospect Theory. Furthermore, we develop a complete calculus, monotonic composition, pointwise minima, quasi arithmetic means, and we apply it to Cobb-Douglas functions, multifactor risk models, and constant function market makers in decentralized finance. Star quasiconvexity thus provides a unified framework for applications in optimization and economic modeling beyond the classical Debreu Koopmans constraint. The introduction discuss economic motivations.
We consider the interaction between centralized trading and decentralized Proof of Stake (PoS) blockchain ecosystems. Motivated by the increasing dominance of centralized exchanges and the institutionalization of crypto markets, we study how trading activities on centralized exchanges affect staking behavior, token allocation, and decentralization within a PoS blockchain. We formulate a continuous-time mean field model, where the miners simultaneously act as validators in the PoS protocol and traders in a centralized market with price impact. Under suitable assumptions, we establish the local well-posedness of the mean field system, and derive a semi-explicit characterization of the equilibrium trading strategy. Numerical results suggest that centralized trading activities may enhance staking participation, and promote decentralization of the staking distribution through market incentives. We also study the effects of transaction costs and token supply mechanisms on the equilibrium staking ratio and concentration profile. These results illustrate how market microstructure and centralized liquidity provision can exert significant influence on decentralized blockchain protocols.
Mining blocks in a blockchain using the \textit{Proof-of-Work} consensus protocol involves significant risk, as network participants face continuous operational costs while earning infrequent capital gains upon successfully mining a block. A common risk mitigation strategy is to join a mining pool, which combines the computing resources of multiple miners to provide a more stable income. This article examines a Pay-per-Share (PPS) reward system, where the pool manager can adjust both the share difficulty and the management fee. Using a simplified wealth model for miners, we explore how miners should allocate their computing resources among different mining pools, considering the trade-off between risk transfer to the manager and management fees.
Multicriteria decision-making methods exhibit critical dependence on the choice of normalization techniques, where different selections can alter 20-40% of the final rankings. Current practice is characterized by the ad-hoc selection of methods without systematic robustness evaluation. We present a framework that addresses this methodological sensitivity through automated exploration of the scaling transformation space. The implementation leverages the existing Scikit-Criteria infrastructure to automatically generate all possible methodological combinations and provide robust comparative analysis.We apply this approach in an evaluation dataset of cryptocurrencies with 6 methodological scenarios, showing a range of correlation between methods, explicitly quantifying the methodological sensitivity limits.
Elliptic Curve Cryptography (ECC) is a fundamental component of modern public-key cryptosystems that enable efficient and secure digital signatures, key exchanges, and encryption. Its core operation, scalar multiplication, denoted as $k \cdot P$, where $P$ is a base point and $k$ is a private scalar, relies heavily on the secrecy and unpredictability of $k$. Conventionally, $k$ is selected using user input or pseudorandom number generators. However, in resource-constrained environments with weak entropy sources, these approaches may yield low-entropy or biased scalars, increasing susceptibility to side-channel and key recovery attacks. To mitigate these vulnerabilities, we introduce an optimization-driven scalar generation method that explicitly maximizes bit-level entropy. Our approach uses differential evolution (DE), a population-based metaheuristic algorithm, to search for scalars whose binary representations exhibit maximal entropy, defined by an even and statistically uniform distribution of ones and zeros. This reformulation of scalar selection as an entropy-optimization problem enhances resistance to entropy-based cryptanalytic techniques and improves overall unpredictability. Experimental results demonstrate that DE-optimized scalars achieve entropy significantly higher than conventionally generated scalars. The proposed method can be integrated into existing ECC-based protocols, offering a deterministic, tunable alternative to traditional randomness, ideal for applications in blockchain, secure messaging, IoT, and other resource-constrained environments.
This paper studies Mean Field Games (MFGs) in which agent dynamics are given by jump processes of controlled intensity, with mean-field interaction via the controls and affecting the jump intensities. We establish the existence of MFG equilibria in a general discrete-time setting, and prove a limit theorem as the time discretization goes to zero, establishing equilibria in the continuous-time setting for a class of MFGs of intensity control. This motivates numerical schemes that involve directly solving discrete-time games as opposed to coupled Hamilton-Jacobi-Bellman and Kolmogorov equations. As an example of the general theory, we consider cryptocurrency mining competition, modeled as an MFG both in continuous and discrete time, and illustrate the effectiveness of the discrete-time algorithm to solve it.
Madelaine Martinez Ferguson, Aliza Sharmin, Mustafa Can Camur, Xueping Li
This paper reviews intermodal transportation systems and their role in decarbonizing freight networks from an operations research perspective, analyzing over a decade of studies (2010-2024). We present a chronological analysis of the literature, illustrating how the field evolved over time while highlighting the emergence of new research avenues. We observe a significant increase in research addressing decarbonization since 2018, driven by regulatory pressures and technological advancements. Our integrated analysis is organized around three themes: a) modality, b) sustainability, and c) solution techniques. Key recommendations include the development of multistage stochastic models to better manage uncertainties and disruptions within intermodal transportation systems. Further research could leverage innovative technologies like machine learning and blockchain to improve decision-making and resource use through stakeholder collaboration. Life cycle assessment models are also suggested to better understand emissions across transportation stages and support the transition to alternative energy sources.
This paper proposes a model that enables permissionless and decentralized networks for complex computations. We explore the integration and optimize load balancing in an open, decentralized computational network. Our model leverages economic incentives and reputation-based mechanisms to dynamically allocate tasks between operators and coprocessors. This approach eliminates the need for specialized hardware or software, thereby reducing operational costs and complexities. We present a mathematical model that enhances restaking processes in blockchain systems by enabling operators to delegate complex tasks to coprocessors. The model's effectiveness is demonstrated through experimental simulations, showcasing its ability to optimize reward distribution, enhance security, and improve operational efficiency. Our approach facilitates a more flexible and scalable network through the use of economic commitments, adaptable dynamic rating models, and a coprocessor load incentivization system. Supported by experimental simulations, the model demonstrates its capability to optimize resource allocation, enhance system resilience, and reduce operational risks. This ensures significant improvements in both security and cost-efficiency for the blockchain ecosystem.
González, AgustÃn Muñoz, Juan I. Sequeira, Rafael Orive Illera
In this work, we present an application of the probabilistic weak formulation of mean field games (MFG) for modeling liquidity pools in a constant product automated market maker (AMM) protocol in the context of decentralized finance. Our work extends one of the most conventional applications of MFG, which is the price impact model in an order book, by incorporating an AMM instead of a traditional order book. The key structural difference is that in the AMM setting, the price is determined by the pool's reserves through a nonlinear mechanism, replacing the linear price-impact function used in classical models. Through our approach, we establish the existence of solutions to the Mean Field Game and, additionally, the existence of approximate Nash equilibria for the finite-player game. We complement the theoretical results with a comprehensive numerical study that validates the equilibrium structure: stability under perturbations, the $\varepsilon$-Nash property via unilateral deviations, finite-player convergence at propagation-of-chaos rates, and sensitivity to cost parameters and incentive targets. These results offer a new game-theoretic perspective for representing strategic behavior in AMM-based liquidity pools and open promising opportunities for future research in this emerging field.
This paper investigates how pricing schemes can achieve efficient allocations in blockchain systems featuring multiple transaction queues under a global capacity constraint. I model a capacity-constrained blockchain where users submit transactions to different queues -- each representing a submarket with unique demand characteristics -- and decide to participate based on posted prices and expected delays. I find that revenue maximization tends to allocate capacity to the highest-paying queue, whereas welfare maximization generally serves all queues. Optimal relative pricing of different queues depends on factors such as market size, demand elasticity, and the balance between local and global congestion. My results have implications for the implementation of local congestion pricing for evolving blockchain architectures, including parallel transaction execution, directed acyclic graph (DAG)-based systems, and multiple concurrent proposers.
The rapid growth of electric vehicles (EVs) and the deployment of vehicle-to-grid (V2G) technology pose significant challenges for distributed power grids, particularly in fostering trust and ensuring effective coordination among stakeholders. Establishing a trustworthy V2G operation environment is crucial for enabling large-scale EV user participation and realizing V2G potential in real-world applications. In this paper, an integrated scheduling and trading framework is developed to conduct transparent and efficacious coordination in V2G operations. In blockchain implementation, a cyber-physical blockchain architecture is proposed to enhance transaction efficiency and scalability by leveraging smart charging points (SCPs) for rapid transaction validation through a fast-path practical byzantine fault tolerance (fast-path PBFT) consensus mechanism. From the energy dispatching perspective, a game-theoretical pricing strategy is employed and smart contracts are utilized for autonomous decision-making between EVs and operators, aiming to optimize the trading process and maximize economic benefits. Numerical evaluation of blockchain consensus shows the effect of the fast-path PBFT consensus in improving systems scalability with a balanced trade-off in robustness. A case study, utilizing real-world data from the Southern University of Science and Technology (SUSTech), demonstrates significant reductions in EV charging costs and the framework potential to support auxiliary grid services.
Web 3.0 is recognized as a pioneering paradigm that empowers users to securely oversee data without reliance on a centralized authority. Blockchains, as a core technology to realize Web 3.0, can facilitate decentralized and transparent data management. Nevertheless, the evolution of blockchain-enabled Web 3.0 is still in its nascent phase, grappling with challenges such as ensuring efficiency and reliability to enhance block propagation performance. In this paper, we design a Graph Attention Network (GAT)-based reliable block propagation optimization framework for blockchain-enabled Web 3.0. We first innovatively apply a data-freshness metric called age of block to measure block propagation efficiency in public blockchains. To achieve the reliability of block propagation, we introduce a reputation mechanism based on the subjective logic model, including the local and recommended opinions to calculate the miner reputation value. Moreover, considering that the GAT possesses the excellent ability to process graph-structured data, we utilize the GAT with reinforcement learning to obtain the optimal block propagation trajectory. Numerical results demonstrate that the proposed scheme exhibits the most outstanding block propagation efficiency and reliability compared with traditional routing mechanisms.
Austin Adams, Ciamac C. Moallemi, Sara Reynolds, Dan Robinson
Automated market makers (AMMs) have emerged as the dominant market mechanism for trading on decentralized exchanges implemented on blockchains. This paper presents a single mechanism that targets two important unsolved problems for AMMs: reducing losses to informed orderflow, and maximizing revenue from uninformed orderflow. The ``auction-managed AMM'' works by running a censorship-resistant onchain auction for the right to temporarily act as ``pool manager'' for a constant-product AMM. The pool manager sets the swap fee rate on the pool, and also receives the accrued fees from swaps. The pool manager can exclusively capture some arbitrage by trading against the pool in response to small price movements, and also can set swap fees incorporating price sensitivity of retail orderflow and adapting to changing market conditions, with the benefits from both ultimately accruing to liquidity providers. Liquidity providers can enter and exit the pool freely in response to changing rent, though they must pay a small fee on withdrawal. We prove that under certain assumptions, this AMM should have higher liquidity in equilibrium than any standard, fixed-fee AMM.
We develop a general and practical framework to address the problem of the optimal design of dynamic fee mechanisms for multiple blockchain resources. Our framework allows to compute policies that optimally trade-off between adjusting resource prices to handle persistent demand shifts versus being robust to local noise in the observed block demand. In the general case with more than one resource, our optimal policies correctly handle cross-effects (complementarity and substitutability) in resource demands. We also show how these cross-effects can be used to inform resource design, i.e. combining resources into bundles that have low demand-side cross-effects can yield simpler and more efficient price-update rules. Our framework is also practical, we demonstrate how it can be used to refine or inform the design of heuristic fee update rules such as EIP-1559 or EIP-4844 with two case studies. We then estimate a uni-dimensional version of our model using real market data from the Ethereum blockchain and empirically compare the performance of our optimal policies to EIP-1559.
Blockchain technology is a breakthrough in changing the ways of business and organization operations, in which the consensus problem is challenging with practical constraints, such as computational power and consensus standard. In this paper, a novel consensus mechanism named Proof-of-Prospect-Theory (PoPT) is designed from the view of game theory, where the game prospect value is considered as an important election criterion of the block-recorder. PoPT portrays the popularity of a node in the network as an attribute, which is constituted by the subjective sensibilities of nodes. Furthermore, the performances of the PoPT and the willingness of ordinary nodes to participate in the consensus are analyzed, exploring fairness, decentralization, credibility, and the motivating ability of the consensus mechanism. Finally, numerical simulations with optimization of the PoPT consensus mechanism are demonstrated in the scenario of a smart grid system to illustrate the effectiveness of the PoPT.
Guillermo Angeris, Tarun Chitra, Theo Diamandis, Alex Evans · 5 authors
Constant function market makers (CFMMs) are the most popular type of decentralized trading venue for cryptocurrency tokens. In this paper, we give a very general geometric framework (or 'axioms') which encompass and generalize many of the known results for CFMMs in the literature, without requiring strong conditions such as differentiability or homogeneity. One particular consequence of this framework is that every CFMM has a (unique) canonical trading function that is nondecreasing, concave, and homogeneous, showing that many results known only for homogeneous trading functions are actually fully general. We also show that CFMMs satisfy a number of intuitive and geometric composition rules, and give a new proof, via conic duality, of the equivalence of the portfolio value function and the trading function. Many results are extended to the general setting where the CFMM is not assumed to be path-independent, but only one trade is allowed. Finally, we show that all 'path-independent' CFMMs have a simple geometric description that does not depend on any notion of a 'trading history'.
With a growing complexity of the intelligent traffic system (ITS), an integrated control of ITS that is capable of considering plentiful heterogeneous intelligent agents is desired. However, existing control methods based on the centralized or the decentralized scheme have not presented their competencies in considering the optimality and the scalability simultaneously. To address this issue, we propose an integrated control method based on the framework of Decentralized Autonomous Organization (DAO). The proposed method achieves a global consensus on energy consumption efficiency (ECE), meanwhile to optimize the local objectives of all involved intelligent agents, through a consensus and incentive mechanism. Furthermore, an operation algorithm is proposed regarding the issue of structural rigidity in DAO. Specifically, the proposed operation approach identifies critical agents to execute the smart contract in DAO, which ultimately extends the capability of DAO-based control. In addition, a numerical experiment is designed to examine the performance of the proposed method. The experiment results indicate that the controlled agents can achieve a consensus faster on the global objective with improved local objectives by the proposed method, compare to existing decentralized control methods. In general, the proposed method shows a great potential in developing an integrated control system in the ITS.
Jason Milionis, Ciamac C. Moallemi, Tim Roughgarden
We consider the impact of trading fees on the profits of arbitrageurs trading against an automated market maker (AMM) or, equivalently, on the adverse selection incurred by liquidity providers (LPs) due to arbitrage. We extend the model of Milionis et al. [2022] for a general class of two asset AMMs to introduce both fees and discrete Poisson block generation times. In our setting, we are able to compute the expected instantaneous rate of arbitrage profit in closed form. When the fees are low, in the fast block asymptotic regime, the impact of fees takes a particularly simple form: fees simply scale down arbitrage profits by the fraction of blocks which present profitable trading opportunities to arbitrageurs. This fraction decreases with an increasing block rate, hence our model yields an important practical insight: faster blockchains will result in reduced LP losses. Further introducing gas fees (fixed costs) in our model, we show that, in the fast block asymptotic regime, lower gas fees lead to smaller losses for LPs.
Public blockchains group submitted transactions into batches, called blocks. A natural question is how to determine which transactions are included in these batches. In this note, we show a gap between the welfare of so-called `fair' ordering, namely first-in-first-out (an ideal that a number of blockchain protocols strive to achieve), where the first transactions to arrive are the ones put into the block, and the welfare of `optimal' inclusion that is, at least approximately, welfare-maximizing, such as choosing which transactions are included in a block via an auction. We show this gap is positive under a simple model with mild assumptions where we assume transactions are, roughly speaking, uniformly drawn from a reasonable distribution. Our results formalize a performance metric for blockchain inclusion rules and consequently provide a framework to help design and compare these rules. The results can be directly extended to ordering mechanisms as well.
This paper extends the existing drawdown modulation control policy to include a novel restart mechanism for trading. It is known that the drawdown modulation policy guarantees the maximum percentage drawdown no larger than a prespecified drawdown limit for all time with probability one. However, when the prespecified limit is approaching in practice, such a modulation policy becomes a stop-loss order, which may miss the profitable follow-up opportunities if any. Motivated by this, we add a data-driven restart mechanism into the drawdown modulation trading system to auto-tune the performance. We find that with the restart mechanism, our policy may achieve a superior trading performance to that without the restart, even with a nonzero transaction costs setting. To support our findings, some empirical studies using equity ETF and cryptocurrency with historical price data are provided.