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Automated marker makers (AMMs) are decentralized exchanges that enable the automated trading of digital assets. Liquidity providers (LPs) deposit digital tokens, which can be used by traders to execute trades, which generate fees for the investing LPs. In AMMs, trade prices are determined algorithmically, unlike classical limit order books. Concentrated liquidity market makers (CLMMs) are a major class of AMMs that offer liquidity providers flexibility to decide not onlyhow muchliquidity to provide, butin what ranges of pricesthey want the liquidity to be used. This flexibility can complicate strategic planning, since fee rewards are shared among LPs. We formulate and analyze a game theoretic model to study the incentives of LPs in CLMMs. Our main results show that while our original formulation admits multiple Nash equilibria and has complexity quadratic in the number of price ticks in the contract, it can be reduced to a game with a unique Nash equilibrium whose complexity is only linear. We further show that the Nash equilibrium of this simplified game follows a waterfilling strategy, in which low-budget LPs use up their full budget, but rich LPs do not. Finally, by fitting our game model to real-world CLMMs, we observe that in liquidity pools with risky assets, LPs adopt investment strategies far from the Nash equilibrium. Under price uncertainty, they generally invest in fewer and wider price ranges than our analysis suggests, with lower-frequency liquidity updates. In such risky pools, by updating their strategy to more closely match the Nash equilibrium of our game, LPs can improve their median daily returns by $116, which corresponds to an increase of 0.009% in median daily return on investment (ROI). At maximum, LPs can improve daily ROI by 0.855% when they reach Nash equilibrium. In contrast, in stable pools (e.g., of only stablecoins), LPs already adopt strategies that more closely resemble the Nash equilibrium of our game. 

Automated Market Makers (AMMs) are essential in Decentralized Finance (DeFi) as they match liquidity supply with demand. They function through liquidity providers (LPs) who deposit assets into liquidity pools. However, the asset trading prices in these pools often trail behind those in more dynamic, centralized exchanges, leading to potential arbitrage losses for LPs. This issue is tackled by adapting market maker bonding curves to trader behavior, based on the classical market microstructure model of Glosten and Milgrom. Our approach ensures a zero-profit condition for the market maker’s prices. We derive the differential equation that an optimal adaptive curve should follow to minimize arbitrage losses while remaining competitive. Solutions to this optimality equation are obtained for standard Gaussian and Lognormal price models using Kalman filtering. A key feature of our method is its ability to estimate the external market price without relying on price or loss oracles. We also provide an equivalent differential equation for the implied dynamics of canonical static bonding curves and establish conditions for their optimality. Our algorithms demonstrate robustness to changing market conditions and adversarial perturbations, and we offer an on-chain implementation using Uniswap v4 alongside off-chain AI co-processors. 

Decentralized finance (DeFi) borrowing and lending platforms are crucial to the decentralized economy, involving two main participants: lenders who provide assets for interest and borrowers who offer collateral exceeding their debt and pay interest. Collateral volatility necessitates over-collateralization to protect lenders and ensure competitive returns. Traditional DeFi platforms use a fixed interest rate curve based on the utilization rate (the fraction of available assets borrowed) and determine over-collateralization offline through simulations to manage risk. This method doesn't adapt well to dynamic market changes, such as price fluctuations and evolving user needs, often resulting in losses for lenders or borrowers. In this paper, we introduce an adaptive, data-driven protocol for DeFi borrowing and lending. Our approach includes a high-frequency controller that dynamically adjusts interest rates to maintain market stability and competitiveness with external markets. Unlike traditional protocols, which rely on user reactions and often adjust slowly, our controller uses a learning-based algorithm to quickly find optimal interest rates, reducing the opportunity cost for users during periods of misalignment with external rates. Additionally, we use a low-frequency planner that analyzes user behavior to set an optimal over-collateralization ratio, balancing risk reduction with profit maximization over the long term. This dual approach is essential for adaptive markets: the short-term component maintains market stability, preventing exploitation, while the long-term planner optimizes market parameters to enhance profitability and reduce risks. We provide theoretical guarantees on the convergence rates and adversarial robustness of the short-term component and the long-term effectiveness of our protocol. Empirical validation confirms our protocol’s theoretical benefits. 

Crash fault tolerant (CFT) consensus algorithms are commonly used in scenarios where system components are trusted - e.g., enterprise settings and government infrastructure. However, CFT consensus can be broken by even a single corrupt node. A desirable property in the face of such potential Byzantine faults is accountability: if a corrupt node breaks the protocol and affects consensus safety, it should be possible to identify the culpable components with cryptographic integrity from the node states. Today, the best-known protocol for providing accountability to CFT protocols is called PeerReview; it essentially records a signed transcript of all messages sent during the CFT protocol. Because PeerReview is agnostic to the underlying CFT protocol, it incurs high communication and storage overhead. We propose CFT-Forensics, an accountability framework for CFT protocols. We show that for a special family of forensics-compliant CFT protocols (which includes widely-used CFT protocols like Raft and multi-Paxos), CFT-Forensics gives provable accountability guarantees. Under realistic deployment settings, we show theoretically that CFT-Forensics operates at a fraction of the cost of PeerReview. We subsequently instantiate CFT-Forensics for Raft, and implement Raft-Forensics as an extension to the popular nuRaft library. In extensive experiments, we demonstrate that Raft-Forensics adds low overhead to vanilla Raft. With 256 byte messages, Raft-Forensics achieves a peak throughput 87.8% of vanilla Raft at 46% higher latency (+44 ms). We finally integrate Raft-Forensics into the open-source central bank digital currency OpenCBDC, and show that in wide-area network experiments, Raft-Forensics achieves 97.8% of the throughput of Raft, with 14.5% higher latency (+326 ms).