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We study the risks of validator reuse across multiple services in a restaking protocol. We characterize the robust security of a restaking network as a function of the buffer between the costs and profits from attacks. For example, our results imply that if attack costs always exceed attack profits by 10%, then a sudden loss of .1% of the overall stake (e.g., due to a software error) cannot result in the ultimate loss of more than 1.1% of the overall stake. We also provide local analogs of these overcollateralization conditions and robust security guarantees that apply specifically for a target service or coalition of services. All of our bounds on worst-case stake loss are the best possible. Finally, we bound the maximum-possible length of a cascade of attacks. Our results suggest measures of robustness that could be exposed to the participants in a restaking protocol. We also suggest polynomial-time computable sufficient conditions that can proxy for these measures. 

We consider the impact of trading fees on the profits of arbitrageurs trading against an automated marker marker (AMM) or, equivalently, on the adverse selection incurred by liquidity providers due to arbitrage. We extend the model of Milionis et al. [2022] for a general class of two asset AMMs to both introduce 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 time that an arriving arbitrageur finds a profitable trade. 

In decentralized finance ("DeFi"), automated market makers (AMMs) enable traders to programmatically exchange one asset for another. Such trades are enabled by the assets deposited by liquidity providers (LPs). The goal of this paper is to characterize and interpret the optimal (i.e., profit-maximizing) strategy of a monopolist liquidity provider, as a function of that LP’s beliefs about asset prices and trader behavior. We introduce a general framework for reasoning about AMMs based on a Bayesian-like belief inference framework, where LPs maintain an asset price estimate, which is updated by incorporating traders' price estimates. In this model, the market maker (i.e., LP) chooses a demand curve that specifies the quantity of a risky asset to be held at each dollar price. Traders arrive sequentially and submit a price bid that can be interpreted as their estimate of the risky asset price; the AMM responds to this submitted bid with an allocation of the risky asset to the trader, a payment that the trader must pay, and a revised internal estimate for the true asset price. We define an incentive-compatible (IC) AMM as one in which a trader’s optimal strategy is to submit its true estimate of the asset price, and characterize the IC AMMs as those with downward-sloping demand curves and payments defined by a formula familiar from Myerson’s optimal auction theory. We generalize Myerson’s virtual values, and characterize the profit-maximizing IC AMM. The optimal demand curve generally has a jump that can be interpreted as a "bid-ask spread," which we show is caused by a combination of adverse selection risk (dominant when the degree of information asymmetry is large) and monopoly pricing (dominant when asymmetry is small). This work opens up new research directions into the study of automated exchange mechanisms from the lens of optimal auction theory and iterative belief inference, using tools of theoretical computer science in a novel way. 

The incentive-compatibility properties of blockchain transaction fee mechanisms have been investigated with passive block producers that are motivated purely by the net rewards earned at the consensus layer. This paper introduces a model of active block producers that have their own private valuations for blocks (representing, for example, additional value derived from the application layer). The block producer surplus in our model can be interpreted as one of the more common colloquial meanings of the phrase "maximal extractable value (MEV)." We first prove that transaction fee mechanism design is fundamentally more difficult with active block producers than with passive ones: With active block producers, no non-trivial or approximately welfare-maximizing transaction fee mechanism can be incentive-compatible for both users and block producers. These results can be interpreted as a mathematical justification for augmenting transaction fee mechanisms with additional components such as order flow auctions, block producer competition, trusted hardware, or cryptographic techniques. We then consider a more fine-grained model of block production that more accurately reflects current practice, in which we distinguish the roles of "searchers" (who actively identify opportunities for value extraction from the application layer and compete for the right to take advantage of them) and "proposers" (who participate directly in the blockchain protocol and make the final choice of the published block). Searchers can effectively act as an "MEV oracle" for a transaction fee mechanism, thereby enlarging the design space. Here, we first consider a TFM that is inspired by how searchers have traditionally been incorporated into the block production process, with each transaction effectively sold off to a searcher through a first-price auction. We then explore the TFM design space with searchers more generally, and design a mechanism that circumvents our impossibility results for TFMs without searchers. Our mechanism (the "SAKA" mechanism) is incentive-compatible (for users, searchers, and the block producer), sybil-proof, and guarantees roughly 50% of the maximum-possible welfare when transaction sizes are small relative to block sizes. We conclude with a matching negative result: even when transaction sizes are small, no DSIC and sybil-proof deterministic TFM can guarantee more than 50% of the maximum-possible welfare. 

Transaction fee mechanism design is a new decentralized mechanism design problem where users bid for space on the blockchain. Several recent works showed that the transaction fee mechanism design fundamentally departs from classical mechanism design. They then systematically explored the mathematical landscape of this new decentralized mechanism design problem in two settings: in the plain setting where no cryptography is employed, and in a cryptography-assisted setting where the rules of the mechanism are enforced by a multi-party computation protocol. Unfortunately, in both settings, prior works showed that if we want the mechanism to incentivize honest behavior for both users as well as miners (possibly colluding with users), then the miner revenue has to be zero. Although adopting a relaxed, approximate notion of incentive compatibility gets around this zero miner-revenue limitation, the scaling of the miner revenue is nonetheless poor. In this paper, we show that if we make a mild reasonable-world assumption that there are sufficiently many honest users, we can circumvent the known limitations on miner revenue, and design auctions that generate asymptotically optimal miner revenue. We also systematically explore the mathematical landscape of transaction fee mechanism design under the new reasonable-world assumptions, and demonstrate how such assumptions can alter the feasibility and infeasibility landscape.