blockchain protocol designers

Abstract: The goal of this paper is to distill insight around the trade-offs present on Bayesian equilibria of transaction fee mechanism (TFM) design under $n$ multiple concurrent proposers (MCP). We conceptualize a technical toolkit that unlocks the analysis of hard-to-characterize equilibria of finite Bayesian MCP TFM games by examining sequences of joint user--proposer mixed equilibria as the number of users increases and keeping the relative congestion $ρ$ that they cause fixed in the sequence limit. We first consider the popular mechanisms of "pay-once" (which charges transactions its bid only once regardless of the duplicate copies that end up being included by proposers) and "pay-per-inclusion" (PPI in short, which charges a transaction for each copy that appears). We prove that PPI is efficient in the limit of equilibria sequences, and incentivizes users to route to only one proposer. We characterize $m$ users' asymptotic behavior in PPI even in finite markets varying with $O(\sqrt{m})$, where we show users in a $Θ(n\sqrt{ρ(1-ρ)/m})$ window near an efficient cutoff exhibit fixed inclusion probability akin to a normal distribution's CDF. We additionally show that on a value-dependent basis, pay-once exhibits a higher degree of duplication and lower probability of inclusion for higher-value transactions than PPI. Pay-once's inefficiency persists even in the large market limit and even in regimes with ample blockspace where all transactions fit across all blocks. We study interpolations between these two mechanisms proving that some higher coefficients (towards PPI) reduce duplication and increase inclusion probability. We then use our tools to show that exclusive proposer payments yield inefficient equilibria (in fact, with maximal possible duplication), even if users still pay multiple times when included more than once and their payment is burnt when non-exclusive.

Abstract: Blockchain participation games model costly entry, random selection, and threshold success; their retraction variants charge completion costs only to selected contributors. We study committee tasks requiring operators to reserve computing or communication capacity before assignment, so preparation costs are incurred even when capacity remains unused. Users choose abstention, bare registration without preparation, or binding commitment to contribute if selected. Success requires sufficiently many selected contributors, creates public value, and may trigger separate rewards for registration and verified contribution. We characterize all pure Nash equilibria under homogeneous selection and analyze ordering under heterogeneous selection. The results distinguish free-riding on public value from registration that earns rewards without productive commitment; more frequently selected users can choose bare registration while less frequently selected users contribute. Our main result characterizes every homogeneous minimum-outlay scheme supporting full contribution, where every user commits, as a Nash equilibrium. When positive rewards are required, these schemes form a line segment. There is always an optimum with no registration reward. It eliminates every equilibrium containing bare registrants at minimum outlay while retaining the full-contribution equilibrium; threshold-coordination failures may remain. Under heterogeneous selection, a two-user instance has a unique optimum using both rewards, cheaper than every zero-registration-reward scheme supporting full contribution. Finally, if full contribution is a positive-welfare social optimum, the homogeneous zero-registration-reward design attains price of stability one. Under arbitrary independent selection probabilities, every full-contribution Nash equilibrium is also a strong equilibrium.

Abstract: Proof-of-Stake (PoS) systems offer a scalable and energy-efficient alternative to Proof-of-Work (PoW). The economic security of PoS relies critically on incentivizing broad and meaningful participation through well-cali\-brated staking reward mechanisms. We study Ethe\-reum's effective-balance rules as a mechanism-design problem in which the protocol chooses a reward coefficient, an activation threshold, and a maximum effective balance, and validators respond in the induced propor\-tional-allocation game. For fixed participating validators and identity counts, we establish a unique Nash equilibrium in validator-level total stakes. When validators can split or merge their visible identities, each candidate identity structure must be evaluated after the market re-clears. Restructuring incentives therefore depend on post-reset payoff comparisons that account for all validators' stake responses. For an illustrative simulation, we construct address-level budget proxies from Beacon Chain deposits and withdrawals, Lido staking flows, Etherscan balances, and calibrated synthetic agents. With illustrative cost coefficients, lowering the reserve price from 32 ETH to 30 ETH increases active identities by 5.922\% and total effective stake by 0.098\%.

Abstract: EIP-4844 gave Ethereum rollups a separate fee dimension for data, governed by a multiplicative update rule that targets three ``blobs'' per block. Whether this target is reached depends on how many independent, self-interested rollups choose to post data, a question that closed-form models address only for a single agent under exogenous prices or in a static equilibrium. We propose a calibrated multi-agent reinforcement learning environment for the blob fee market in which the blob base fee is endogenous, set by the EIP-4844 rule on the aggregated decisions of heterogeneous rollups fit to post-Dencun Ethereum data. After confirming that the environment reproduces the known single-agent analytical optimum, we show that independent learners, with no convergence guarantee, still settle near the target without coordination ($3.32\pm0.01$ blobs per block over five seeds). Over a fiftyfold demand range ($10\times$ to $500\times$), supply stays at the target from $10\times$ to $200\times$ and rises above it at higher demand, where the fee can no longer hold it. Posting frequency increases with rollup size, an emergent analog of the size threshold predicted by prior theory. A costless layer-1 calldata outside option pushes the fee down by roughly an order of magnitude while aggregate supply stays at the target, so the fee rule acts as a negative-feedback controller on decentralized supply.

Abstract: We consider the problem of parameter selection for EIP-1559, a widely used gas pricing mechanism for blockchains. As opposed to previous work, we aim to achieve economic security, where the chosen parameters guarantee a lower bound on total collected gas fees whenever usage over a given time window exceeds a specified threshold. This bound can be set prohibitively high, thereby economically deterring usage above a desired level. Such guarantees are particularly relevant to long-term objectives such as limiting state growth. We apply our approach to the pure exponential version of EIP-1559 which Ethereum uses and to a variant used by Robinhood Chain and Arbitrum. To achieve economic security, we first characterize the revenue-minimizing gas-usage distribution for the exponential version and for the other variant we construct a distribution whose associated fee revenue provably approximates the minimum. Using these results, we then demonstrate how to set economically secure mechanism parameters for both variants and we discuss the associated tradeoffs.

Abstract: Flashblocks divide a block's priority gas auction into shorter sequential auctions that commit transaction order before the block is complete. We ask how this auction cadence affects bidding and competition among automated arbitrageurs, or searchers. In July 2025 Base replaced a single 2 s auction with ten 200 ms auctions. We use this change to estimate the searcher response from on-chain data alone. On an address-day panel of 3,032 searchers and 8,053 activity-matched controls, a difference-in-differences design estimates a 0.187 gwei fall in the effective priority fee (59% of the searcher pre-period mean). The share of searcher priority-fee value paid in the first tenth of block gas falls from 0.98 to 0.28. This fee compression is the identified effect. The revert-rate response is not (causally) identified and is reported descriptively. At the level of a single opportunity, the winning fee splits into an approximately invariant floor and a competitive premium. The premium scales about linearly with auction duration at high contention and less steeply at low contention. A first-price auction model with uncertain arrival and partial payments by losing searchers accounts for this pattern. We match attempts to the pool they contest. A higher-fee transaction reverts behind a lower-fee winner that landed earlier in 1.9 to 2.7% of contested opportunities by value, an upper bound. Latency therefore decides part of the ordering. A micro-auction model projects diminishing returns from shortening the window below 200 ms, as bids approach a nonzero floor. Rollups such as Arbitrum One now make auction cadence a governance tunable parameter, so these estimates inform how it is set.

Abstract: Ethereum's randomness beacon (RANDAO) is well-known to be manipulable, and prior work [AW24] computes the precise fraction of blocks a strategic proposer can propose. The fraction of blocks proposed, however, is only a proxy for participants' rewards. We propose a generalized reward model capturing many canonical forms of rewards: consensus reward rollover, multi-block MEV, CEX-DEX arbitrage, oracle manipulation, and others. We provide a methodology that computes an ε-optimal strategy for any reward scheme in our model (and in particular, any combination of the above rewards). Finally, we apply our methodology to several canonical examples, and establish the sensitivity of RANDAO manipulation to the underlying rewards. We find that if rewards partially roll over, or scale super-linearly with consecutive blocks, the incentive to manipulate RANDAO is amplified. Lastly, we investigate tail-slot slashing, which can be modeled as a reward function, and show that honest equilibria can be recovered.

Abstract: We study bandwidth fee mechanisms (BFMs) for pricing threshold-certified transaction dissemination before consensus. Analogous to transaction fee mechanisms for computation, BFMs price blockchain communication, which is especially relevant when dissemination is separated from consensus and execution. We model BFMs as two-sided procurement auctions between users submitting transactions and validators receiving and forwarding them. Any validator may serve as a transaction's source and forward it to a threshold of attesters. The model accounts for receipt from the user and subsequent transfers between validators, while abstracting away unrestricted multi-hop gossip and network topology. We establish limits on myopic incentive compatibility: no nontrivial transcript-based BFM prevents profitable collusion between two validators, and no nontrivial BFM simultaneously satisfies incentive compatibility for individual users, individual validators, and coalitions of one validator and one user. On the feasibility side, we give a greedy-route posted-price mechanism that is incentive compatible for every individual user and validator. We also study bandwidth pricing across blocks. Assuming honest validator execution, we propose an EIP-1559-style price-update rule whose fluid approximation has a unique fixed point that is locally stable for sufficiently small step sizes. In large markets, prices starting near this point remain nearby with high probability over any fixed time horizon.

Abstract: Market microstructure studies how trading rules turn orders into prices and allocations. Those rules have been rebuilt repeatedly: for floor traders, electronic limit order books and high-frequency trading, batch auctions and dark pools, blockchains run by automated market makers and block builders, and now AI agents that discover, pay for, and compete over resources. This survey traces that evolution through one question: can a market allocate scarce goods efficiently and fairly without participants revealing everything they know and want? Each technological shift moved the binding constraint of market design from trader rationality to speed, to control over transaction ordering, to the dimensionality of what participants can report. Impossibility results persist; only their cost moves. We review evidence on high-frequency trading, trading venues, automated market makers, extractable value and algorithmic collusion, and identify allocation as the missing layer of the agent-commerce protocol stack.

Abstract: Slashing is commonly argued to secure proof-of-stake blockchains by confiscating the stake of misbehaving validators. The usual justification is that, without slashing, validators can solicit an equivocation attack by signing conflicting blocks: if enough others join, the attack succeeds; otherwise, the attempt incurs no loss. Slashing is intended to make such attempts costly and thereby guarantee the security of applications whose economic value is comparable to the bonded stake. This rationale, however, rests on heuristic arguments rather than a formal game-theoretic guarantee. We challenge this rationale by constructing a risk-free coordination protocol for rational validators under algorithmic slashing. We show that the prescribed strategy profile, in which rational validators solicit other validators to equivocate, constitutes an ex post Nash equilibrium, even when validators do not know in advance how many others will participate. The equilibrium holds for any gain $ε>0$ from successful equivocation, however small relative to the bonded stake. Thus, slashing alone does not guarantee economic security proportional to the value of bonded stake. Our results expose a fundamental limitation of algorithmic slashing. Whereas conventional collateral arrangements in many real-world scenarios can rely on external enforcement, for example through courts, algorithmic slashing depends on the same consensus process that the attackers control. These findings call for a formal analysis of slashing's security, rather than overly simplistic arguments drawn from financial systems with independent enforcement.

Abstract: Byzantine Fault-Tolerant (BFT) protocols guarantee safety and liveness despite the malicious failure of nodes. However, they do not prevent adversarial manipulation of transaction order, where the order a proposer assigns diverges from the order in which clients submitted their transactions. Exploiting this discretion for profit is known as maximal extractable value (MEV), and it is intensified in DAG-based BFT protocols, where every replica proposes blocks concurrently rather than routing transactions through a single designated proposer each round. The proliferation of MEV attacks on DAG-based BFT protocols has made the resulting landscape difficult to navigate: attacks are reported individually, on different protocols, and under different metrics, making it unclear whether two attacks differ fundamentally or merely in how they are described. This paper closes that gap by presenting an attack space for MEV on DAG-based BFT protocols, organized around four families: the adversary, the protocol, the target, and the deployment. For each family, we identify the dimensions that shape an attack's impact. Each point in the attack space fixes one value per dimension, thereby representing a distinct, potential MEV attack, which can then be instantiated on a specific DAG-based BFT protocol. We perform a set of experiments, each isolating a single dimension where the protocol permits it, to empirically measure its effect on the success rate of MEV attacks against six production DAG-based BFT protocols. Our experimental evaluation reveals that every protocol we evaluate is vulnerable to at least a subset of the MEV attacks in this space, and that which attacks succeed is mostly dictated by the protocol's own design rather than by attacker effort.

Abstract: Multidimensional approximate agreement requires $n$ processes with inputs in $\mathbb{R}^d$ to output vectors close to each other, despite up to $t$ Byzantine faults. Under convex validity, outputs must lie in the convex hull of the correct inputs, which leads to resilience thresholds that grow with the dimension. We instead study Minimum Enclosing Ball (MEB) validity and its multiplicative relaxation $c$-MEB validity. Our first contribution is Adaptive MEB Contraction, a coordinate-free algorithm that, in the synchronous model with $n>(d+1)t$ contracts the correct MEB radius by $1/\sqrt2$ per round for $α=1$ while satisfying $\sqrt2$-MEB validity. We also give an example showing that this bound is tight for our analysis. Our main technical contribution is a dimension-free inflation theorem: if every $β$ balls in a finite family of Euclidean balls have a common point, then inflating each radius by $\sqrt{β/(β-1)}$ guarantees a common intersection. Applying the theorem to the candidate balls defining the local MEB-safe areas results in a synchronous algorithm with optimal resilience $n>3t$, contraction factor $\sqrt3/2$ and $\sqrt6$-MEB validity. To the best of our knowledge, this is the first multidimensional approximate agreement algorithm with optimal resilience, constant $c$-MEB validity and coordinate-free contraction. We further extend the approach to the asynchronous setting. Without inflation we obtain resilience $n>(d+2)t$, contraction factor $\sqrt{2/3}$ and $\sqrt6$-MEB validity, whereas with inflation for $n>4t$ we get the contraction factor $\sqrt{15}/4$ and $2\sqrt{10}$-MEB validity. Finally, we compare our guarantees with existing algorithms, including Minimum-Diameter Averaging (MDA), for which we derive MEB-validity guarantees. Our algorithms achieve strictly better resilience while providing substantially stronger MEB-validity guarantees than MDA.