arXiv subjects

Christoph Schlegel

Publications and source records attributed to Christoph Schlegel.

13 recordsLinked to original sources

arXiv2026

The price of anarchy in the max-distance network creation game is not constant

At edge price $α=1$, we construct an infinite family of pure Nash equilibria of the unilateral max-distance network creation game with $\PoA\ge2^{\sqrt{\log_2 n}-O(\log\log n)}$. Together with the known upper bound, this gives $2^{Θ(\sqrt{\log n})}$ along the constructed sequence of population sizes. We subdivide every edge of the bipartite double cover of a distance-uniform graph with large diameter constructed by Lavrov, Loh and Messegué, and let each subdivision vertex buy its two incident edges. A distance calculation rules out every profitable unilateral deviation. The equilibria are not strict. We also give a short proof that the price of anarchy is constant for every polynomially vanishing edge price.

cs.GT↗

arXiv2026

Bi-Compositional Division Rules

We characterise the division rules for claims problems that satisfy equal treatment of equals, bilateral consistency, composition down, and composition up. The rules are precisely the members of a one-parameter log-exponential family $\{r^θ\}_{θ\in[-\infty,+\infty]}$, with constrained equal awards (CEA) and constrained equal losses (CEL) as its endpoints. For finite $θ$, $r^θ$ is the equal-sacrifice rule in awards for $u_θ=\logφ_θ$, where \[ φ_θ(x):=\frac{e^{θx}-1}θ\quad(θ\ne0), \qquad φ_0(x):=x, \] and simultaneously the equal-sacrifice rule in losses for the dual utility $u_{-θ}$. The proportional rule is the midpoint, $θ=0$. Continuity of the rules are not assumed but a consequence of the other axioms.

econ.TH↗

arXiv2026

Just-in-Time Resale in an Ahead-of-Time Auction for Faster Execution

We study Arbitrum's Timeboost auction, an ahead-of-time mechanism that sells a 200ms ordering advantage in an otherwise first-come, first-served transaction ordering policy. The market naturally divides into two phases: a competition phase, in which the dominant searchers compete directly in the primary auction, and a coordination phase, in which they source fast-lane access through Kairos, a Just-in-Time resale intermediary. We use auction bids, time-boosted transactions, and on-chain payment traces to study how well ahead-of-time bids predict realized CEX--DEX arbitrage profits and how the emergence of resale changes surplus allocation. We find that ahead-of-time bids are noisy predictors of short-horizon arbitrage profits. During the competition phase, bid--profit correlations are statistically significant but economically modest at the round level, while correlations increase when profits are aggregated over longer horizons. This suggests that bidders can identify favorable market conditions but face substantial uncertainty about the realized value of any individual one-minute fast-lane interval. After the Kairos transition, competition in the primary auction weakens sharply: in our focused transition-analysis window, paid bids fall from 62.7% of the top bid before the transition to 14.8% thereafter, while total searcher profits remain broadly similar. The resulting dynamics are most consistent with coordination through a common intermediary rather than direct competition in the primary auction. More broadly, our findings suggest that ahead-of-time allocation mechanisms can be vulnerable to secondary-market intermediation when competition among dominant participants is weak.

cs.GT↗

arXiv2026

Competing Auctions in Intermediated Markets

We analyze competing auctions in intermediated markets, where a seller selects among parallel mechanisms for the sale of a single good, most prominently the relay-and-protocol architecture of proposer-builder separation in Ethereum. When the intermediary can enforce single-homing on its bidders, sealed-bid second-price intermediary auctions fully unravel into the sealed first-price principal auction; open bidding-format intermediaries unravel only partially, collapsing into first-price in equilibrium under symmetric latency and sorting fast bidders to the intermediary under asymmetric latency. Any last-look advantage is removed through the availability of a credible sealed bidding channel. These results extend to multi-plexing environments (no enforcement by the intermediary). While the unraveling result indicates that the availability of a sealed first-price bidding channel pushes the overall market to the same auction structure, the very assumption of the credibility of such channel is problematic, as the seller may have an incentive to leak information: a first-price auction is leakage-resistant in the presence of a single ``fast'' bidder but not against two or more. However, if the seller can credibly commit to not leak bids, it is optimal for them to do so. A main motivation is the forthcoming Glamsterdam update of Ethereum: our analysis suggests that the availability of an in-protocol (first-price) bidding channel severely limits the design space for out-of-protocol auctions by relays and other intermediaries.

cs.GT↗

arXiv2026

Transaction Ordering Auctions

We study equilibrium investment into bidding and latency reduction for different sequencing policies. For a batch auction design, we observe that bidders shade bids according to the likelihood that competing bidders land in the current batch. Moreover, in equilibrium, in the ex-ante investment stage before the auction, bidders invest into latency until they make zero profit in expectation. We compare the batch auction design to continuous time bidding policies (time boost) and observe that (depending on the choice of parameters) they obtain similar revenue and welfare guarantees.

cs.GT↗

arXiv2026

Timing Games: Probabilistic backrunning and spam

There are $n$ players who compete by timing their actions. An opportunity appears randomly on a time interval. Whoever takes an action the fastest after the opportunity has arisen wins. The occurrence of the opportunity is observed only with a delay. Taking actions is costly. We characterize the unique symmetric equilibrium of this game and study worst-case inefficiency of equilibria. Our main motivation is the study of ``probabilistic backrunning" on blockchains, where arbitrageurs want to place an order immediately after a trade that impacts the price on an exchange or after an oracle update. In this context, the number of actions taken can be interpreted as a measure of costly ``spam" generated to compete for the opportunity.

cs.GT↗

arXiv2026

On Sybil-proof Mechanisms

We show that in the single-parameter mechanism design environment, the only non-wasteful, symmetric, incentive compatible and Sybil-proof direct mechanism is a second price auction with symmetric tie-breaking. Thus, if there is private information, lotteries or other mechanisms that do not always allocate to a highest-value bidder are not Sybil-proof or not incentive compatible. Moreover, we show that our main (im)possibility result extends beyond linear valuations, but not to multi-unit object allocation with capacity constrained bidders. We also provide examples of mechanisms (with higher interim payoff for the bidders than a second price auction) that satisfy all of the other axioms and a weaker, Bayesian notion of Sybil-proofness. Thus, our (im)possibility result does not generalize to the Bayesian setting and we have a larger design space: With Sybil constraints, equivalence between dominant strategy and Bayesian implementation (that holds in classical single-parameter mechanism design without Sybils) no longer holds.

cs.GT↗

arXiv2026

The Free Option Problem of ePBS

Ethereum's upcoming Glamsterdam upgrade introduces EIP-7732 enshrined Proposer--Builder Separation (ePBS), which improves the block production pipeline by addressing trust and scalability challenges. Yet it also creates a new liveness risk: builders gain a short-dated ``free'' option to prevent the execution payload they committed to from becoming canonical, without incurring an additional penalty. Exercising this option renders an empty block for the slot in question, thereby degrading network liveness. We present the first systematic study of the free option problem. Our theoretical results predict that option value and exercise probability grow with market volatility, the length of the option window, and the share of block value derived from external signals such as external market prices. The availability of a free option will lead to mispricing and LP losses. The problem would be exacerbated if Ethereum further scales and attracts more liquidity. Empirical estimates of values and exercise probabilities on historical blocks largely confirm our theoretical predictions. While the option is rarely profitable to exercise on average (0.82\% of blocks assuming an 8-second option time window), it becomes significant in volatile periods, reaching up to 6\% of blocks on high-volatility days -- precisely when users most require timely execution. Moreover, builders whose block value relies heavily on CEX-DEX arbitrage are more likely to exercise the option. We demonstrate that mitigation strategies -- shortening the option window or penalizing exercised options -- effectively reduce liveness risk.

cs.GT↗

arXiv2025

Arbitrage with bounded Liquidity

We derive the arbitrage gains or, equivalently, Loss Versus Rebalancing (LVR) for arbitrage between \textit{two imperfectly liquid} markets, extending prior work that assumes the existence of an infinitely liquid reference market. Our result highlights that the LVR depends on the relative liquidity and relative trading volume of the two markets between which arbitrage gains are extracted. Our model assumes that trading costs on at least one of the markets is quadratic. This assumption holds well in practice, with the exception of highly liquid major pairs on centralized exchanges, for which we discuss extensions to other cost functions.

q-fin.MF↗

arXiv2025

TimeBoost: Do Ahead-of-Time Auctions Work?

We study the performance of the TimeBoost auction, by comparing cumulative fixed time markout of fast lane trades over the TimeBoost interval to bids for the fast lane. Such comparison allows us to assess how well bids predict future extracted value from the time advantage. The correlation between winning bids and markouts is weak across bidders, suggesting that bids are a noisy predictor of extracted value. The correlation slightly improves when comparing paid bids (the second highest bid) instead of winning bids to markouts, which we attribute to the fact that the auction is more of a common value type. In all settings, the relative order of the most frequent bidder performance remains the same, together with their absolute profits. Bids and markouts aggregated over long time intervals exhibit much higher correlation, indicating that bidders detect trends much better than identify when the high arbitrage value is exactly available. One possible explanation for this is the fact that the correlation between previous minute markouts and current minute bids is significant, suggesting that the previous minute markouts is used to predict the next minute value when bidding.

cs.GT↗

arXiv2025

Conditional Recall

In the neon-lit nights of 2026, Johnson \& Johnson unveiled X. A pill, not larger than a snowflake, that promised a tempest of change. This miraculous drug didn't just allow people to cherry-pick memories to erase from their minds, it could also leave a reminder of this erasure in the minds of those who ingested it. Amidst the iconic red-bricked walls of Harvard Law, you, with books in one hand and dreams in the other, are on a mission. You are not just another student; you carry the hope of revolutionizing the archaic chambers of the legal world. Each night, as you pore over the tomes of law, you wonder what greatness society can achieve. On a cold evening, your phone buzzes. It's Dex, your old college friend turned underground dealer. His message is simple: ``Got X. Special price for you.'' The temptation swirls around you. Would you trade the lessons of the past for a clearer, yet incomplete future? The decision rests in your hands. We explore the game theoretic implications of a technology (such as TEEs) that allows agents to commit to forget information and discuss several applications.

cs.GT↗

arXiv2025

Searcher Competition in Block Building

We study the amount of maximal extractable value (MEV) captured by validators, as a function of searcher competition, in blockchains with competitive block building markets such as Ethereum. We argue that the core is a suitable solution concept in this context that makes robust predictions that are independent of implementation details or specific mechanisms chosen. We characterize how much value validators extract in the core and quantify the surplus share of validators as a function of searcher competition. Searchers can obtain at most the marginal value increase of the winning block relative to the best block that can be built without their bundles. Dually this gives a lower bound on the value extracted by the validator. If arbitrages are easy to find and many searchers find similar bundles, the validator gets paid all value almost surely, while searchers can capture most value if there is little searcher competition per arbitrage. For the case of passive block-proposers we study, moreover, mechanisms that implement core allocations in dominant strategies and find that for submodular value, there is a unique dominant-strategy incentive compatible core-selecting mechanism that gives each searcher exactly their marginal value contribution to the winning block. We validate our theoretical prediction empirically with aggregate bundle data and find a significant positive relation between the number of submitted backruns for the same opportunity and the median value captured by the proposer from the opportunity.

cs.GT↗

arXiv2025

Cross-Chain Arbitrage: The Next Frontier of MEV in Decentralized Finance

Decentralized finance (DeFi) markets spread across Layer-1 (L1) and Layer-2 (L2) blockchains rely on arbitrage to keep prices aligned. Today most price gaps are closed against centralized exchanges (CEXes), whose deep liquidity and fast execution make them the primary venue for price discovery. As trading volume migrates on-chain, cross-chain arbitrage between decentralized exchanges (DEXes) will become the canonical mechanism for price alignment. Yet, despite its importance to DeFi-and the on-chain transparency making real activity tractable in a way CEX-to-DEX arbitrage is not-existing research remains confined to conceptual overviews and hypothetical opportunity analyses. We study cross-chain arbitrage with a profit-cost model and a year-long measurement. The model shows that opportunity frequency, bridging time, and token depreciation determine whether inventory- or bridge-based execution is more profitable. Empirically, we analyze one year of transactions (September 2023 - August 2024) across nine blockchains and identify 242,535 executed arbitrages totaling 868.64 million USD volume. Activity clusters on Ethereum-centric L1-L2 pairs, grows 5.5x over the study period, and surges-higher volume, more trades, lower fees-after the Dencun upgrade (March 13, 2024). Most trades use pre-positioned inventory (66.96%) and settle in 9s, whereas bridge-based arbitrages take 242s, underscoring the latency cost of today's bridges. Market concentration is high: the five largest addresses execute more than half of all trades, and one alone captures almost 40% of daily volume post-Dencun. We conclude that cross-chain arbitrage fosters vertical integration, centralizing sequencing infrastructure and economic power and thereby exacerbating censorship, liveness, and finality risks; decentralizing block building and lowering entry barriers are critical to countering these threats.

cs.CR↗