Julian Ma

Aikaterini-Panagiota Stouka, Julian Ma, Thomas Thiery

Transaction Fee Mechanism (TFM) design in blockchain protocols has gained significant attention following the pioneering work of Roughgarden [EC' 21], which established a formal framework for analyzing user and block proposer incentives under various Transaction Fee Mechanisms, including Ethereum's current fee mechanism EIP-1559. However, the original TFM framework and follow-up TFM works overlook the critical challenge of censorship resistance-specifically in the presence of an external malicious actor who is willing to bribe the proposer to censor a transaction. In this paper, we extend the Roughgarden's framework to capture censorship resistance under bribery attacks via a Bayesian game, where a strategic block proposer's "type" is determined by a bribe function from an external malicious actor. Under this framework, the definition of a standard TFM is extended to a bribery-aware TFM. This technique is broadly applicable to analyze censorship resistance under bribery attacks of both single and multiple proposer protocols within the original TFM scope. We choose to utilize it to evaluate the incentive compatibility and censorship resistance of several TFMs within the context of a multiple proposer protocol called Fork-Choice Enforced Inclusion Lists (FOCIL). FOCIL represents a critical evolution in the Ethereum roadmap, serving as the consensus and censorship resistance flagship for the upcoming Hegota hard fork. It aims to bolster Ethereum's censorship resistance by enabling multiple proposers to contribute to block construction. While recent works such as Garimidi et al.[FC' 25] have extended the TFM framework to multiple proposer settings, they do not aim to capture censorship under bribery attacks and they are not compatible with the unique hierarchical structure of FOCIL.

Yaqi Sun, Julian Ma, David Mguni

A central challenge in game theory and learning systems such as GANs is understanding which algorithms can efficiently compute equilibria across the heterogeneous landscape of games. Equilibrium computation is typically studied solver by solver and game class by game class, yielding strong local guarantees but a fragmented view of solver behaviour. Existing discrete taxonomies often provide an incomplete account of where algorithms succeed. We study this problem through a solver-game map linking games to effective solver dynamics. Classical theory identifies isolated regions of this map but provides limited insight into intermediate or overlapping regimes, suggesting that solvability is governed by latent structural properties defining a continuous solver-aligned geometry of games. We formalise this perspective through structure-aware solver synthesis. A learned structure recogniser maps each game to a low-dimensional solver-aligned representation, and a policy maps this representation to effective primitive mechanisms, adapting solver behaviour across regimes. This reveals regions where particular solver dynamics are effective and where mixtures of primitives are required rather than a single dominant solver. A bounded residual acts as a local corrector and diagnostic signal for incomplete solver bases or representations. The framework yields both an adaptive solver and an analytical lens: games with similar optimisation dynamics cluster together, revealing continuous regions of algorithmic validity and overlapping solver behaviour. Empirically, we show that fixed primitives exhibit systematic regime mismatch, while the learned representation organises game space into a structured cartography aligned with solver behaviour. These results suggest viewing equilibrium computation as the joint problem of learning solver mechanisms and mapping the geometry of solvability.

Julian Ma, Jun Wang, Zafeirios Fountas

Large language models (LLMs) excel at explicit reasoning, but their implicit computational strategies remain underexplored. Decades of psychophysics research show that humans intuitively process and integrate noisy signals using near-optimal Bayesian strategies in perceptual tasks. We ask whether LLMs exhibit similar behaviour and perform optimal multimodal integration without explicit training or instruction. Adopting the psychophysics paradigm, we infer computational principles of LLMs from systematic behavioural studies. We introduce a behavioural benchmark - BayesBench: four magnitude estimation tasks (length, location, distance, and duration) over text and image, inspired by classic psychophysics, and evaluate a diverse set of nine LLMs alongside human judgments for calibration. Through controlled ablations of noise, context, and instruction prompts, we measure performance, behaviour and efficiency in multimodal cue-combination. Beyond accuracy and efficiency metrics, we introduce a Bayesian Consistency Score that detects Bayes-consistent behavioural shifts even when accuracy saturates. Our results show that while capable models often adapt in Bayes-consistent ways, accuracy does not guarantee robustness. Notably, GPT-5 Mini achieves perfect text accuracy but fails to integrate visual cues efficiently. This reveals a critical dissociation between capability and strategy, suggesting accuracy-centric benchmarks may over-index on performance while missing brittle uncertainty handling. These findings reveal emergent principled handling of uncertainty and highlight the correlation between accuracy and Bayesian tendencies. We release our psychophysics benchmark and consistency metric (https://bayes-bench.github.io) as evaluation tools and to inform future multimodal architecture designs.