Directly compare the marginal price algorithm with the conjugate convex formulation

Conduct a direct head-to-head empirical performance comparison between the marginal price optimization algorithm and the conjugate convex formulation of Diamandis et al. (2023), which was not implemented here and therefore cannot presently be directly compared.

Background

The paper repeatedly compares its marginal price method with the token-space convex formulation of Angeris et al. (2021), showing large speedups. However, the authors did not implement the conjugate convex problem (Diamandis et al., 2023) and thus cannot provide a direct comparison.

A direct comparison would clarify the relative performance and robustness of the two dual formulations on the same benchmarks and market configurations.