arXiv subjects

Vasilis Christoforidis

Publications and source records attributed to Vasilis Christoforidis.

5 recordsLinked to original sources

arXiv2026

A Note on EFX Inapproximability for Chores

We study the approximability of EFX allocations for indivisible chores under complement-free cost functions. The non-existence of exact EFX allocations for general monotone functions for chores is known from \cite{CS24}, and a result of \cite{akrami2026} transfers such comparison-based non-existence results to monotone submodular, and hence subadditive, functions. We strengthen this picture by giving explicit constant-factor inapproximability results for submodular and subadditive functions. Our main construction is a three-agent, six-chore instance with monotone subadditive cost functions for which no $α$-EFX allocation exists for any $1\le α<2^{1/3}\approx 1.26$, thus narrowing the gap with the known upper bound of $2$. The construction is obtained by refining the original counterexample of \cite{CS24} and using the approach of \cite{mackenzie2026}. We also give a weighted-coverage realization of the ordinal profile, yielding an instance in which no $α$-EFX allocation exists for any $1\le α<20/19$ under submodular costs. Thus, even within well-studied complement-free classes, EFX for chores admits nontrivial constant lower bounds on approximability.

cs.GT↗

arXiv2025

Improving the Price of Anarchy via Predictions in Parallel-Link Networks

We study non-atomic congestion games on parallel-link networks with affine cost functions. We investigate the power of machine-learned predictions in the design of coordination mechanisms aimed at minimizing the impact of selfishness. Our main results demonstrate that enhancing coordination mechanisms with a simple advice on the input rate can optimize the social cost whenever the advice is accurate (consistency), while only incurring minimal losses even when the predictions are arbitrarily inaccurate (bounded robustness). Moreover, we provide a full characterization of the consistent mechanisms that holds for all monotone cost functions, and show that our suggested mechanism is optimal with respect to the robustness. We further explore the notion of smoothness within this context: we extend our mechanism to achieve error-tolerance, i.e. we provide an approximation guarantee that degrades smoothly as a function of the prediction error, up to a predetermined threshold, while achieving a bounded robustness.

cs.GT↗

arXiv2025

Fair and Truthful Allocations Under Leveled Valuations

We study the problem of fairly allocating indivisible goods among agents which are equipped with {\em leveled} valuation functions. Such preferences, that have been studied before in economics and fair division literature, capture a simple and intuitive economic behavior; larger bundles are always preferred to smaller ones. We provide a fine-grained analysis for various subclasses of leveled valuations focusing on two extensively studied notions of fairness, (approximate) MMS and EFX. In particular, we present a general positive result, showing the existence of $2/3$-MMS allocations under valuations that are both leveled and submodular. We also show how some of our ideas can be used beyond the class of leveled valuations; for the case of two submodular (not necessarily leveled) agents we show that there always exists a $2/3$-MMS allocation, complementing a recent impossibility result. Then, we switch to the case of subadditive and fractionally subadditive leveled agents, where we are able to show tight (lower and upper) bounds of $1/2$ on the approximation factor of MMS. Moreover, we show the existence of exact EFX allocations under general leveled valuations via a simple protocol that in addition satisfies several natural economic properties. Finally, we take a mechanism design approach and we propose protocols that are both truthful and approximately fair under leveled valuations.

cs.GT↗

arXiv2025

Maximin Share Guarantees for Few Agents with Subadditive Valuations

We study the problem of fairly allocating a set of indivisible items among a set of agents. We consider the notion of (approximate) maximin share (MMS) and we provide an improved lower bound of $1/2$ (which is tight) for the case of subadditive valuations when the number of agents is at most four. We also provide a tight lower bound for the case of multiple agents, when they are equipped with one of two possible types of valuations. Moreover, we propose a new model that extends previously studied models in the area of fair division, which will hopefully give rise to further research. We demonstrate the usefulness of this model by employing it as a technical tool to derive our main result, and we provide a thorough analysis for this model for the case of three agents. Finally, we provide an improved impossibility result for the case of three submodular agents.

cs.GT↗

arXiv2024

On The Pursuit of EFX for Chores: Non-Existence and Approximations

We study the problem of fairly allocating a set of chores to a group of agents. The existence of envy-free up to any item (EFX) allocations is a long-standing open question for both goods and chores. We resolve this question by providing a negative answer for the latter, presenting a simple construction that admits no EFX solutions for allocating six items to three agents equipped with superadditive cost functions, thus proving a separation result between goods and bads. In fact, we uncover a deeper insight, showing that the instance has unbounded approximation ratio. Moreover, we show that deciding whether an EFX allocation exists is NP-complete. On the positive side, we establish the existence of EFX allocations under general monotone cost functions when the number of items is at most $n+2$. We then shift our attention to additive cost functions. We employ a general framework in order to improve the approximation guarantees in the well-studied case of three additive agents, and provide several conditional approximation bounds that leverage ordinal information.

cs.GT↗