arXiv subjects

Eleni Batziou

Publications and source records attributed to Eleni Batziou.

5 recordsLinked to original sources

arXiv2026

Position Auctions with a Capacity Constraint

Sponsored search auctions are commonly modeled as an assignment of a fixed set of slots (positions) to a set of advertisers, with welfare maximization being reducible to a standard matching problem. Motivated by modern ad formats, we study a richer variant of the classical position auctions model, in which ads have heterogeneous sizes and the platform must jointly select and assign a subset of ads to positions subject to a global space constraint. We formulate this as a matching problem with a capacity constraint, and propose an algorithmic technique that goes beyond simple greedy methods while achieving constant factor approximation guarantees. Our allocation rule augments density-based ordering with capacity-aware local improvements, which allow for re-allocations that improve welfare, while respecting the capacity constraint. Applied in the context of position auctions, we analyze this mechanism under the assumption of single-parameter agents and position-dependent click-through-rates (CTRs). We show that a minor modification to our approach yields a universally truthful randomized mechanism with a constant factor approximation guarantee. To the best of our knowledge, this is the first truthful constant-approximation mechanism for this variant of capacity-constrained matching.

cs.GT↗

arXiv2026

The Complexity of Sparse Win-Lose Bimatrix Games

We prove that computing an $\epsilon$-approximate Nash equilibrium of a win-lose bimatrix game with constant sparsity is PPAD-hard for inverse-polynomial $\epsilon$. Our result holds for 3-sparse games, which is tight given that 2-sparse win-lose bimatrix games can be solved in polynomial time.

cs.CC↗

arXiv2024

Monotone Contractions

We study functions $f : [0, 1]^d \rightarrow [0, 1]^d$ that are both monotone and contracting, and we consider the problem of finding an $\varepsilon$-approximate fixed point of $f$. We show that the problem lies in the complexity class UEOPL. We give an algorithm that finds an $\varepsilon$-approximate fixed point of a three-dimensional monotone contraction using $O(\log (1/\varepsilon))$ queries to $f$. We also give a decomposition theorem that allows us to use this result to obtain an algorithm that finds an $\varepsilon$-approximate fixed point of a $d$-dimensional monotone contraction using $O((c \cdot \log (1/\varepsilon))^{\lceil d / 3 \rceil})$ queries to $f$ for some constant $c$. Moreover, each step of both of our algorithms takes time that is polynomial in the representation of $f$. These results are strictly better than the best-known results for functions that are only monotone, or only contracting. All of our results also apply to Shapley stochastic games, which are known to be reducible to the monotone contraction problem. Thus we put Shapley games in UEOPL, and we give a faster algorithm for approximating the value of a Shapley game.

cs.CC↗

arXiv2022

Assignment Markets with Budget Constraints

This paper studies markets where a set of indivisible items is sold to bidders with quasilinear, unit-demand valuations, subject to a hard budget constraint. Without financial constraints the well-known assignment market model of Shapley and Shubik (1971) allows for a simple ascending auction format that is incentive-compatible, and strongly Pareto-optimal. However, this auction model does not capture the possibility that bidders face hard budget constraints. We design an iterative auction that depends on demand queries and an easily verifiable additional condition to maintain the properties in the presence of budget constraints. If instead this additional condition does not hold, incentive compatibility and core stability are at odds, and we cannot hope to achieve strong Pareto optimality in a simple ascending auction even with truthful bidding. Moreover, even in a complete information model where the auctioneer has access to valuations and budget constraints, the problem is NP-hard.

cs.GT↗

arXiv2021

Strong Approximate Consensus Halving and the Borsuk-Ulam Theorem

In the consensus halving problem we are given n agents with valuations over the interval $[0,1]$. The goal is to divide the interval into at most $n+1$ pieces (by placing at most n cuts), which may be combined to give a partition of $[0,1]$ into two sets valued equally by all agents. The existence of a solution may be established by the Borsuk-Ulam theorem. We consider the task of computing an approximation of an exact solution of the consensus halving problem, where the valuations are given by distribution functions computed by algebraic circuits. Here approximation refers to computing a point that $\varepsilon$-close to an exact solution, also called strong approximation. We show that this task is polynomial time equivalent to computing an approximation to an exact solution of the Borsuk-Ulam search problem defined by a continuous function that is computed by an algebraic circuit. The Borsuk-Ulam search problem is the defining problem of the complexity class BU. We introduce a new complexity class BBU to also capture an alternative formulation of the Borsuk-Ulam theorem from a computational point of view. We investigate their relationship and prove several structural results for these classes as well as for the complexity class FIXP.

cs.GT↗