Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.39532

Tight Liquid Welfare Guarantees for Auctions with Budgets via LP Duality

Twan Kroll·Guido Schäfer·Artem Tsikiridis
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the efficiency of auctions with budget-constrained bidders and derive tight price of anarchy (PoA) bounds for coarse correlated equilibria (CCE). To this end, we develop a general framework that reduces proving PoA guarantees to finding feasible solutions to the dual of a linear program. The LP is formulated over a small number of per-bidder equilibrium statistics, incorporates constraints implied by the auction setting and equilibrium behavior, and captures a novel smoothness notion tailored to budget-constrained environments; we provide a reduction from classical smoothness to this new notion. Our approach enables simple and tight PoA analyses across a broad range of auction formats. Using our framework, we obtain tight liquid welfare guarantees for simultaneous first-price, second-price, and all-pay auctions, simultaneous auctions with restricted uniform bidding interfaces, discriminatory and uniform price multi-unit auctions, and generalized first-price position auctions. Beyond budget-constrained settings, we derive new lower bounds for the budget-free uniform price auction and generalized second-price auction; in particular, our lower bound for the uniform price auction matches the upper bound of $3.146$ by de Keijzer et al. (2013).

Explore related subjects

cs.GT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Twan Kroll, Guido Schäfer, Artem Tsikiridis. 2026-09-30. Tight Liquid Welfare Guarantees for Auctions with Budgets via LP Duality. https://arxiv.org/abs/2609.39532

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Connecting Strategy Improvement, the Simplex Algorithm and Lopsidedness

The strategy improvement algorithm for mean payoff games and parity games is a local improvement algorithm, just like the simplex algorithm for linear programs. Their similarity has turned out very useful: many lower bounds on running time for the simplex algorithm have been created, by first constructing lower bounds for strategy improvement in a game, and then transforming these into a linear program. However, earlier connections between these algorithms required constructing an intermediate Markov decision process, which is not always possible. We prove a formal, direct connection between the two algorithms, showing that many variants of strategy improvement for parity and mean payoff games are truly an instance of the simplex algorithm, under mild nondegeneracy assumptions. The linear programming formulation of these games leads to what we call hypercubelike polyhedra. These polyhedra allow us to show combinatorial properties of various games on graphs. In particular, we show a connection between strategy sets of games and lopsided sets.

cs.GT↗
arXiv2026

Deterministic algorithms for inhomogeneous Bernoulli trials: Shapley value of network devices

Suppose that $n$ computer devices are to be connected to a network via inhomogeneous Bernoulli trials. The Shapley value of a device quantifies how much the network's value increases due to the participation of that device. Characteristic functions of such games are naturally taken as the belief function (containment function) and Choquet capacity (hitting probability) of a random set (random network of devices). Traditionally, the Shapley value is either calculated as the expected marginal contribution over all possible coalitions (subnetworks), which results in exponential computational complexity, or approximated by the Monte Carlo sampling technique, where the performance is highly dependent on the stochastic sampling process. The purpose of this study is to design deterministic algorithms for games formulated via inhomogeneous Bernoulli trials that approximate the Shapley value in linear or quadratic time, with rigorous error analysis (Sections 3 and 4). Additionally, we provide a review of relevant literature on existing calculation methods in Remark 3.1 and Appendix I. A further goal is to supplement Shapley's original proof by deriving the Shapley value formula using a rigorous approach based on definite integrals and combinatorial analysis. This method explicitly highlights the roles of the Binomial Theorem and the Beta function in the proof, addressing a gap in Shapley's work (Appendix II).

cs.GT↗
arXiv2026

Blockchain Monetary Policy, Strategic Participation, and the Dynamics of Decentralization

Blockchain systems must navigate a fundamental tradeoff between rewarding capable participants for performance and preserving a sufficiently decentralized distribution of stake. We study this tradeoff through algorithmic reward policies in dynamic blockchain environments with publicly known capability types and evolving token stakes. We analyze two settings. First, under full participation, we study virtual-stake policies that combine type and stake in winner selection. We show that fixed virtual-stake rules exhibit strong path dependence, and that this limitation extends to broader winner-selection rules based on virtual stake; when the type weight varies over time, the winner distribution asymptotically approaches either stake-proportional or type-proportional selection. Second, we study a repeated participation game in which agents may abstain, rewards update stake, and token value depends on the decentralization of the participating stake. We characterize stage equilibria under myopic behavior. In this environment, strongly performance-favoring winner-take-most policies can drive the system to minimum decentralization under myopic play. We then identify policies that preserve participation or decentralization only by departing from strict performance-first reward design. In particular, our analysis identifies three benchmarks: policies that spread winner eligibility across the top-$k$ types, policies that simulate lookahead, and broad-sharing reward rules. Each mitigates failures of performance-first designs with different tradeoffs in participation, robustness, and performance priority. Overall, our results suggest that winner selection alone does not robustly resolve the capability-stake tradeoff: sustaining decentralization requires reward rules that react explicitly to concentration, even when this entails sacrificing some immediate performance advantage.

cs.GT↗