Most Competitive Mechanisms in Online Fair Division

Martin Aleksandrov; Toby Walsh

Home/Archive/arXiv

arXiv · 2006.15909

Most Competitive Mechanisms in Online Fair Division

Martin Aleksandrov·Toby Walsh

View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper combines two key ingredients for online algorithms - competitive analysis (e.g. the competitive ratio) and advice complexity (e.g. the number of advice bits needed to improve online decisions) - in the context of a simple online fair division model where items arrive one by one and are allocated to agents via some mechanism. We consider four such online mechanisms: the popular Ranking matching mechanism adapted from online bipartite matching and the Like, Balanced Like and Maximum Like allocation mechanisms firstly introduced for online fair division problems. Our first contribution is that we perform a competitive analysis of these mechanisms with respect to the expected size of the matching, the utilitarian welfare, and the egalitarian welfare. We also suppose that an oracle can give a number of advice bits to the mechanisms. Our second contribution is to give several impossibility results; e.g. no mechanism can achieve the egalitarian outcome of the optimal offline mechanism supposing they receive partial advice from the oracle. Our third contribution is that we quantify the competitive performance of these four mechanisms w.r.t. the number of oracle requests they can make. We thus present a most-competitive mechanism for each objective.

Explore related subjects

cs.GT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Martin Aleksandrov, Toby Walsh. 2020-06-29. Most Competitive Mechanisms in Online Fair Division. https://arxiv.org/abs/2006.15909

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

KEEP EXPLORING

Related papers

arXiv2026

Learning in Structured Stackelberg Games

We initiate the study of structured Stackelberg games, a novel form of strategic interaction between a leader and a follower where contextual information can be predictive of the follower's (unknown) type. Motivated by applications such as security games and AI safety, we show how this additional structure can help the leader learn a utility-maximizing policy in both the online and distributional settings. In the online setting, we first prove that standard learning-theoretic measures of complexity do not characterize the difficulty of the leader's learning task. Notably, we find that there exists a learning-theoretic measure of complexity, analogous to the Littlestone dimension in online classification, that tightly characterizes the leader's instance-optimal regret. We term this the Stackelberg-Littlestone dimension, and leverage it to provide a provably optimal online learning algorithm. In the distributional setting, we provide analogous results by showing that two new dimensions control the sample complexity upper- and lower-bound.

cs.GT↗

arXiv2026

Equilibrium and Infeasibility: A new solution concept for games

Addressing infeasibility in non-cooperative games has become an important topic, as many problems across different applications face this issue. In this paper, we propose a new solution concept for generalized games with possibly infeasible individual constraints. A solution is defined as the limit of a sequence of generalized Nash equilibria induced by games with penalty terms relaxing the individual constraints. Existence is established for a broad range of games and we provide conditions allowing to characterize a $ψ$-penalized solution as a strategy profile maximizing every player's utility over all her penalty minimizing strategies. A variation of Divide-the-Dollar serves as an illustrative example. We further establish the compatibility with the GNE and the solution to the Nash bargaining.

cs.GT↗

arXiv2026

Subgame-Perfect Nash Equilibria of Plurality Voting with Abstention: a PSPACE-Completeness Result for Restricted Ballots

We consider sequential Plurality elections in which each voter may abstain or vote for a single candidate. Each voter assigns utilities to all candidates; for each voter, this induces a (weak) order over the candidates. Ties are resolved uniformly at random, and voting has a small positive cost, so that a voter prefers to abstain when their vote cannot change the election outcome. We consider a variant of this model where, for each voter, we additionally specify a prefix of her ranking, so that she is only allowed to vote for a candidate from that prefix (or abstain). We prove that for this variant of the model, deciding whether a designated candidate is among the election winners in a subgame-perfect equilibrium of the associated extensive-form game is PSPACE-complete. This partially resolves an open problem from the work of Desmedt and Elkind [2010].

cs.GT↗