Work

On the Nisan–Ronen Conjecture for Submodular Valuations

Year: 2025

Type: article

Abstract: . We consider mechanisms for scheduling [Formula: see text] unrelated machines when the valuations of the players (i.e., machines) are submodular. We give a lower bound of [Formula: see text] on the approximation ratio of incentive compatible deterministic mechanisms. This lower bound holds for supermodular valuations and also when all players, except for one, have additive valuations. This is an information-theoretic impossibility result on the approximation ratio of mechanisms that provides strong evidence for the Nisan–Ronen conjecture, which states that the approximation ratio is [Formula: see text] when the valuations of all machines are additive. Our approach is based on a novel multiplayer characterization of appropriately selected instances that allows us to focus on a particular type of algorithm, linear mechanisms, and it is a potential stepping stone towards the full resolution of the Nisan–Ronen conjecture.

Source: SIAM Journal on Computing

DOI: 10.1137/22m1483141

Authors: George Christodoulou, Elias Koutsoupias, Annamária Kovács

Institutions: University of Liverpool, Aristotle University of Thessaloniki, Athena Research and Innovation Center In Information Communication & Knowledge Technologies, University of Oxford, Goethe University Frankfurt

Language: English

Topic: Auction Theory and Applications

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: green

Funder: Assessment, Strategy And Risk Reduction for Tsunamis in Europe

Award: G4681393210