Mechanisms for Scheduling with Single-Bit Private Values

Abstract

We study the problem of designing truthful mechanisms for makespan minimization in scheduling. In particular, we consider randomized mechanisms for a restriction of the general multi-dimensional domain (i.e., unrelated machines). In a sense, our setting is the simplest multi-dimensional setting, where each machine holds privately only a single-bit of information. Some of the impossibility results for deterministic mechanisms carry over our setting as well. We prove a separation between truthful-in-expectation and universally truthful mechanisms for makespan minimization: We first show how to design an optimal truthful-in-expectation mechanism, and then prove lower bounds on the approximation guarantee of universally truthful mechanisms

Online scheduling of jobs with favorite machines

“…Kedad-Sidhoum et al (2018) consider the two types of machines (CPU-GPU cluster) problem, and Gehrke et al (2018) consider a generalization, the few types of machines problem. Some work also study similar models in a game-theoretic setting (Lavi and Swamy, 2009;Auletta et al, 2015). Regarding online algorithms, several works consider restricted assignment with additional assumptions on the problem structure like hierarchical server topologies (Bar-Noy et al, 2001) (see also Crescenzi et al (2007)).…”

No truthful mechanism can be better than n approximate for two natural problems

“…Intuitively, the former is a stronger requirement which says that truth-telling is a dominant strategy, even if agents would know the random bits, while the latter needs agents to care about their expected utility. For a separation result in a subclass of the two-values domains in unrelated machines see Auletta et al [3]. Like for deterministic mechanisms, the known upper bounds for randomized mechanisms are optimal if one restricts to task-independent mechanisms ( n+1 2 is a lower bound [18]).…”

Selfish Jobs with Favorite Machines: Price of Anarchy vs. Strong Price of Anarchy

“…Do these bounds improve for larger k? Another interesting restriction would be the case of unit-size jobs, which means that each job has processing time 1 or s. Such two-values restrictions have been studied in the mechanism design setting with selfish machines [23,3], where players are machines and they possibly speculate on their true cost. Considering other well studied solution concepts would also be interesting, including sequential P oA [24,6,12,19], approximate SP oA [14], and the price of stochastic anarchy [10].…”