Truthfulness on a budget: trading money for approximation through monitoring

Abstract

Albeit a pervasive desideratum when computing a novel paradigm wherein agents' declarations can be partially checked against their actual costs. in the presence of selfish agents, truthfulness typically imposes severe limitations to what can be implemented. The price of these limitations is typically paid either economically, in terms of the financial resources needed to enforce truthfulness, or algorithmically, in terms of restricting the set of implementable objective functions, which often leads to renouncing optimality and resorting to approximate allocations. In this paper, with regards to utilitarian problems, we ask two fundamental questions: (i) what is the a minimum sufficient budget needed by optimal truthful mechanisms, and (ii) whether it is possible to sacrifice optimality in order to achieve truthfulness with a lower budget. To answer these questions, we connect two streams of work on mechanism design and look at monitoring-a paradigm wherein agents' actual costs are bound to their declarations. In this setting, we prove that the social cost is always a sufficient budget, even for collusion-resistant mechanisms, and, under mild conditions, also a necessary budget for a large class of utilitarian problems that encompass set system problems. Furthermore, for facility location, a well-studied problem outside of this class, we draw a novel picture about the relationship between approximation and frugality.

Approximation Guarantee of OSP Mechanisms: The Case of Machine Scheduling and Facility Location

“…1 We first prove that, no matter the algorithm at hand, there exists an OSP mechanism with monitoring that always compensates the agents their costs. This reimbursement mechanism, introduced in the context of mechanisms with monitoring by Serafino et al [40] (with the name of first-price mechanisms), yields a couple of interesting observations in the context of OSP mechanisms. Firstly, it is the first direct-revelation OSP mechanism.…”

“…We design the interval mechanism for facility location that is optimal, OSP with monitoring and charges (rather than paying) the agents. This construction adapts the first-price mechanism in [40] to guarantee obvious strategyproofness even in absence of funds to pay the agents.…”

“…Finally, we focus on the frugality [12,25,40,41] of the interval mechanism, i.e., on the possibility to implement an optimal mechanism that is OSP with monitoring and charges agents with less demanding payments. To this aim, we introduce the optimized interval mechanism (OIM), that allows to reduce payments in some cases.…”

Truthful Aggregation of Budget Proposals with Proportionality Guarantees

“…We use an additive approximation measure. Such measures has been used both in the approximation mechanism [2,19] and the mechanism design [11,35,34] literature.…”

Efficient Truthful Scheduling and Resource Allocation through Monitoring

“…Kovács, Meyer, and Ventre (2015) study mechanisms with monitoring where the principal is the operating system and the agents are computational processes. Different payment schemes for mechanisms with monitoring are studied in (Serafino, Ventre, and Vidali 2020). The monitoring paradigm is also studied in absence of transfers in (Koutsoupias 2014;Giannakopoulos, Koutsoupias, and Kyropoulou 2016), and in the context of truthfulness with bounded rationality in (Ferraioli and Ventre 2017;Kyropoulou and Ventre 2019).…”