Truthful Secretaries with Budgets

TL;DR

This paper introduces truthful online auction mechanisms for agents with budgets and private types, achieving constant approximation ratios for revenue and welfare in dynamic, multi-unit settings, a novel contribution in online budgeted auctions.

Contribution

It presents the first truthful mechanisms for online auctions with budgeted agents, transforming offline mechanisms into online ones with approximation guarantees.

Findings

Achieves constant approximation for revenue in online settings.

Provides a truthful mechanism with constant approximation for liquid welfare.

Addresses the challenge of combining online dynamics with budget constraints.

Abstract

We study online auction settings in which agents arrive and depart dynamically in a random (secretary) order, and each agent's private type consists of the agent's arrival and departure times, value and budget. We consider multi-unit auctions with additive agents for the allocation of both divisible and indivisible items. For both settings, we devise truthful mechanisms that give a constant approximation with respect to the auctioneer's revenue, under a large market assumption. For divisible items, we devise in addition a truthful mechanism that gives a constant approximation with respect to the liquid welfare --- a natural efficiency measure for budgeted settings introduced by Dobzinski and Paes Leme [ICALP'14]. Our techniques provide high-level principles for transforming offline truthful mechanisms into online ones, with or without budget constraints. To the best of our knowledge, this is the first work that addresses the non-trivial challenge of combining online settings with budgeted agents.