Truthful Assignment without Money
Shaddin Dughmi, Arpita Ghosh

TL;DR
This paper develops truthful, money-free mechanisms for the generalized assignment problem and its variants, achieving optimal or near-optimal approximations through LP-based techniques and addressing private information challenges.
Contribution
It introduces a novel LP-based framework for designing strategyproof mechanisms without payments for complex assignment problems.
Findings
Optimal strategyproof mechanism for unweighted matching
2-approximate strategyproof mechanism for maximum weight bipartite matching
Constant approximation ratios for knapsack-like problems
Abstract
We study the design of truthful mechanisms that do not use payments for the generalized assignment problem (GAP) and its variants. An instance of the GAP consists of a bipartite graph with jobs on one side and machines on the other. Machines have capacities and edges have values and sizes; the goal is to construct a welfare maximizing feasible assignment. In our model of private valuations, motivated by impossibility results, the value and sizes on all job-machine pairs are public information; however, whether an edge exists or not in the bipartite graph is a job's private information. We study several variants of the GAP starting with matching. For the unweighted version, we give an optimal strategyproof mechanism; for maximum weight bipartite matching, however, we show give a 2-approximate strategyproof mechanism and show by a matching lowerbound that this is optimal. Next we study…
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Taxonomy
TopicsAuction Theory and Applications · Optimization and Search Problems · Game Theory and Voting Systems
