Eisenberg-Gale markets: algorithms and structural properties
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Algorithmic Game Theory
Optimal mechanism design and money burning
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Market equilibrium via a primal--dual algorithm for a convex program
Journal of the ACM (JACM)
Approximate mechanism design without money
Proceedings of the 10th ACM conference on Electronic commerce
The combinatorial assignment problem: approximate competitive equilibrium from equal incomes
Proceedings of the Behavioral and Quantitative Game Theory: Conference on Future Directions
Finding approximate competitive equilibria: efficient and fair course allocation
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Strategy-proof allocation of multiple items between two agents without payments or priors
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Reducing Untruthful Manipulation in Envy-Free Pareto Optimal Resource Allocation
WI-IAT '10 Proceedings of the 2010 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology - Volume 02
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Dominant resource fairness: fair allocation of multiple resource types
Proceedings of the 8th USENIX conference on Networked systems design and implementation
No justified complaints: on fair sharing of multiple resources
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
The Efficiency of Fair Division
Theory of Computing Systems
On strategy-proof allocation without payments or priors
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Beyond dominant resource fairness: extensions, limitations, and indivisibilities
Proceedings of the 13th ACM Conference on Electronic Commerce
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Incentive compatible two player cake cutting
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Positive results for mechanism design without money
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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We revisit the classic problem of fair division from a mechanism design perspective and provide an elegant truthful mechanism that yields surprisingly good approximation guarantees for the widely used solution of Proportional Fairness. This solution, which is closely related to Nash bargaining and the competitive equilibrium, is known to be not implementable in a truthful fashion, which has been its main drawback. To alleviate this issue, we propose a new mechanism, which we call the Partial Allocation mechanism, that discards a carefully chosen fraction of the allocated resources in order to incentivize the agents to be truthful in reporting their valuations. This mechanism introduces a way to implement interesting truthful outcomes in settings where monetary payments are not an option. For a multi-dimensional domain with an arbitrary number of agents and items, and for the very large class of homogeneous valuation functions, we prove that our mechanism provides every agent with at least a 1/e ≈ 0.368 fraction of her Proportionally Fair valuation. To the best of our knowledge, this is the first result that gives a constant factor approximation to every agent for the Proportionally Fair solution. To complement this result, we show that no truthful mechanism can guarantee more than 0.5 approximation, even for the restricted class of additive linear valuations. In addition to this, we uncover a connection between the Partial Allocation mechanism and VCG-based mechanism design. We also ask whether better approximation ratios are possible in more restricted settings. In particular, motivated by the massive privatization auction in the Czech republic in the early 90s we provide another mechanism for additive linear valuations that works really well when all the items are highly demanded.