Advances in Mechanism Design and Fair Division

The field of mechanism design and fair division is witnessing significant developments, with a focus on designing innovative solutions for complex problems. Researchers are exploring new approaches to achieve fairness, truthfulness, and efficiency in various settings, including graph-based models, geometric analyses, and multidimensional budget-feasible mechanisms. Notably, recent studies have made progress in resolving envy, allocating goods, and procuring items of maximum value. The introduction of new benchmarks and approximation guarantees has also enabled meaningful comparisons of mechanisms. Some noteworthy papers in this regard include: The paper On Approximate MMS Allocations on Restricted Graph Classes, which shows the existence of approximate allocations for several well-studied graph classes. The paper Multidimensional Budget-Feasible Mechanism Design, which obtains the first approximation guarantees for multidimensional budget feasible mechanism design.

Sources

On Approximate MMS Allocations on Restricted Graph Classes

A Geometric Analysis of Gains from Trade

Truthful Two-Obnoxious-Facility Location Games with Optional Preferences and Minimum Distance Constraint

Constrained Distributed Heterogeneous Two-Facility Location Problems with Max-Variant Cost

Short Proof: Exact Solution to the Finite Frobenius Coin Problem

How to Resolve Envy by Adding Goods

Multidimensional Budget-Feasible Mechanism Design

The Price of EF1 for Few Agents with Additive Ternary Valuations

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