The distortion of threshold approval matching
Mohamad Latifian1, Alexandros A Voudouris2
1School of Informatics, University of Edinburgh, Scotland, UK.
Autonomous Agents and Multi-Agent Systems
|October 20, 2025
Summary
This study analyzes matching algorithms for resource allocation, focusing on maximizing social welfare with limited agent utility information. It establishes distortion bounds for deterministic and randomized approaches in one-sided matching scenarios.
Area of Science:
- Computer Science
- Algorithmic Game Theory
- Discrete Mathematics
Background:
- Agents possess private utilities for items.
- Agents report item partitions into utility thresholds.
- The objective is to maximize social welfare under cardinality constraints.
Purpose of the Study:
- To analyze matching algorithms in settings with private agent utilities.
- To compute item assignments that approximate maximum social welfare.
- To establish distortion bounds for deterministic and randomized algorithms.
Main Methods:
- Investigated one-sided matching with one item per agent.
- Analyzed algorithms with 't' threshold utility levels.
- Extended analysis to settings with multiple item copies and agent capacities.
Main Results:
- Determined distortion bounds for deterministic matching algorithms: [Formula: see text].
- Determined distortion bounds for randomized matching algorithms: [Formula: see text].
- Demonstrated that distortion bounds generalize to more complex matching scenarios.
Conclusions:
- The study provides theoretical bounds on the efficiency of matching algorithms.
- Limited utility information necessitates approximation algorithms.
- The findings are applicable to various resource allocation problems.
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