Matching Outcomes in TTC vs. The Crawler

This paper compares the matching outcomes and mechanism characteristics of two algorithms: TTC (Gale's Top Trading Cycles) and the Crawler, under single-peaked preferences. The TTC algorithm matches through a cycle-pointing process, which theoretically guarantees efficiency and strategy-proofness, but in practice, it is more complex, particularly when implementing obviously dominant strategies. In contrast, the Crawler algorithm provides a more intuitive and easier-to-understand matching process by screening agents in order of house sizes, making it particularly suitable for environments with single-peaked preferences. This paper analyzes the strengths and weaknesses of both algorithms and explores their applicability and differences in matching outcomes across various scenarios. The conclusion drawn is that in the domain of single-peaked preferences, the Crawler algorithm offers significant advantages in terms of comprehension and implementation, while TTC, despite its broader applicability, poses higher operational complexity under specific preference structures.