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arXiv · 2610.08096

The lattice structure of the crawler

Hinata Kurashita
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Abstract

We study object reallocation problems with single-peaked preferences. On the unrestricted domain of strict preferences, top trading cycles (TTC) is the unique rule that satisfies efficiency, individual rationality, and strategy-proofness. On the single-peaked preference domain, the crawler introduced by Bade (2019) satisfies the same properties. We show that the Nash equilibrium allocations of the crawler's direct revelation game form a complete lattice under weak Pareto dominance. The truthful allocation is the greatest element of this lattice, while the initial endowment allocation is its least element.

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Hinata Kurashita. 2026-10-06. The lattice structure of the crawler. https://arxiv.org/abs/2610.08096

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