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Strategyproof facility location mechanisms on discrete trees

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Abstract

We address the problem of strategyproof (SP) facility location mechanisms on discrete trees. Our main result is a full characterization of onto and SP mechanisms. In particular, we prove that when a single agent significantly affects the outcome, the trajectory of the facility is almost contained in the trajectory of the agent, and both move in the same direction along the common edges. We show tight relations of our characterization to previous results on discrete lines and on continuous trees. We then derive further implications of the main result for infinite discrete lines.

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Notes

  1. Intuitively, consistency means that projecting on different pairs of vertices should not yield contradicting outcomes. We omit the exact definition since it is not relevant for our purpose.

  2. This is different from the tree monotonicity property in [29].

  3. This property is sometimes called “tops-only" or “peaks-only”.

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Acknowledgement

This research was supported by the Israel Science Foundation (ISF; Grant No. 2539/20).

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  1. Technion - Israel Institute of Technology, Haifa, Israel

    Alina Filimonov & Reshef Meir

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  1. Alina Filimonov
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  2. Reshef Meir
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Correspondence to Alina Filimonov.

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Filimonov, A., Meir, R. Strategyproof facility location mechanisms on discrete trees. Auton Agent Multi-Agent Syst 37, 10 (2023). https://doi.org/10.1007/s10458-022-09592-4

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