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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.
We study variants of the stable marriage and college admissions models in which the agents are allowed to express weak preferences over the set of agents on the other side of the market and the option of remaining unmatched. For the problems that we
We consider a new setting of facility location games with ordinal preferences. In such a setting, we have a set of agents and a set of facilities. Each agent is located on a line and has an ordinal preference over the facilities. Our goal is to desig
Recommendation systems are extremely popular tools for matching users and contents. However, when content providers are strategic, the basic principle of matching users to the closest content, where both users and contents are modeled as points in so
The study of approximate mechanism design for facility location problems has been in the center of research at the intersection of artificial intelligence and economics for the last decades, largely due to its practical importance in various domains,
We consider a facility location game in which $n$ agents reside at known locations on a path, and $k$ heterogeneous facilities are to be constructed on the path. Each agent is adversely affected by some subset of the facilities, and is unaffected by