Αλγοριθμική Θεωρία Παιγνίων

ΠΕΡΙΛΗΨΗ: In this thesis, we study k-Facility Location games, where n strategic agents have different ideal locations on a metric space. A mechanism maps the locations reported by the agents to k facilities. Each agent seeks to minimize her cost, namely the distance between her location and the nearest facility, which may incentivize her to misreport her location. Our goal is to design strategyproof (i.e, no agent can benefit by misreporting her location) mechanisms with a bounded approximation ratio to the optimal social cost. To overcome the impossibility results for deterministic strategyproof mechanisms, we restrict our attention in perturbation stable instances. The notion of perturbation stability was first introduced for the Max-Cut Problem and later was adapted for the Clustering Problems. This captures the "real world" instances in which the optimal solution is well-defined and unaffected by small perturbation on the input. Since k-Facility Location games and k-Clustering are closely related problems, we are interested to see how perturbation stability can help us design strategyproof mechanisms with stronger guarantees. Given the recent results in k-Facility location in stable instances on the line, we are interested in extending those results in more general metric spaces.