Algorithmic Game Theory
Approximate mechanism design without money
Proceedings of the 10th ACM conference on Electronic commerce
Tighter Bounds for Facility Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Asymptotically optimal strategy-proof mechanisms for two-facility games
Proceedings of the 11th ACM conference on Electronic commerce
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Strategy-proof mechanisms for facility location games with many facilities
ADT'11 Proceedings of the Second international conference on Algorithmic decision theory
Approximately optimal mechanism design via differential privacy
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Mechanism design on discrete lines and cycles
Proceedings of the 13th ACM Conference on Electronic Commerce
Winner-imposing strategyproof mechanisms for multiple Facility Location games
Theoretical Computer Science
Strategyproof facility location and the least squares objective
Proceedings of the fourteenth ACM conference on Electronic commerce
On the power of deterministic mechanisms for facility location games
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We consider k-Facility Location games, where n strategic agents report their locations on the real line, and a mechanism maps them to k facilities. Each agent seeks to minimize his connection cost, given by a nonnegative increasing function of his distance to the nearest facility. Departing from previous work, that mostly considers the identity cost function, we are interested in mechanisms without payments that are (group) strategyproof for any given cost function, and achieve a good approximation ratio for the social cost and/or the maximum cost of the agents. We present a randomized mechanism, called Equal Cost, which is group strategyproof and achieves a bounded approximation ratio for all k and n, for any given concave cost function. The approximation ratio is at most 2 for Max Cost and at most n for Social Cost. To the best of our knowledge, this is the first mechanism with a bounded approximation ratio for instances with k ≥ 3 facilities and any number of agents. Our result implies an interesting separation between deterministic mechanisms, whose approximation ratio for Max Cost jumps from 2 to unbounded when $k$ increases from 2 to 3, and randomized mechanisms, whose approximation ratio remains at most 2 for all k. On the negative side, we exclude the possibility of a mechanism with the properties of Equal Cost for strictly convex cost functions. We also present a randomized mechanism, called Pick the Loser, which applies to instances with k facilities and only n = k+1 agents. For any given concave cost function, Pick the Loser is strongly group strategy proof and achieves an approximation ratio of 2 for Social Cost.