A Survey on Approximation Mechanism Design without Money for Facility Games

In a facility game one or more facilities are placed in a metric space to serve a set of selfish agents whose addresses are their private information. In a classical facility game, each agent wants to be as close to a facility as possible, and the cost of an agent can be defined as the distance between her location and the closest facility. In an obnoxious facility game, each agent wants to be far away from all facilities, and her utility is the distance from her location to the facility set. The objective of each agent is to minimize her cost or maximize her utility. An agent may lie if, by doing so, more benefit can be obtained. We are interested in social choice mechanisms that do not utilize payments. The game designer aims at a mechanism that is strategy-proof, in the sense that any agent cannot benefit by misreporting her address, or, even better, group strategy-proof, in the sense that any coalition of agents cannot all benefit by lying. Meanwhile, it is desirable to have the mechanism to be approximately optimal with respect to a chosen objective function. Several models for such approximation mechanism design without money for facility games have been proposed. In this paper we briefly review these models and related results for both deterministic and randomized mechanisms, and meanwhile we present a general framework for approximation mechanism design without money for facility games

Heterogeneous Facility Location with Limited Resources

We initiate the study of the heterogeneous facility location problem with limited resources. We mainly focus on the fundamental case where a set of agents are positioned in the line segment [0,1] and have approval preferences over two available facilities. A mechanism takes as input the positions and the preferences of the agents, and chooses to locate a single facility based on this information. We study mechanisms that aim to maximize the social welfare (the total utility the agents derive from facilities they approve), under the constraint of incentivizing the agents to truthfully report their positions and preferences. We consider three different settings depending on the level of agent-related information that is public or private. For each setting, we design deterministic and randomized strategyproof mechanisms that achieve a good approximation of the optimal social welfare, and complement these with nearly-tight impossibility results