Asymptotically optimal strategy-proof mechanisms for two-facility games

ABSTRACT We consider the problem of locating facilities in a metric space to serve a set of selfish agents. The cost of an agent is the distance between her own location and the nearest facility. The social cost is the total cost of the agents. We are interested in designing strategy-proof mechanisms without payment that have a small approximation ratio for social cost. A mechanism is a (possibly randomized) algorithm which maps the locations reported by the agents to the locations of the facilities. A mechanism is strategy-proof if no agent can benefit from misreporting her location in any configuration. This setting was first studied by Procaccia and Tennenholtz We first prove an Ω(n) lower bound of the social cost approximation ratio for deterministic strategy-proof mechanisms. Our lower bound even holds for the line metric space. This significantly improves the previous constant lower bound

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

Asymptotically Truthful Equilibrium Selection in Large Congestion Games

Studying games in the complete information model makes them analytically tractable. However, large $n$ player interactions are more realistically modeled as games of incomplete information, where players may know little to nothing about the types of other players. Unfortunately, games in incomplete information settings lose many of the nice properties of complete information games: the quality of equilibria can become worse, the equilibria lose their ex-post properties, and coordinating on an equilibrium becomes even more difficult. Because of these problems, we would like to study games of incomplete information, but still implement equilibria of the complete information game induced by the (unknown) realized player types. This problem was recently studied by Kearns et al. and solved in large games by means of introducing a weak mediator: their mediator took as input reported types of players, and output suggested actions which formed a correlated equilibrium of the underlying game. Players had the option to play independently of the mediator, or ignore its suggestions, but crucially, if they decided to opt-in to the mediator, they did not have the power to lie about their type. In this paper, we rectify this deficiency in the setting of large congestion games. We give, in a sense, the weakest possible mediator: it cannot enforce participation, verify types, or enforce its suggestions. Moreover, our mediator implements a Nash equilibrium of the complete information game. We show that it is an (asymptotic) ex-post equilibrium of the incomplete information game for all players to use the mediator honestly, and that when they do so, they end up playing an approximate Nash equilibrium of the induced complete information game. In particular, truthful use of the mediator is a Bayes-Nash equilibrium in any Bayesian game for any prior.Comment: The conference version of this paper appeared in EC 2014. This manuscript has been merged and subsumed by the preprint "Robust Mediators in Large Games": http://arxiv.org/abs/1512.0269