Facility Location Games Beyond Single-Peakedness: the Entrance Fee Model

TL;DR

This paper introduces a facility location game model with entrance fees, exploring strategyproof mechanisms and approximation bounds beyond the classical single-peaked preferences, addressing new complexities in mechanism design.

Contribution

It proposes a novel entrance fee model in facility location games, analyzing strategyproof mechanisms and establishing approximation bounds with tight impossibility results.

Findings

Developed strategyproof mechanisms with good approximation ratios.

Provided upper and lower bounds for one- and two-facility games.

Established nearly-tight impossibility results for various objectives.

Abstract

The facility location game has been studied extensively in mechanism design. In the classical model, each agent's cost is solely determined by her distance to the nearest facility. In this paper, we introduce a novel model where each facility charges an entrance fee. Thus, the cost of each agent is determined by both the distance to the facility and the entrance fee of the facility. In our model, the entrance fee function is allowed to be an arbitrary function, causing agents' preferences may no longer be single-peaked anymore: This departure from the classical model introduces additional challenges. We systematically delve into the intricacies of the model, designing strategyproof mechanisms with favorable approximation ratios. Additionally, we complement these ratios with nearly-tight impossibility results. Specifically, for one-facility and two-facility games, we provide upper and lower bounds for the approximation ratios given by deterministic and randomized mechanisms with respect to utilitarian and egalitarian objectives.