The Capacity Constrained Facility Location problem

TL;DR

This paper studies the capacity constrained facility location problem from a mechanism design perspective, characterizing incentive-compatible mechanisms and analyzing their efficiency bounds.

Contribution

It provides a complete characterization of DIC mechanisms via GMMs and establishes tight bounds on their approximation ratios, revealing new insights into social choice mechanisms.

Findings

Median mechanism is optimal within DIC mechanisms for certain capacities.

Social welfare optimal mechanism is not DIC, highlighting trade-offs.

Introduces a new framework linking GMMs to capacity constrained facility location.

Abstract

We initiate the study of the capacity constrained facility location problem from a mechanism design perspective. The capacity constrained setting leads to a new strategic environment where a facility serves a subset of the population, which is endogenously determined by the ex-post Nash equilibrium of an induced subgame and is not directly controlled by the mechanism designer. Our focus is on mechanisms that are ex-post dominant-strategy incentive compatible (DIC) at the reporting stage. We provide a complete characterization of DIC mechanisms via the family of Generalized Median Mechanisms (GMMs). In general, the social welfare optimal mechanism is not DIC. Adopting the worst-case approximation measure, we attain tight lower bounds on the approximation ratio of any DIC mechanism. The well-known median mechanism is shown to be optimal among the family of DIC mechanisms for certain capacity ranges. Surprisingly, the framework we introduce provides a new characterization for the family of GMMs, and is responsive to gaps in the current social choice literature highlighted by Border and Jordan (1983) and Barbar{\`a}, Mass{\'o} and Serizawa (1998).