Efficient Facility Assignment with Fair Cost Sharing: Equilibrium Computation and Strategyproof Mechanism Design

Core Concepts

The authors study the one-dimensional Facility Assignment Game with Fair Cost Sharing (FAG-FCS) from a game-theoretical perspective, exploring equilibrium computation and strategyproof mechanism design.

Abstract

The paper investigates the one-dimensional FAG-FCS from two game-theoretical settings:

Equilibrium Computation:

In this setting, agents can directly select any facility, and the authors focus on computing a pure Nash equilibrium (PNE).
They devise a dynamic programming algorithm that computes a PNE in polynomial time, and show that the PNE attained approximates the optimal social cost within a factor of ln n.

Strategyproof Mechanism Design:

In this setting, agents report their positions to a mechanism, which then assigns them to facilities.
The authors provide a complete characterization of strategyproof and anonymous mechanisms for the case of m = n = 2, and establish a strong lower bound: no such mechanism can guarantee a bounded approximation ratio.
Inspired by the characterization, the authors design a class of non-trivial strategyproof, unanimous, and anonymous mechanisms for any n and m.

The authors demonstrate that in the one-dimensional FAG-FCS, the computation of exact PNEs is possible in polynomial time, in contrast to the general metric case. However, they also reveal a fundamental tension between strategyproofness and social cost optimization, even in the simplest congestion games.

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Key Insights Distilled From

Facility Assignment with Fair Cost Sharing: Equilibrium and Mechanism Design

by Mengfan Ma,M... at arxiv.org 04-16-2024

https://arxiv.org/pdf/2404.08963.pdf

Deeper Inquiries

What are the potential applications of the one-dimensional FAG-FCS model beyond the examples provided in the paper

The one-dimensional Facility Assignment Game with Fair Cost Sharing (FAG-FCS) model has potential applications beyond the scenarios mentioned in the paper. One possible application could be in the allocation of resources in a shared workspace or co-working environment. In this setting, multiple individuals or companies share common facilities like meeting rooms, printers, or common areas. By using the FAG-FCS model, a fair and efficient allocation of these resources can be achieved, ensuring that the costs are shared equitably among the users based on their utilization.
Another application could be in the context of ride-sharing or transportation services. In a one-dimensional space representing a route or road, multiple passengers or vehicles need to be assigned to different pick-up or drop-off points. The FAG-FCS model can help optimize the assignment of passengers to vehicles or the allocation of vehicles to different locations, considering both the building costs (vehicle maintenance, fuel, etc.) and the connection costs (distance traveled, time taken) for each assignment.
Furthermore, the model could be applied in the design of supply chain networks, where multiple entities need to be assigned to distribution centers or warehouses along a linear network. By using the FAG-FCS framework, companies can determine the most cost-effective and fair assignment of entities to facilities, taking into account both the shared building costs and individual connection costs.

How can the insights from the characterization of strategyproof and anonymous mechanisms be extended to more general facility assignment problems with different cost structures

The insights gained from the characterization of strategyproof and anonymous mechanisms in the one-dimensional FAG-FCS model can be extended to more general facility assignment problems with different cost structures by adapting the principles of strategyproofness and anonymity to suit the specific requirements of the problem.
For facility assignment problems with varying cost structures, such as different types of building costs or connection costs, the concept of strategyproofness can be applied to ensure that no agent has an incentive to misreport their information to manipulate the assignment process. By designing mechanisms that are strategyproof and anonymous, the fairness and efficiency of the assignment can be maintained, regardless of the specific cost structures involved.
Additionally, the characterization of mechanisms for the one-dimensional FAG-FCS model can serve as a foundation for developing similar strategies for more complex facility assignment problems. By analyzing the trade-offs between different cost structures and the impact on the assignment process, researchers can tailor the mechanisms to suit the specific constraints and objectives of the problem at hand.

Are there alternative game-theoretical solution concepts, beyond PNE and strategyproofness, that could be explored to better understand the trade-offs in the one-dimensional FAG-FCS

In addition to Pure Nash Equilibrium (PNE) and strategyproofness, alternative game-theoretical solution concepts can be explored to better understand the trade-offs in the one-dimensional FAG-FCS model. One such concept is the concept of Core Stability, which focuses on ensuring that no group of agents can benefit by deviating from the assigned facilities collectively.
By analyzing the Core Stability of the assignment, researchers can evaluate the robustness of the assignment against coalitions of agents trying to improve their outcomes. This concept can provide insights into the stability and fairness of the assignment, considering the interactions between different groups of agents and their strategic behaviors.
Furthermore, concepts like Sequential Equilibrium or Evolutionarily Stable Strategies can be explored to study the dynamics of facility assignment over time. These concepts can help in understanding how the assignment process evolves as agents adapt their strategies based on the outcomes and interactions with other agents, providing a more comprehensive view of the equilibrium concepts in the FAG-FCS model.