DeepAI AI Chat
Log In Sign Up

Strategy Proof Mechanisms for Facility Location in Euclidean and Manhattan Space

by   Toby Walsh, et al.

We study the impact on mechanisms for facility location of moving from one dimension to two (or more) dimensions and Euclidean or Manhattan distances. We consider three fundamental axiomatic properties: anonymity which is a basic fairness property, Pareto optimality which is one of the most important efficiency properties, and strategy proofness which ensures agents do not have an incentive to mis-report. We also consider how well such mechanisms can approximate the optimal welfare. Our results are somewhat negative. Moving from one dimension to two (or more) dimensions often makes these axiomatic properties more difficult to achieve. For example, with two facilities in Euclidean space or with just a single facility in Manhattan space, no mechanism is anonymous, Pareto optimal and strategy proof. By contrast, mechanisms on the line exist with all three properties.We also show that approximation ratios may increase when moving to two (or more) dimensions. All our impossibility results are minimal. If we drop one of the three axioms (anonymity, Pareto optimality or strategy proofness) multiple mechanisms satisfy the other two axioms.


page 1

page 2

page 3

page 4


Manipulation-resistant facility location mechanisms for ZV-line graphs

In many real-life scenarios, a group of agents needs to agree on a commo...

Fairness and Efficiency in Cake-Cutting with Single-Peaked Preferences

We study the cake-cutting problem when agents have single-peaked prefere...

Randomized Wagering Mechanisms

Wagering mechanisms are one-shot betting mechanisms that elicit agents' ...

Strategy Proof Mechanisms for Facility Location with Capacity Limits

An important feature of many real world facility location problems are c...

Selling Data to a Competitor

We study the costs and benefits of selling data to a competitor. Althoug...

Mechanism Design for Two-Opposite-Facility Location Games with Penalties on Distance

This paper is devoted to the two-opposite-facility location games with a...

Mechanism Learning for Trading Networks

We study the problem of designing mechanisms for trading networks that s...