# Truthful Mechanisms for Delivery with Mobile Agents

## TL;DR

This paper introduces truthful mechanisms for selecting and routing mobile agents to deliver multiple items efficiently, ensuring agents reveal private energy costs and achieve near-optimal total energy consumption.

## Contribution

It presents three novel truthful mechanisms that guarantee voluntary participation and approximate the optimal energy use in delivery tasks with private agent costs.

## Key findings

- Mechanisms are truthful and ensure voluntary participation.
- Approximate the optimal energy consumption within a constant factor.
- Payments can be bounded in terms of the optimum for certain single-package cases.

## Abstract

We study the game-theoretic task of selecting mobile agents to deliver multiple items on a network. An instance is given by $m$ messages (physical objects) which have to be transported between specified source-target pairs in a weighted undirected graph, and $k$ mobile heterogeneous agents, each being able to transport one message at a time. Following a recent model by [B\"artschi et al. 2016], each agent $i$ consumes energy proportional to the distance it travels in the graph, where the different rates of energy consumption are given by weight factors $w_i$. We are interested in optimizing or approximating the total energy consumption over all selected agents. Unlike previous research, we assume the weights to be private values known only to the respective agents. We present three different mechanisms which select, route and pay the agents in a truthful way that guarantees voluntary participation of the agents, while approximating the optimum energy consumption by a constant factor. To this end we analyze a previous structural result and an approximation algorithm given by [B\"artschi et al. 2017]. Finally, we show that for some instances in the case of a single package, the sum of the payments can be bounded in terms of the optimum.