# Mechanism Design for Maximum Vectors

## TL;DR

This paper studies the strategic version of the Maximum Vectors problem, analyzing how to design mechanisms that incentivize truthful reporting by selfish agents in multiobjective optimization contexts.

## Contribution

It introduces the first mechanism design framework for the Maximum Vectors problem, providing both impossibility and positive results under different assumptions.

## Key findings

- Impossibility results for truthful mechanisms in certain settings.
- Conditions under which truthful reporting can be incentivized.
- Connections to Pareto curve computation in multiobjective optimization.

## Abstract

We consider the Maximum Vectors problem in a strategic setting. In the classical setting this problem consists, given a set of $k$-dimensional vectors, in computing the set of all nondominated vectors. Recall that a vector $v=(v^1, v^2, \ldots, v^k)$ is said to be nondominated if there does not exist another vector $v_*=(v_*^1, v_*^2, \ldots, v_*^k)$ such that $v^l \leq v_*^{l}$ for $1\leq l\leq k$, with at least one strict inequality among the $k$ inequalities. This problem is strongly related to other known problems such as the Pareto curve computation in multiobjective optimization. In a strategic setting each vector is owned by a selfish agent which can misreport her values in order to become nondominated by other vectors. Our work explores under which conditions it is possible to incentivize agents to report their true values using the algorithmic mechanism design framework. We provide both impossibility results along with positive ones, according to various assumptions.