  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.
