  This paper concerns the design of a multidimensional Chebyshev interpolation
based method for a differential game theory problem. In continuous game theory
problems, it might be difficult to find analytical solutions, so numerical
methods have to be applied. As the number of players grows, this may increase
computational costs due to the curse of dimensionality. To handle this, several
techniques may be applied and paralellization can be employed to reduce the
computational time cost. Chebyshev multidimensional interpolation allows
efficient multiple evaluations simultaneously along several dimensions, so this
can be employed to design a tensorial method which performs many computations
at the same time. This method can also be adapted to handle parallel
computation and, the combination of these techniques, greatly reduces the total
computational time cost. We show how this technique can be applied in a
pollution differential game. Numerical results, including error behaviour and
computational time cost, comparing this technique with a spline-parallelized
method are also included.
