Before revision:  Several examples are presented to show how this multidimensional approach is applied to a class of agent-based model and to the problem of risk allocation .
After revision:  Similarly to the one dimensional case, a sufficient condition for a multidimensional dynamic risk measure to be a g-expectation is also explored. As to applications, we show how this multidimensional approach is applied to a class of agent-based model and to the problem of risk allocation .