We consider a variant of the graph searching games that is closely related to the routing reconfiguration problem in WDM networks. In the digraph processing game, a team of agents is aiming at clearing, or processing, the vertices of a digraph D. In this game, two important measures arise: 1) the total number of agents used, and 2) the total number of vertices occupied by an agent during the processing of D. Previous works have studied the problem of minimizing each of these parameters independently. In particular, both of these optimization problems are not in APX. In this paper, we study the tradeoff between both these conflicting objectives. More precisely, we prove that there exist some instances for which minimizing one of these objectives arbitrarily impairs the quality of the solution for the other one. We show that such bad tradeoffs may happen even in the case of basic network topologies. On the other hand, we exhibit classes of instances where good tradeoffs can be achieved. We also show that minimizing one of these parameters while the other is constrained is not in APX.