  In many multiagent domains a set of agents exert effort towards a joint
outcome, yet the individual effort levels cannot be easily observed. A typical
example for such a scenario is routing in communication networks, where the
sender can only observe whether the packet reached its destination, but often
has no information about the actions of the intermediate routers, which
influences the final outcome. We study a setting where a principal needs to
motivate a team of agents whose combination of hidden efforts stochastically
determines an outcome. In a companion paper we devise and study a basic
combinatorial agency model for this setting, where the principal is restricted
to inducing a pure Nash equilibrium. Here we study various implications of this
restriction. First, we show that, in contrast to the case of observable
efforts, inducing a mixed-strategies equilibrium may be beneficial for the
principal. Second, we present a sufficient condition for technologies for which
no gain can be generated. Third, we bound the principals gain for various
families of technologies. Finally, we study the robustness of mixed equilibria
to coalitional deviations and the computational hardness of the optimal mixed
equilibria.
