Mixed strategies in combinatorial agency

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 principal's 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.