Mixed Strategies in Combinatorial Agency

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 show that the principal may possibly gain from inducing a mixed equilibrium, but this gain can be bounded for various families of technologies (in particular if a technology has symmetric combinatorial structure). In addition, we present a sufficient condition under which mixed strategies yield no gain to the principal.