Free-riding and free-labor in combinatorial agency

This paper studies a setting where a principal needs to motivate teams of agents whose efforts lead to an outcome that stochastically depends on the combination of agents' actions, which are not directly observable by the principal. In [1] we suggest and study a basic "combinatorial agency" model for this setting. In this paper we expose a somewhat surprising phenomenon found in this setting: cases where the principal can gain by asking agents to reduce their effort level, even when this increased effort comes for free. This phenomenon cannot occur in a setting where the principal can observe the agents' actions, but we show that it can occur in the hidden-actions setting. We prove that for the family of technologies that exhibit "increasing returns to scale" this phenomenon cannot happen, and that in some sense this is a maximal family of technologies for which the phenomenon cannot occur. Finally, we relate our results to a basic question in production design in firms.