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Scapegoats and Optimal Allocation of Responsibility

We consider a model of hierarchical organizations in which agents have the option of reducing the probability of failure by investing towards their decisions. A mechanism specifies a distribution of sanctions in case of failure across the levels of the hierarchy. It is said to be investment-inducing if it induces all agents to invest in equilibrium. It is said to be optimal if it does so at minimal total punishment. We characterize optimal investment-inducing mechanisms in several versions of our benchmark model. In particular we refer to the problem of allocating individuals with diverse qualifications to different levels of the hierarchy as well as allocating tasks of different importance across different hierarchy levels. We also address the issue of incentive-optimal hierarchy architectures.