Contract Design Beyond Hidden-Actions

In the classical principal-agent hidden-action contract model, a principal delegates the execution of a costly task to an agent. In order to complete the task, the agent chooses an action from a set of actions, where each potential action is associated with a cost and a success probability to accomplish the task. To incentivize the agent to exert effort, the principal can commit to a contract, which is the amount of payment based on the task's success but not on the hidden-action chosen by the agent. In this work, we study the contract design framework under binary outcomes where we relax the hidden-action assumption. We introduce new models where the principal is allowed to inspect subsets of actions at some cost that depends on the inspected subset. If the principal discovers that the agent did not select the agreed-upon action through the inspection, the principal can withhold payment. This relaxation of the model introduces a broader strategy space for the principal, who now faces a tradeoff between positive incentives (increasing payment) and negative incentives (increasing inspection). We devise algorithms for finding the best deterministic and randomized incentive-compatible inspection schemes for various assumptions on the inspection cost function. In particular, we show the tractability of the case of submodular inspection cost functions. We complement our results by showing that it is impossible to efficiently find the optimal randomized inspection scheme for the more general case of XOS inspection cost functions, and that there is no PTAS for the case of subadditive inspection cost functions.