Signaling-based Robust Incentive Designs with Randomized Monitoring

Incentive design problems entail hierarchical decision-making where a leader crafts a strategy to induce a desired response from a follower. Such dynamic games with decentralized information structures have been well-studied under three assumptions-the leader must have access to the follower's observations, actions, and the objective function. Lack of knowledge on any of these can potentially lead to performance loss for the leader. In this paper, we first study a setup where the leader observes the follower's action through a random monitoring channel and learns about the follower's observation through a follower-designed signal. In this setup, we establish the existence of a signaling-based incentive equilibrium strategy for the leader that induces honest reporting and desired control response from the follower. Then, we study a setting, where the follower's costs are parametric, but the parameters are not known to the leader. We construct an incentive strategy that reduces the sensitivity of the leader's performance to uncertainty in the parameter, close to an initial estimate. More generally, for the case when the leader's knowledge about the follower's cost and distributions of cost-relevant random variables is inaccurate, we establish the existence of a robust incentive equilibrium strategy that bounds the performance loss from the inaccuracy in the model.