Repeated Principal-Agent Games with Unobserved Agent Rewards and Perfect-Knowledge Agents

System designers frequently use the idea of providing incentives to stakeholders as a powerful means of steering the stakeholders for their own benefit. Operations management includes many such examples, such as offering performance-based bonuses to ride-hailing drivers, providing monetary incentives to patients for medical adherence, quality-contingent bonus payments for workers in crowdsourcing platforms, and vertical collaboration between shippers and carriers in transportation planning. In many real-world settings, the problem of designing efficient incentives can be posed as a repeated principal-agent problem where a principal (i.e., system designer) designs sequential incentive policies to motivate an agent (i.e., stakeholder) to convey certain behaviors that eventually serve the goal of maximizing the principal's cumulative net reward. Typically, there is an element of information asymmetry in these systems which arises between the principal and the agent in the form of either adverse selection (i.e., hidden information) or moral hazard (i.e., hidden actions) (Bolton and Dewatripont 2004). For instance, in the context of employment incentives designed by an employer, the hidden information in an adverse selection setting could be the level of productivity of an employee whereas a hidden action in the moral hazard setting could be the total effort level of the employee. More generally, the hidden information in the adverse selection setting can be seen as an unknown "type" or "preferences" of the agent that directly affects the action chosen by the agent, which in turn determines both the agent's utility and the principal's reward. These situations require specification of the agent's private information and the distributional-knowledge that the principal has concerning that information. Existing literature on repeated principal-agent models mostly studies the moral hazard setting, with a more recent focus on the problem of estimating agent's unknown model parameters under hidden actions (e.g., Ho et al. 2016, Kaynar and Siddiq 2022). On the other hand, the adverse selection setting is mostly studied either for single-period static games (Navabi and Nayyar 2018, Chade and Swinkels 2019, Gottlieb and Moreira 2022) or else for the repeated dynamic games where restrictive assumptions are made on, for example, dimension of the agent's action space, utility Dogan et.