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This lecture covers the concepts of incentive compatibility and individual rationality in agency theory, emphasizing the importance of aligning the interests of principals and agents through optimal contracts. It discusses the optimization problems faced by both parties, the need for incentives to induce desired actions, and the calculation of utility and optimal actions. The lecture explores how optimal contracts are designed to maximize the principal's payoff while ensuring the agent's rational behavior. It also delves into benchmark scenarios, first-best outcomes, and the agency cost incurred due to the principal-agent relationship.