Salesforce contract design, joint pricing and production planning with asymmetric overconfidence sales agent

We study a supply chain in which a rational manufacturer relies on an overconfident sales agent to sell the products. The actual sales outcome is determined by the sales agent's selling effort, the product price and a random market condition, and the sales agent is overconfident in their estimation of sales outcome. Apart from them, both of the sales agent's degree of overconfidence and selling effort are his private information. We consider the salesforce incentive to motivate the sales agent and screen his real degree of overconfidence using a principle-agent method under dual information asymmetry, then the manufacturer uses the information to realize her joint decision on pricing and production. Furthermore, we derive the optimal compensation contract as well as the optimal pricing and production, and compare it to the symmetric overconfidence scenario. Finally, some interesting insights are found: when the manufacturer is uncertain about the sales agent's the degree of overconfidence, her expected profit decreases while the sales agent with private information exerts less effort but obtains higher income, which implies the value of information; the manufacturer should hire a more overconfident sales agent, while a higher commission rate is not guaranteed. These results suggest that the manufacturer should not only focus on hiring the overconfident sales agent but also on disclosing the degree of overconfidence.