Essays on contracting for experimentation
This thesis is composed of four chapters and addresses the contracting issue under strategic experimentation. The first chapter presents an overview of the thesis and introduces the strategic bandit model, which is commonly adopted in the other three chapters. The chapter also previews the main results and implications of the thesis. The second chapter discusses the contracting issue between a principal and a team of agents where the actions of agents are unobservable to the principal. The main contribution of this chapter is to fill the gap of strategic experimentation literature by introducing the free-rider problem in teamwork. The chapter first deals with the optimal hiring choice of the principal under perfect information. Since the belief of the state being good decreases if no one succeeds over time, the paper shows that the principal tends to hire fewer agents in response to the downward-adjusted posterior belief. When the principal can neither monitor the agents' actions nor distinguish the agents who succeed, this chapter shows the optimal incentivising contract consists of an upfront payment from the agents to the principal, a bonus to every agent conditioning on success and a stopping time. Under this contract, the principal can implement first-best experimentation and incentivise all agents to work until the optimal stopping time. The third and fourth chapters discuss the financial contracting issue in innovation where an innovator requires external funding from an investor. The third chapter adopts a \bad news" exponential bandit to study the financial contracting under adverse selection between the innovator and the investor. The innovator, owns the innovation project, is privately informed of either a high or low prior belief of the good state but seeks a large amount of external investment from the less-informed investor. Experimentation is conducted by the innovator using internal funding before the external investment. The posterior belief about the good state increases in the amount of internal funding if no bad news arrives during experimentation, but the project will be abandoned as long as bad news arrives. The chapter shows that the amount of internal funding can be used by the investor to separate the agents with different priors. Under the unique least-costly separating equilibrium, the high-prior innovator spends even more than the low-prior first-best internal funding in order to deter the low-prior one from mimicking, and the low-prior one remains at his first-best. This chapter enriches the financial experimentation literature by proposing internal funding as a novel signalling tool and establishing a Pareto dominating separating equilibrium. The fourth chapter studies a multi-stage innovation financing problem between an agent and an investor with asymmetric information on the progress of the project. The innovation is comprised of two stages where the agent needs to complete the first development stage in order to proceed to the second experiment stage. The model assumes that the completion of the first stage can be early or late following a binary distribution, and the arrival of success in the experimentation stage follows a "good news" exponential bandit. Each period, a fixed amount of investment is needed from the investor. However, the investor can not observe nor verify the project progress. The chapter shows that the optimal incentive-compatible contract consists of differential maximum funding periods in the event of early and late completion of the first stage respectively and subsequent bonuses to the investor conditioning on a success in the second stage. We prove that the first-best experimentation time is attainable as long as the bonus of the late completion exceeds that of the early completion, and the difference between the two bonuses should be confined within a certain range. In the extension, we consider the case when the first stage completion time is informative such that an early completion indicates a higher prior in the good state than the late completion. Under imperfect information, the agent has a stronger incentive to mimic the early completion if the first stage is completed late as a longer experimentation time will be granted according the first-best contract. The chapter proves that the first-best is still achievable under a similar bonus contract but the difference between the two bonuses becomes smaller. This chapter contributes to the experimentation financing literature including the information imperfectness on project progress and multi-stage spillover effects.