Essays in Experimentation and Learning

Durandard, Théo

doi:https://doi.org/10.21985/n2-jdzq-dp98

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Essays in Experimentation and Learning

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This dissertation comprises three essays in distinct areas of economic theory, yet all are related to experimentation and learning. In the first chapter, I study how organizations assign tasks to identify the best candidate to promote among a pool of workers. Task allocation and workers’ motivation interact through the organization’s promotion decisions. The organization designs the workers’ careers to both screen and develop talent. When only non-routine tasks are informative about a worker’s type and non-routine tasks are scarce, the organization’s preferred promotion system is an index contest. Each worker is assigned a number that depends only on his own type. The principal delegates the non-routine task to the worker whose current index is the highest and promotes the first worker whose type exceeds a threshold. Each worker’s threshold is independent of the other workers’ types. Competition is mediated by the allocation of tasks: who gets the opportunity to prove themselves is a determinant factor in promotions. Finally, features of the optimal promotion contest rationalize the prevalence of fast-track promotion, the role of seniority, or when a group of workers is systemically advantaged. The second chapter is co-authored with Matteo Camboni. We formulate a general optimal stopping problem that can accommodate various non-stationary environments, such as situations where the decision maker’s patience, time pressure, and learning speed can change gradually and abruptly over time. We show that, under mild regularity conditions, this problem has a well-defined solution. Furthermore, we characterize the shape of the stopping region in a large class of monotone environments and obtain comparative statics on the timing and quality of decisions for many sequential sampling problems à la Wald. For example, we show that accuracy increases (decreases) over time when, over time, (i) the learning speed increases (decreases), or (ii) the discount rate decreases (increases) (i.e., the decision maker values the future more (less) over time), or (iii) the time pressure decreases (increases). Since our main comparative static results hold locally, we can also capture non-monotone relations between time and accuracy that consistently arise in perceptual and cognitive testing. The final chapter, co-authored with Udayan Vaidya and Boli Xu, concerns robustness in mechanism design, with a particular emphasis on dynamic problems of learning and experimentation. We develop a new approach to identify the class of mechanisms that contains a robust optimum. Notably, our approach avoids the issues associated with explicitly solving for the worst-case scenario, allowing us to consider new applications of robustness to dynamic problems. In particular, we use our tools to characterize the robustly optimal dynamic mechanism in a repeated seller-buyer model and the robustly optimal mechanism in a principal-agent model in which the agent can search à la Weitzman (1979). In the first case, the seller offers a sequence of statically optimal random posted prices, while in the second, a debt contract is optimal.

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