Three Essays on Optimal Decisions under Uncertainties or in the Presence of Strategic Customers
Subscription Pricing , Optimal Control , Presence Monitoring , Endangered Species Monitoring , Strategic Customers , Discrete Choice Theory , Decision Analysis , POMDP
Three essays on decision-making form this thesis under uncertainties or in the presence of strategic customers. In the first essay, we studied subscription pricing. Subscriptions are agreements between customers and a company that commits to deliver a product or provide a service. We present a continuous-time dynamic pricing model for a monopolist offering a fixed-term subscription contract, without per-use charges and access limits, to strategic customers whose utility is affected by the number of subscribers. We formulate the monopolist’s problem in terms of optimal control, derive its optimality conditions, and study the structure of the stationary optimal solution. We study the transient and steady states of the problem and show that the firm can capitalize on the strategic behavior of customers. We also observe that the firm is better off not offering subscriptions for myopic customers or customers with a low evaluation of the service. Finally, we demonstrate the robustness of the optimal pricing results in a setting in which we relax significant assumptions. The second essay considers the joint monitoring and learning of a partially observable dynamic system in which all parameters are unknown. This problem is motivated by the monitoring of cryptic threatened species. The objective is to detect a change in the hidden state while simultaneously learning about the system dynamics and observability. We formulate the problem in the framework of Bayes-adaptive partially observable Markov decision processes (Bayes-adaptive POMDP). A distinguishing feature is that decisions are made under the coupling of state uncertainty, parameter uncertainty, and state dynamics. We identify a low-dimensional sufficient statistic and reformulate the dynamic program in three dimensions. We fully characterize the optimal policy structure. The advantages of the monitoring-while-learning strategy are demonstrated with a case study on the Sumatran tiger conservation in Indonesia. The third essay investigates a dynamic pricing problem in a stochastic setting and proves that the scaled version of the problem has a fluid limit. The deterministic problem has continuous variables and equations. The optimal control tool is a perfect method to analyze similar continuous-time problems, and it delivers results that are not available in a stochastic setting efficiently.