Balancing Suspense and Surprise: Timely Decision Making with Endogenous Information Acquisition

We develop a Bayesian model for decision-making under time p ressure with endogenous information acquisition. In our model, the decisi on-maker decides when to observe (costly) information by sampling an underlying c ontinuous-time stochastic process (time series) that conveys informa tion about the potential occurrence/non-occurrence of an adverse event which will t erminate the decision-making process. In her attempt to predict the occurrence of t he adverse event, the decision-maker follows a policy that determines when to acquire information from the time series (continuation), and when to stop acquiring information and make a final prediction (stopping). We show that the optimal polic y has a " rendezvous" structure, i.e. a structure in which whenever a new informat ion sample is gathered from the time series, the optimal "date" for acquiring the ne xt sample becomes computable. The optimal interval between two information s amples balances a trade-off between the decision maker's "surprise", i.e. th e drift in her posterior belief after observing new information, and "suspense", i. e. the probability that the adverse event occurs in the time interval between two inf ormation samples. Moreover, we characterize the continuation and stopping re gions in the decision-maker's state-space, and show that they depend not only on th e decision-maker's beliefs, but also on the "context", i.e. the current realiza tion of the time series.