Common learning

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case

Time-to-birth prediction models and the influence of expert opinions

Preterm birth is the leading cause of death among children under five years old. The pathophysiology and etiology of preterm labor are not yet fully understood. This causes a large number of unnecessary hospitalizations due to high--sensitivity clinical policies, which has a significant psychological and economic impact. In this study, we present a predictive model, based on a new dataset containing information of 1,243 admissions, that predicts whether a patient will give birth within a given time after admission. Such a model could provide support in the clinical decision-making process. Predictions for birth within 48 h or 7 days after admission yield an Area Under the Curve of the Receiver Operating Characteristic (AUC) of 0.72 for both tasks. Furthermore, we show that by incorporating predictions made by experts at admission, which introduces a potential bias, the prediction effectiveness increases to an AUC score of 0.83 and 0.81 for these respective tasks

Sequential two-player games with ambiguity

Author's pre-printIf players' beliefs are strictly nonadditive, the Dempster–Shafer updating rule can be used to define beliefs off the equilibrium path. We define an equilibrium concept in sequential two-person games where players update their beliefs with the Dempster–Shafer updating rule. We show that in the limit as uncertainty tends to zero, our equilibrium approximates Bayesian Nash equilibrium. We argue that our equilibrium can be used to define a refinement of Bayesian Nash equilibrium by imposing context-dependent constraints on beliefs under uncertainty.ESRC senior research fellowship scheme, H5242750259

To share or not to share: the optimal advertising effort with asymmetric advertising effectiveness

In this paper, we study a two-stage model in which a manufacturer expands to a new market through a local retailer and has private information on the advertising effectiveness. The manufacturer chooses the information sharing format with the retailer, either no information sharing or mandatory information sharing. Under no information sharing format, the manufacturer and the retailer play a signaling game. We derive both separating and pooling equilibria and conduct equilibrium refinements for the signaling game. Under mandatory information sharing format, the manufacturer simply informs the retailer the advertising effectiveness. We also establish the stylized model and derive the optimal advertising effort. By comparing the manufacturer’s ex ante profit under the two information sharing formats, we find that the manufacturer always prefers mandatory information sharing, under which both the advertising effort and profit can be higher. We also observe that unlike the common case that the channel members may have different preference over the information sharing formats, the manufacturer and the retailer can actually achieve alignment. While some previous studies suggest that the manufacturer and the retailer may have different preference over the information sharing formats, we find that they can actually achieve alignment with asymmetric information on advertising effectiveness