Optimal learning of transition probabilities in the two-agent newsvendor problem

We examine a newsvendor problem with two agents: a requesting agent that observes private demand information, and an oversight agent that must determine how to allocate resources upon receiving a bid from the requesting agent. Because the two agents have different cost structures, the requesting agent tends to bid higher than the amount that is actually needed. As a result, the allocating agent needs to adaptively learn how to interpret the bids and estimate the requesting agent's biases. Learning must occur as quickly as possible, because each suboptimal resource allocation incurs an economic cost. We present a mathematical model that casts the problem as a Markov decision process with unknown transition probabilities. We then perform a simulation study comparing four different techniques for optimal learning of transition probabilities. The best technique is shown to be a knowledge gradient algorithm, based on a one-period look-ahead approach.