Probe: Learning Users’ Personal Projection Bias in Inter-Temporal Choices

Inter-temporal choices involve making decisions that require weighing costs in the present against benefits in the future. One specific type of inter-temporal choice is the decision between purchasing an individual item at full price or opting for a bundle including that item at a discounted price. Previous works assume that users have accurate expectations of factors involved in these decisions. However, in reality, users’ perceptions of these factors are often biased, leading to irrational and suboptimal decision-making. In this work, we focus on two commonly observed biases: the projection bias and the reference-point effect. To address these biases, we propose a novel bias-embedded preference model called Probe. Probe introduces prospect theory from behavioral economics to model these biases, which incorporates a weight function to capture the projection bias and a value function to account for the reference-point effect. We propose a new method to learn users’ individual projection biases from historical records and present four methods to estimate the reference point within the value function. We theoretically analyze the impact of projection bias on bundle pricing strategies. Through experimental results, we show that the proposed Probe model outperforms existing methods and leads to a better understanding of users’ behaviors in bundle purchases. This investigation can facilitate a deeper comprehension of users’ decision-making processes, enable personalized services, and help sellers design better product bundling strategies.