  Intertemporal choices involve making decisions that require weighing the
costs in the present against the benefits in the future. One specific type of
intertemporal choice is the decision between purchasing an individual item or
opting for a bundle that includes that item. Previous research assumes that
individuals have accurate expectations of the factors involved in these
choices. However, in reality, users' perceptions of these factors are often
biased, leading to irrational and suboptimal decision-making. In this work, we
specifically focus on two commonly observed biases: projection bias and the
reference-point effect. To address these biases, we propose a novel
bias-embedded preference model called Probe. The Probe incorporates a weight
function to capture users' projection bias and a value function to account for
the reference-point effect, and introduce prospect theory from behavioral
economics to combine the weight and value functions. This allows us to
determine the probability of users selecting the bundle or a single item. We
provide a thorough theoretical analysis to demonstrate the impact of projection
bias on the design of bundle sales strategies. Through experimental results, we
show that the proposed Probe model outperforms existing methods and contributes
to a better understanding of users' irrational behaviors in bundle purchases.
This investigation can facilitate a deeper comprehension of users'
decision-making mechanisms, enable the provision of personalized services, and
assist users in making more rational and optimal decisions.
