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.

翻译：跨期选择涉及需要权衡当前成本与未来收益的决策。一种特定的跨期选择是购买单个商品或选择包含该商品的捆绑包之间的决策。以往研究假设个体对这些选择中涉及的因素具有准确预期。然而现实中，用户对这些因素的感知常存在偏差，导致非理性和次优决策。本文重点关注两种常见偏差：投射偏差和参考点效应。为解决这些偏差，我们提出了一种新颖的偏差嵌入偏好模型——Probe。该模型通过权重函数捕捉用户的投射偏差，通过价值函数解释参考点效应，并引入行为经济学中的前景理论将权重函数与价值函数相结合，从而确定用户选择捆绑包或单个商品概率。我们通过详实的理论分析论证了投射偏差对捆绑销售策略设计的影响。实验结果表明，所提出的Probe模型优于现有方法，有助于更深入理解用户在捆绑购买中的非理性行为。本研究可促进对用户决策机制的深层认知，支持个性化服务提供，并帮助用户做出更理性、更优的决策。