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：跨期选择涉及需要在当前成本与未来收益之间权衡的决策。其中一种特定类型的跨期选择是决定是购买单个物品还是选择包含该物品的捆绑包。以往研究假设用户对这些选择所涉及的因素具有准确预期。然而实际中，用户对这些因素的感知往往存在偏差，导致非理性和次优决策。本文重点关注两种常见的偏差：投射偏差和参照点效应。为解决这些偏差，我们提出一种新型偏差嵌入偏好模型Probe。该模型通过权重函数捕获用户的投射偏差，通过价值函数描述参照点效应，并引入行为经济学中的前景理论对权重函数与价值函数进行整合，进而确定用户选择捆绑包或单个物品的概率。我们通过详尽的理论分析展示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理解，支持个性化服务的提供，并协助用户做出更理性、更优化的决策。