A loot box is a probabilistic allocation of virtual products, the exact outcome of which is known to consumers only after purchase. Consumers sometimes purchase these goods multiple times until their preferred products are obtained. As loot boxes have been gaining enormous popularity in recent years, they are often criticized as exploitative and socially wasteful. In this study, we develop a stylized model to study the optimal design of loot boxes and its impact on profits and social welfare. We find that firms may assign asymmetric probabilities to ex ante symmetric products. Firms could use loot boxes to offer products at low prices to users who would not buy these products under the traditional pricing strategy. Loot boxes enable firms to earn higher profits due to better price discrimination and market expansion. Contrary to the widespread criticism of loot boxes as socially harmful, our analysis reveals that the loot box strategy can improve social welfare. Some platforms promise that consumers can obtain their preferred products with no more than a certain number of purchases. Contrary to conventional wisdom, our analysis reveals that such a strategy can increase firm’s profits while reducing consumer welfare.

Firms often offer subscriptions for services such as extended warranties for automobiles or appliances, and subscription plans for golf or symphony. Before purchasing a subscription, consumers need to estimate the probability of needing the service in the future. Most of the prior research assumes that consumers form an unbiased estimate of their future needs. Empirical evidence, however, shows that consumers often make errors in predicting future needs. We draw on the literature on the availability bias (Tversky and Kahneman 1973) to model how consumers form subjective probabilities of needing the service. We develop a dynamic model in which a firm offers a menu of contracts to consumers, and the menu prices can change over time. We show that availability bias can lead firms to offering subscription plans with below marginal cost pricing for all consumers at the time of service. Contrary to intuition, we find that availability bias can sometimes benefit consumers at the expense of firms. We also find that even perfect competition cannot eliminate the negative impact of availability bias on social welfare, and that consumer and social welfare can be negative even under perfect competition.

Managers frequently offer limited-time products across various industries, yet few studies examine consumers' dynamic decisions to guide managerial choices about re-issuing previous products or introducing new ones. We develop ProductGPT, a novel deep generative pre-trained Transformer designed to predict sequential purchase decisions in limited-time product settings.

Three key features differentiate our ProductGPT from standard Transformer models. First, it uses triplet input tokens simultaneously encapsulate decision history, the supply-side sequence of limited-time products, and the demand-side sequence of observed decision outcomes. This approach enables ProductGPT to capture meaningful product representations for all products in the assortment. Second, using the encoded long-range and short-range contexts, ProductGPT predicts consumer decision sequences under alternative limited-time product schemes. Third, ProductGPT supports new product design by incorporating product features as covariates and forecasting consumer responses through feature-based product embeddings.

We apply ProductGPT to a unique 20-month transaction dataset of video game loot boxes. Our model consistently outperforms several sophisticated benchmark models in sequential purchase predictions. We demonstrate its ability to forecast aggregate sales, discover behavioral patterns, and support product sequencing strategies.

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