Strategic Joining and Optimal Pricing in a Single‐Server Batch Arrival Queue With Different Information of Batch Size

ABSTRACT This study explores the strategic behavior of customers in a single‐server batch arrival queue, where the batch size is a random variable. Each customer makes a decision to either join or balk under a linear reward‐cost structure. The utility of each customer is contingent on her individual decision and the decisions of her companions. The research considers two scenarios distinguished by the level of information: the batch size observable case, where customers are aware of their batch size information, and the batch size unobservable case, where customers lack information upon arrival. In both cases, a unique Nash equilibrium joining strategy and a socially optimal joining strategy are derived. To bridge the gap between the individual equilibrium joining strategy and the socially optimal strategy, a proposed fee imposed on customers is introduced. By comparing outcomes across both information scenarios, we derive managerial insights regarding optimal information‐disclosure policies. The key insight from our numerical experiments is that regulating the mean and variance of the batch size distribution is key to maximizing overall system throughput and social welfare.