We study a sequential selling problem in which an agent receives daily offers to sell a good, incurs a holding cost each day, and is subject to sunk cost bias---allowing past, irrecoverable costs to influence present decisions. We introduce a formal model parameterizing the degree of sunk cost bias and distinguish between three behavioral types: optimistic (who ignore future bias), naive (who assume their current bias persists), and sophisticated (who anticipate the evolution of their own bias). For each type, we characterize the optimal selling strategy and precisely quantify the worst-case gap in expected objective profit compared to an unbiased agent. Our results show that optimistic agents can suffer a quadratic loss in profit due to excessive waiting, naive agents perform identically to unbiased agents, and sophisticated agents limit their losses to a linear function of the time horizon. These findings clarify how different anticipations of sunk cost bias affect sequential decision-making and suggest targeted interventions to mitigate inefficiency.

In this paper, we introduce the problem of Online Matching with Delays and Size-based Costs (OMDSC). The OMDSC problem involves m requests arriving online. At any time, a group can be formed by matching any number of requests that have been received but remain unmatched. The cost associated with each group is determined by the waiting time for each request within the group and size-dependent cost. The size-dependent cost is specified by a penalty function. Our goal is to partition all the incoming requests into multiple groups while minimizing the total associated cost. This problem is an extension of the TCP acknowledgment problem proposed by Dooly et al. (J. ACM, 2001). It generalizes the cost model for sending acknowledgments. This study reveals the competitive ratios for a fundamental case, in which the penalty function takes only values of either 0 or 1. We classify such penalty functions into three distinct cases: (i) a fixed penalty of 1 regardless of the group size, (ii) a penalty of 0 if and only if the group size is a multiple of a specific integer k, and (iii) other situations. The problem in case (i) is equivalent to the TCP acknowledgment problem, for which Dooly et al. proposed a 2-competitive algorithm. For case (ii), we first show that natural algorithms that match all remaining requests are Ω(√k)-competitive. We then propose an O(log k / log log k)-competitive deterministic algorithm by carefully managing the match size and timing, and prove its optimality. For any penalty function in case (iii), we demonstrate the non-existence of a competitive online algorithm. Additionally, we discuss competitive ratios for other typical penalty functions that are not restricted to take values of 0 or 1.