Competition in Optimal Stopping: Behavioral Insights

Abstract

Problem definition: We study settings where agents sequentially search among different options under competition. Motivated by labor markets and the allocation of kidneys from deceased donors, we focus on the effect of (i) the mechanism to collect decisions, i.e., whether all agents make their decisions simultaneously or sequentially, and (ii) competition, i.e., the number of agents who are searching from a shared pool of options. Methodologies/results: We introduce a model of sequential search under competition, in which agents are exogenously prioritized and must decide when to stop their search to maximize the chosen option's value. We characterize the optimal policy, which defines a sequence of thresholds that dictates when each agent should accept an option based on their priority relative to others still searching and the number of remaining options. Our analysis reveals that neither the mechanism for collecting agents' decisions nor the number of lower-priority agents influences the optimal policy. To test these predictions, we designed and conducted a lab experiment replicating our theoretical model. The results indicate significant deviations from the optimal policy. Moreover, we find that the mechanism significantly affects agents' decisions due to primarily two drivers: (i) saliency of competition and (ii) frustration. Finally, we identify an "illusion of competition" effect, whereby agents use significantly lower thresholds when the number of agents with lower priority increases. Managerial implications: Our results show that a higher perception of competition and using a simultaneous mechanism (i.e., batch offering) significantly decrease the thresholds that agents use to guide their search, making them stop their search earlier. Thus, clearinghouses that suffer from inefficient discard of options should increase the saliency of competition and use batch offerings to reduce agents' selectivity and mitigate waste.

Keywords: behavioral operations, optimal stopping, search, competition, frustration

JEL Classification: D49