Algorithmic technological progress presents both opportunities and challenges for organizational management. The success of online labor platforms hinges on algorithmic control, making it imperative to explore how this control affects gig workers' prosocial service behaviors. Drawing from affective event theory, our study delves into the factors influencing gig workers' prosocial service behaviors in the online labor platform setting. We utilize the challenge-hindrance appraisal framework to highlight the pivotal role of algorithmic control. To rigorously test our hypotheses, we gathered empirical data from an online questionnaire survey of 660 gig workers. Our results indicate that challenge appraisals and hindrance appraisals in regard to platform algorithm control have a nuanced dual impact on gig workers' prosocial service behaviors. This relationship is clarified by the mediating function of work engagement. A challenge appraisal of platform algorithmic control can positively influence gig workers' prosocial service behaviors. However, hindrance appraisal of platform algorithmic control can negatively influence gig workers' prosocial service behaviors. Interestingly, workplace interpersonal capitalization boosts the effect of challenge appraisal on employees' prosocial service behaviors. However, it does not mitigate the adverse effects of hindrance appraisal on such behaviors. This study has multiple theoretical implications, and it also provides valuable practical insights into organizational management.