Purpose: The purpose of this paper is to study the decision-making behavior of the initiator and the participant under innovative and project-based tasks, respectively. It further explores the impact of the participant's loss aversion and the initiator's incentive level on the participant's optimal effort level to reveal the implicit managerial mechanism. Design/methodology/approach: This paper uses the Principal-agent Theory, Prospect Theory and Game Theory to study the decision-making behavior in crowdsourcing tasks. First, according to the return at the reference point, it establishes the utility function models of the participant and the initiator. Second, based on diverse loss aversion coefficient and incentive coefficient, it constructs the decision-making models of two types of task respectively. Third, it verifies the validity of models through simulation analysis. Findings: For innovative task, the participant's optimal effort level increases with the increment of loss aversion and incentive level, but decreases with the increase of his effort cost. For project-based task, the participant's optimal effort level rises with the decrease of loss aversion; if the initiator does not take appropriate incentives, information asymmetry will lead to the task becoming a low-level innovation approach. Moreover, under innovative task, when the participant has loss aversion (or loss aversion reversal), his optimal effort level is higher (or lower) than that with no loss aversion, while the result under project-based task is just the opposite. Originality/value: This paper characterizes two types of crowdsourcing task. Based on the prospect theory, it develops the decision-making models of the participant and the initiator under innovative and project-based tasks, thus exploring the impact of loss aversion and incentive level on their decision-making behavior. According to the findings in this paper, the initiator may effectively speculate the participant's effort level and adopt reasonable monetary incentive measures to optimize the crowdsourcing return. In addition, this study can provide some reference for the design of incentive mechanism in crowdsourcing tasks and improve the relevant research of crowdsourcing. [ABSTRACT FROM AUTHOR]