Abstract: With the dramatic growth of crowdfunding industry which have provided entrepreneurs a new way of financing, more and more issues have been studied to improve the success rates of crowdfunding projects. To motivate more early investors to pledge in the project, entrepreneurs are often encouraged to motivate early investors. Inspired by practical problems, this paper considers the strategic delay behaviors of investors and their influences on the pricing and incentive strategies in crowdfunding projects.
Strategic delay behaviors make investors spontaneously invest in correspondingly period according to their valuations during the investing process. In addition, some early investors may deliberately delay their investment for free-riding because the risks and the waiting cost are both higher in the early stage of crowdfunding. The free-riding behavior will worsen the performance of projects in early stage and decrease the overall success rate.
A two-period model is adopted to depict the investing behaviors of investors and compared the Bayesian equilibriums in the sequential model (no strategic delay) with the spontaneous model (with strategic delay), respectively. To depict the crowdfunding process, I₁ and I₂ are used to denote the investors arriving in two periods and use δ to denote the waiting cost of early investor. Therefore, the pledging probabilities of two investors q₁ and q₂ are concluded,as well as the success rate S=q₁×q₂.The strategic behaviors in our model is considered by allowing investors to choose the entry time spontaneously. By comparing the success rates in different scenarios and adjusting the prices p_i for different investors, the optimal pricing strategies in many occasions can be concluded.
Our results show that the waiting cost of early investor induces the strategic delay behaviors. Moreover,the strategic delay behaviors of investors could influence the optimal incentive decisions when entrepreneurs choose to improve success rates with price discrimination.When there exists the constraint of fixed target, if the investors can't strategic delay, the entrepreneur should motivate the early investors and improve the success rate through making up their waiting cost. In contrast, when the investors can strategic delay, investors with high valuations will spontaneously invest in the early period and are willing to take the higher price, therefore the entrepreneur should motivate the late investors instead. When there is no target constraint, the entrepreneur should motivate the early investors for higher success rate and expected profit no matter if the investors strategic delay.
In conclusion, the managerial guidance is provided for entrepreneurs on improving the projects according to the targets and the behaviors of investors. In addition, the practical value of our conclusions is tested by providing realistic examples and empirical studies, including 575 projects on one of the largest crowdfunding platforms in China. Our limitation and future goals which provide more directions and inspirations for relevant research in the future are also stated.

Key words: crowdfunding, strategic delay, pricing, incentive mechanism