The often fierce competition on crowdfunding markets can significantly affect project success. While various factors have been considered in predicting the success of crowdfunding projects, to the best knowledge of the authors, the phenomenon of competition has not been investigated. In this paper, we study the competition on crowdfunding markets through data analysis, and propose a probabilistic generative model, Dynamic Market Competition (DMC) model, to capture the competitiveness of projects in crowdfunding. Through an empirical evaluation using the pledging history of past crowdfunding projects, our approach has shown to capture the competitiveness of projects very well, and significantly outperforms several baseline approaches in predicting the daily collected funds of crowdfunding projects, reducing errors by 31.73% to 45.14%. In addition, our analyses on the correlations between project competitiveness, project design factors, and project success indicate that highly competitive projects, while being winners under various setting of project design factors, are particularly impressive with high pledging goals and high price rewards, comparing to medium and low competitive projects. Finally, the competitiveness of projects learned by DMC is shown to be very useful in applications of predicting final success and days taken to hit pledging goal, reaching 85% accuracy and error of less than 7 days, respectively, with limited information at early pledging stage.