This paper analyzes participation behaviors in design crowdsourcing by modeling interactions between participants and design contests as a bipartite network. Such a network consists of two types of nodes, participant nodes and design contest nodes, and the links indicating participation decisions. The exponential random graph models (ERGMs) are utilized to test the interdependence between participants' decisions. ERGMs enable the utilization of different network configurations (e.g., stars and triangles) to characterize different forms of dependencies and to identify the factors that influence the link formation. A case study of an online design crowdsourcing platform is carried out. Our results indicate that designer, contest, incentive, and factors of dependent relations have significant effects on participation in online contests. The results reveal some unique features about the effects of incentives, e.g., the fraction of total prize allocated to the first prize negatively influences participation. Further, we observe that the contest popularity modeled by the alternating k-star network statistic has a significant influence on participation, whereas associations between participants modeled by the alternating two-path network statistic do not. These insights are useful to system designers for initiating effective crowdsourcing mechanisms to support product design and development. The approach is validated by applying the estimated ERGMs to predict participants' decisions and comparing with their actual decisions.

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