With the rapid development of crowdsourcing all over the world, crowdsourcing for software engineering begins to attract more and more considerable attentions from software developers, coders and researchers. And many successful online platforms such as TopCoder has demonstrated crowdsourcing's capability and potential for supporting various software development activities. In order to study the competitive behaviours for software crowdsourcing, we apply the famous game theory to model the 2-player algorithm challenges on TopCoder. And as all the participants are aware of other players' information and they make decisions almost simultaneously, this article adopts the theory of static games with complete information. Through Nash equilibria computing, we find that the value of successfully challenging probability can be used to deduce specific competitive decisions of coders in the algorithm challenge stage. Specifically, if a coder's probability to make a successful challenge exceeds some certain value, then he will always choose to challenge. The paper provides a new research perspective for software engineering crowdsourcing, and empirical research will be done in the next step of work.
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