  We study the existence of pure Nash equilibrium (PNE) for the mechanisms used
in Internet services (e.g., online reviews and question-answer websites) to
incentivize users to generate high-quality content. Most existing work assumes
that users are homogeneous and have the same ability. However, real-world users
are heterogeneous and their abilities can be very different from each other due
to their diverse background, culture, and profession. In this work, we consider
heterogeneous users with the following framework: (1) the users are
heterogeneous and each of them has a private type indicating the best quality
of the content she can generate; (2) there is a fixed amount of reward to
allocate to the participated users. Under this framework, we study the
existence of pure Nash equilibrium of several mechanisms composed by different
allocation rules, action spaces, and information settings. We prove the
existence of PNE for some mechanisms and the non-existence of PNE for some
mechanisms. We also discuss how to find a PNE for those mechanisms with PNE
either through a constructive way or a search algorithm.
