Models for online markets with reputation system The only relevant model I'm aware of is Liu Qingmin(2011 R.E.S). Is there any other decent models dealing with the mechanism of online markets under reputation system, and perhaps linking to regulation?
I would suggest you start by looking at


  C. Dellarocas. "The Digitization of Word-of-Mouth: Promise and
  Challenges of Online Reputation Systems". Management Science 49
  (10), October 2003, 1407-1424.


for a review of relevant literature and


  Friedman &amp; Resnick "The Social Cost of Cheap Pseudonyms". Journal of
  Economcs and Management Strategy. 10 (2), 173–199.


and


  "Sustainable Reputations with Rating Systems," 2011. Journal of
  Economic Theory, 146, 2, 479-503


for some models of online reputation systems that comes to mind. If I think of any others, I will update this answer.