This question is with reference to the paper 'Efficient Trade with Interdependent Values' by Marek Pycia and Peng Wang,2015(See here).
At page no. 4 of the paper, the authors describe $v_i$ as the private signal observed by each agent. Are these signals i.i.d random variables (the paper says that the signals are drawn independently from the same distribution $F$, I'm not sure whether it translates to the i.i.d case or not)?
Also, it is given that the agents report their private signals. So, as far as calculating the transfer and allocation profile for the mechanism is considered, wouldn't it be more relevant if the valuations are submitted instead of the private signals?