sorry for the late reply drdeca, technical problem. Have still to parse your reply. I will try to give you a response anyway. 1) Well, there is no product of \

sorry for the late reply drdeca, technical problem. Have still to parse your reply. I will try to give you a response anyway. 1) Well, there is no product of \Theta_i, it's sets. It's the set of all the \Theta_i. 2) the article is sequential, so it's {\Theta_i | i in U}. 3) M is the set of all the possible messages that can be sent by the agents, not the actual messages sent. That's why it's message space. 4) the cost mechanism depends on the service itself, that's why its shape is know beforehand. If you have to allocate M&Ms, you know the cost of any unit, the logistic costs (let's say an average or a worse case scenario), etc. 5) nothing is implied on the order of the message submissions. 6) I don't think so, but you are the reader. I'm taking feedbacks to improve in the next articles. One was to add images and diagrams. The claim is just that we cannot have efficiency, incentive-compatibility and no deficits cause we cannot have prices that act perfectly both as a way to recover costs and a way to incentivize agents. 7) fair. At start I wanted it to be longer, and then I understood that a) it was taunting to read somehow b) I had to split it. It's the first of a series. Worst case scenario I will link to this first article in the next ones. Tradeoffs maybe. I wanted to be correct, not just to describe the problem. 8) point 6. 9) from the first source I've taken the general description of mechanism design, and the second was the best I found on the problem. To be honest, the second constrained me to choose the first. And the first and some lectures from Bonn university (Germany) were the best I've found so far. Happy to answer to further questions, and, again, apologies for the late reply.