4 ms·

I am guessing that by \Theta , the author means the product of the \Theta_i ? In the third paragraph, they say it is the “set of type profiles of all the agent

by drdeca 8y ago

I am guessing that by \Theta , the author means the product of the \Theta_i ? In the third paragraph, they say it is the “set of type profiles of all the agents”, which seems to suggest maybe {\Theta_i | i in U}, or maybe the disjoint union of the \Theta_i , but for the social choice function being from \Theta to X to make any sense to me, \Theta has to be the product of the \Theta_i over i in U. So I assume this is what is meant. The author also writes that M is “the set of all message spaces”, which seems to mean { M_i | i in U }, but again, I cannot make sense of that with regards to the decision rule \varphi having it as the domain. So, I also assume that M is actually meant to be the product of the M_i (with i ranging over U). It seems strange that the cost-sharing mechanism is defined as being a function only of the agent index? It seems like the term “mechanism” should mean that it includes how the cost imposed on each agent is determined, not just, be the result of what cost is imposed on each agent? I’m confused about the example. Are the different agents making offers sequentially? I don’t think the author clearly established (or, really, even clearly stated) their claim. They define a bunch of terms (like \Theta , M, \varphi ) but then they don’t do anything with them, or really say much of anything about them after they defined them. They might have something interesting they are trying to say, but I don’t think they make it clear. The second source it cites ( at https://crypto.stanford.edu/portia/papers/mukind-thesis.pdf https://crypto.stanford.edu/portia/papers/mukind-thesis.pdf ) looks interesting though, and I think is where they got the thing they were trying to explain (though it is much longer!).

chritchens 8y ago
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.

by drdeca 8y ago

chritchens 8y ago

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.