VCG multiple item auction: Alice, Bob, Charlie want to purchase video streaming servi

cathex

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Apr 20, 2018
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Hello, I am having a slight issue regarding a problem that involves Vickrey-Clarke-Groves (VCG) auction. Now, I do know that this subthread is for probability/statistics but I couldn't find any other place which could fit more for mechanism design problem. (moderators, please move my thread to place where it belongs). Thank you.

The problem:

Alice, Bob and Charlie want to purchase video streaming service and each of them has the value of 2 for the service. To serve the customer, the provider must connect the person on the network (outlined below) to the root (marked as a star). The cost for sublease of each link is also stated. The provider can sublease each link in the network for certain costs (given in the picture). Once the link is subleased, the provider can send as much data along this link as he wants.

vcg.png

The provider runs VCG mechanism that maximizes social surplus. Who the provider should serve and how much they should pay?

The solution I came up:

The provider should serve all of them. The total value [Alice, Bob, Charlie] = $6. The most cost effective way of serving them is shown below:

vcg2.png

The total cost (to connect everyone to the network and the root) = ($1 + $0 + $1 + $1 + $1) = $4.

Social welfare = total value – total cost = $6 - $4 = $2.

In fact, the payment can be zero ($0) i.e. they can be served for free, even though the provider incurs the total cost of $4. Because the social welfare is $2 which equals to the value of each person, one can be served for free.

This is an example showing the fact that VCG mechanism sometimes can be not budget-balanced (spends more than it collects from the players). The focus is on maximizing the social surplus.

My concern:

Unsure whether the payment actually can be zero. The logic I followed seems to be solid (at least fto me) but I am still not certain about the solution.

Can someone check the whole problem and give me some advices/suggestions? Your help will be much appreciated. Thank you.
 
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