After showing how the Vickrey auction efficiently allocates a private good we revisit some of the other social choice problems discussed at the beginning and speculate how to extend the Vickrey logic to those problems.  We look at the auction with externalities and see how the rules of the Vickrey auction can be modified to achieve efficiency.  At first the modification seems strange, but then we see a theme emerge.  Agents should pay the negative externalities they impose on the rest of society (and receive payment in compensation for the postive externalities.

We distill this idea into a general formula which measures these externalities and define a transfer function according to that formula.  The resulting efficient mechanism is called the Vickrey-Clarke-Groves mechanism.  We show that the VCG mechanism is dominant-strategy incentive compatible and we show how it works in a few examples.

We conclude by returning to the roomate/espresso machine example.  Here we explicitly calculate the contributions each roomate should make when the espresso machine is purchased.  We remind ourselves of the constraint that the total contributions should cover the cost of the machine and we see that the VCG mechanism falls short.  Next we show that in fact the VCG mechanism is the only dominant-strategy efficient mechanism for this problem and arrive at this lecture’s punch line.

There is no efficient, budget-balanced, dominant-strategy mechanism.

Here are the slides.