A Local Computation Mechanism Design

Assume that we would like to design an auction for millions of buyers and items. Alternatively, we have a cloud of hundreds of thousands of computers on which we would like to schedule several millions of jobs. In the not-so-distant past, these ideas would have been unthinkable, but today, technological advances, especially the Internet, have led us to the point where they are not only possible, but necessary. One can easily conceive a cloud computation with thousands of selfish computers, each one wanting to minimize its work load. Alternatively, an ad-auction for millions of businesses competing for advertising on millions of web sites does not appear to be a far away dream. In cases like these, the data sets on which we need to work are so large, that polynomialtime tractability may not be enough. Sometimes, even computing a solution in linear