First-Passage Percolation on a Width-2 Strip and the Path Cost in a VCG Auction
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- Flaxman A., Gamarnik D., Sorkin G.B. (2006) First-Passage Percolation on a Width-2 Strip and the Path Cost in a VCG Auction. In: Spirakis P., Mavronicolas M., Kontogiannis S. (eds) Internet and Network Economics. WINE 2006. Lecture Notes in Computer Science, vol 4286. Springer, Berlin, Heidelberg
We study both the time constant for first-passage percolation, and the Vickery-Clarke-Groves (VCG) payment for the shortest path, on a width-2 strip with random edge costs. These statistics attempt to describe two seemingly unrelated phenomena, arising in physics and economics respectively: the first-passage percolation time predicts how long it takes for a fluid to spread through a random medium, while the VCG payment for the shortest path is the cost of maximizing social welfare among selfish agents. However, our analyses of the two are quite similar, and require solving (slightly different) recursive distributional equations. Using Harris chains, we can characterize distributions, not just expectations.
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