## Combinatorics Seminar

When: Sunday, December 22, 10am
Where: Schreiber 309
Speaker: Po-Shen Loh, Carnegie Mellon University
Title: Anarchy is free in network creation

## Abstract:

The Internet has emerged as the most important network in modern computing, but miraculously, it was created through the individual actions of a multitude of agents rather than by a central authority. This motivates the game theoretic study of network formation, and we consider one of the best-studied models, due to Fabrikant et al. In it, each of n agents is a vertex, which creates edges to other vertices at a cost of \alpha each. Every edge can be freely used by every agent, regardless of who paid the creation cost. To reflect the desire to be close to other vertices, each agent's cost function is further augmented by the sum of its (graph theoretic) distances to all other vertices.

Previous research proved that in many regimes of the (\alpha,n) parameter space, every Nash equilibrium has total social cost (sum of all agents' costs) within a constant factor of the optimal social cost. In algorithmic game theory, this approximation ratio is called the price of anarchy. We significantly sharpen some of those results, proving that for all constant non-integral \alpha>2, the price of anarchy is not only bounded by a constant, but tends to 1 as n tends to infinity. For constant integral \alpha>=2, we show that the price of anarchy is bounded away from 1.

Joint work with Ronald Graham, Linus Hamilton, and Ariel Levavi.