Some Recent Results in Algorithmic Game Theory

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There are three major trends in the field of Algorithmic Game Theory: computational mechanism design, the price of anarchy, and the computation of equilibria; this talk describes one recent result in each. We show computational complexity lower bounds on truthful and approximately efficient mechanisms; we revisit the Roughgarden-Tardos result on selfish routing when routing decisions are made by the nodes, not the flows; and we show that Nash equilibria can be approximated well in several broad, unexpected, and useful classes of games. (Joint work with Costis Daskalakis, Michael Schapira, Yaron Singer, and Greg Valiant).