  We study the price of anarchy of the first-price auction in the autobidding
world, where bidders can be either utility maximizers (i.e., traditional
bidders) or value maximizers (i.e., autobidders). We show that with autobidders
only, the price of anarchy of the first-price auction is $1/2$, and with both
kinds of bidders, the price of anarchy degrades to about $0.457$ (the precise
number is given by an optimization). These results complement the recent result
by Jin and Lu [2022] showing that the price of anarchy of the first-price
auction with traditional bidders only is $1 - 1/e^2$. We further investigate a
setting where the seller can utilize machine-learned advice to improve the
efficiency of the auctions. There, we show that as the accuracy of the advice
increases, the price of anarchy improves smoothly from about $0.457$ to $1$.
