Advertising is the economic engine of the internet. Online advertising opportunities are predominantly sold through real-time auctions: whenever a user visits the platform, an auction is run among interested advertisers, and the winner gets to display their ad to the user. Motivated by online advertising, this talk will develop a theory of bidding in auctions under budget constraints, with the goal of informing the design of automated bidding algorithms and analyzing the market-level outcomes that emerge from their simultaneous use.

First, I will present our work on the problem faced by an individual advertiser, namely developing data-driven algorithms for bidding in repeated auctions under a global budget constraint. We study a non-stationary stochastic model of sequential auctions, which despite immense practical importance has received little attention, and propose a natural algorithm for it. With access to just one historical sample per auction/distribution, we show that our algorithm attains (nearly) the same performance as that possible under full knowledge of the distributions, while also being robust to distribution shifts between the sampling and true distributions. Next, I will present our analysis of the market as a whole when each of the individual advertisers are attempting to maximize their own utility subject to budget constraints. We prove the existence of a well-structured Bayes-Nash equilibrium for all standard auctions, including first-price and second-price auctions. We then leverage its structure to establish a revenue equivalence result and bound the price of anarchy of liquid welfare.