We study the design of credible auctions when a seller has private information about her costs and cannot commit to public announcements. Akbarpour and Li [2020] show that when the reserve price is common knowledge, the first-price auction is the unique mechanism that is simultaneously optimal, static, and credible. Our paper demonstrates that this conclusion is overturned when the seller is privately informed about her cost, a common feature in many real-world markets.

Motivated by online advertising auctions, we study auction design in repeated auctions played by simple Artificial Intelligence algorithms (Q-learning). We find that first-price auctions with no additional feedback lead to tacit-collusive outcomes (bids lower than values), while second-price auctions do not. We show that the difference is driven by the incentive in first-price auctions to outbid opponents by just one bid increment. This facilitates re-coordination on low bids after a phase of experimentation. We also show that providing information about the lowest bid to win, as introduced by Google at the time of the switch to first-price auctions, increases competitiveness of auctions.

We model the strategic decisions of web sites in content markets, where sites may reduce user search cost by aggregating content. Example aggregations include political news, technology, and other niche-topic websites. We model this market scenario as an extensive form game of complete information, where sites choose a set of content to aggregate and users associate with sites that are nearest to their interests. Thus, our scenario is a location game in which sites choose to aggregate content at a certain point in user-preference space, and our choice of distance metric, Jacquard distance, induces a lattice structure on the game. We provide two variants of this scenario: one where users associate with the first site to enter amongst sites of equal distances, and a second where users choose uniformly between sites at equal distances. We show that subgame perfect Nash equilibria exist for both games. While it appears to be computationally hard to compute equilibria in both games, we show a polynomial-time satisficing strategy called Frontier Descent for the first game. A satisficing strategy is not a best response, but ensures that earlier sites will have positive profits, assuming all subsequent sites also have positive profits. By contrast, we show that the second game has no satisficing solution.