Auctions between Regret-Minimizing Agents

We analyze a scenario in which software agents implemented as regret-minimizing algorithms engage in a repeated auction on behalf of their users. We study first-price and second-price auctions, as well as their generalized versions (e.g., as those used for ad auctions). Using both theoretical analysis and simulations, we show that, surprisingly, in second-price auctions the players have incentives to misreport their true valuations to their own learning agents, while in first-price auctions it is a dominant strategy for all players to truthfully report their valuations to their agents.