First-Price Auctions Hold Up Better in Agentic Markets

"An agentic market is a decentralized serving-time market where AI agents bid to claim each user prompt." That is the setup Shubhendu Trivedi, Jacob Eisenstein, Alekh Agarwal, Ian Gemp, Michael Kaisers and Adam Fisch take as given in a 40-page arxiv paper before asking whether the simplest auction format, first-price with the highest bidder paying its bid, wastes much welfare when agents behave strategically.

Their answer: less than the standard worst-case bound suggests. First-price auctions are not truthful, the authors write; "participants may bid less than their true value in the hope of a larger profit, and the prompt may then be allocated to someone other than the bidder who values it the most." That inefficiency is quantified by the price of anarchy, and the general-case guarantee is a factor of 1 − 1/e of optimal welfare. The paper argues two features of agentic markets push the bound higher.

The first is a "competitive floor," which kicks in "when multiple bidders usually value the prompt above some baseline share of the optimal welfare (e.g., because the best models are often distilled into cheaper alternatives, which perform similarly)." Competition among them, the authors argue, "limits the welfare loss, which can be driven to zero as the floor rises." The second is near-independence of values after conditioning on the prompt, which holds when most predictable variation in expected value comes down to prompt difficulty. In that limit, "we can derive an efficiency guarantee that approaches a factor of 1 - 1/e² of the optimal welfare," tighter than the general 1 − 1/e bound.

The paper validates these bounds "empirically using auctions with strategic bidders simulated on the EmbedLLM prompt routing dataset." That is simulation, not production routing data. The abstract publishes no per-experiment efficiency numbers from those runs. Two researchers we track have been passing the paper around.