Price of Anarchy of First-Price Auctions in Agentic Markets

A paper submitted to arXiv on 14 Oct 2026 argues that first-price auctions used to allocate user prompts among bidding AI agents suffer less welfare loss than the general worst case, because agentic markets tend to have a competitive floor and near-independent values once conditioned on the prompt. The authors show that as the competitive floor rises the welfare loss can be driven to zero, and that as value distributions approach conditional independence the efficiency guarantee approaches a factor of 1 - 1/e^2 of optimal welfare, both better than the general-case bound of 1 - 1/e. The results were validated empirically using auctions with strategic bidders simulated on the EmbedLLM prompt routing dataset.

Computer Science Computer Science and Game Theory Submitted on 14 Oct 2026 Title:Price of Anarchy of First-Price Auctions in Agentic Markets View PDF http://arxiv.org/pdf/2610.20587v1 HTML experimental https://arxiv.org/html/2610.20587v1 Abstract:An agentic market is a decentralized serving-time market where AI agents bid to claim each user prompt. An agent's bid is based on its expected value for the prompt, which is the expectation of the reward for its response minus its inference costs. First-price auctions FPAs , in which the highest bidder pays its bid and receives the prompt, are a natural way to allocate prompts in such a market, since they are simple and transparent to run, and do not require central knowledge of private capabilities and costs. However, FPAs are not truthful: 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. This welfare loss is quantified by the $\textit{price-of-anarchy}$ PoA . In this paper, we argue that agentic markets are likely to possess features that reduce the price-of-anarchy. The first is a $\textit{competitive floor}$, which occurs 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 . We show that competition among them then limits the welfare loss, which can be driven to zero as the floor rises. The second feature is $\textit{near-independence}$ of values after conditioning on the prompt, which occurs when most of the predictable variation in the expected value is determined by the difficulty of the prompt. As the value distribution approaches conditional independence, we can derive an efficiency guarantee that approaches a factor of $1 - 1/e^2$ of the optimal welfare. Thus, both features give rise to welfare lower bounds that are significantly better than the well-known general case of $1 - 1/e$. We validate these results empirically using auctions with strategic bidders simulated on the EmbedLLM prompt routing dataset. Additional Features Current browse context: cs.GT References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .