Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.19316

Truthful and Expected-Payment-Optimal Model Routing in Graph-Based Agentic Workflows

Jiayuan Liu·Mingyu Guo·Jiarui Gan·Vincent Conitzer
View original source ↗Read source document ↗Export metadata ↓

Abstract

Assigning routine tasks to cheaper large language model (LLM) providers can reduce generation cost, but switching providers may require processing accumulated context again. Keeping dependent tasks with the same provider can instead reuse eligible context. Graph-based workflows therefore couple routing decisions across tasks. Independent providers may also privately know their real-time unit costs and strategically misreport them. We formulate this routing problem as a single-parameter procurement auction and propose STAR (Strategy-proof Topology-aware Agent Routing), which minimizes virtual-cost-weighted graph workloads. Its allocation rule and payments, computed by integrating workload over possible cost reports, make truthful reporting utility-maximizing regardless of other providers' reports and cover each truthful provider's execution cost. With independent cost distributions and non-decreasing virtual costs, STAR additionally minimizes the user's expected total payment to providers. Controlled synthetic experiments separate the execution-cost benefit of topology awareness from the payment benefit of virtual-cost optimization: the former grows with fan-out and transferred payload, while the latter increases gradually along the tested prior-shape heterogeneity path. A paired sensitivity study quantifies how payment savings vary with prior misspecification while strategy-proofness is preserved.

Explore related subjects

cs.GTcs.CLcs.MA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jiayuan Liu, Mingyu Guo, Jiarui Gan, Vincent Conitzer. 2026-10-13. Truthful and Expected-Payment-Optimal Model Routing in Graph-Based Agentic Workflows. https://arxiv.org/abs/2610.19316

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Incentivize Contribution and Learn Parameters Too: Federated Learning with Strategic Data Owners

In federated learning (FL), a center trains a shared model from updates that clients compute on their private data. Collecting and training on data is costly, so a strategic client may contribute little data and free-ride on the model trained by the others. We study mechanisms that incentivize data contribution and learn the model at the same time. Our first mechanism, UPBReD, updates the clients ' contributions and the model jointly, and converges at a geometric rate to a Nash equilibrium of the contribution game together with the welfare-maximizing model for those contributions. This equilibrium can involve under-contribution, so our second mechanism, 2P-UPBReD, adds budget-balanced transfers that make full contribution a dominant strategy, after which training converges to the optimal model; we also give conditions under which every client prefers to participate. Both mechanisms trust what clients report about the data they use and the gradients they compute. We show that no payment rule can reward unverifiable contributions unless something the center observes depends on the data actually used. Building on this, T-2P-UPBReD checks each client's reported contribution against the other clients ' realized valuations of the trained model, and prices gradient reports with a budget-balanced charge. It elicits truthful contribution reports, makes gradient reports approximately truthful, still reaches full contribution and the optimal model, and never runs a deficit. Experiments on CIFAR-10, FEMNIST, and Twitter show that 2P-UPBReD matches the welfare of FedAvg trained on all data, while strategic clients without incentives lower the welfare of the learned model.

cs.GT↗
arXiv2026

Likes, Budgets, and Equilibria: Designing Contests for Socially Optimal Advertising

We study competitive advertising on a social network. Each of $m$ firms allocates a budget across consumers, and a platform decides, through a contest success function (CSF), what share of each consumer's attention every firm captures; awareness then spreads through the network. We model awareness and budgets on two timescales and bound how many fast steps awareness needs to settle between budget updates. On the slow timescale, best-response dynamics converge at a geometric rate to a Nash equilibrium whenever the firms' utilities are strongly concave and smooth, and a subclass of the standard ratio-form CSFs satisfies these conditions. Their equilibrium, however, need not maximize welfare: a firm's spending lowers its rivals' shares of attention, so individual and social optima differ, and a constant per-unit charge cannot close this gap in general. We give a sufficient condition for the equilibrium to coincide with the welfare optimum. To meet it, we multiply each firm's ratio share by a function of the total spending at the consumer, a class we call scaled ratio CSFs (SRCSFs), and show that within this class the condition holds exactly when this function is a power of the total spending, which gives the Power RCSF. The Power RCSF alone falls short in two ways. Its equilibrium is optimal only when firms exhaust their budgets, which we remove with a budget-balanced per-unit charge. Its curvature also becomes unbounded as spending at a consumer approaches zero, breaking convergence, which we restore by requiring every firm to spend a small minimum on each consumer. With both additions, best-response dynamics converge to a unique, symmetric equilibrium that maximizes $p$-mean social welfare for every $p \le 1$ simultaneously, so the Price of Anarchy is one.

cs.GT↗
arXiv2026

Fair Allocation with Dichotomous Preferences over Item Complements

We study the problem of fair allocation when agents have dichotomous submodular preferences over groups of, rather than individual, items. These preferences naturally extend existing models, and have a natural interpretation in settings such as course allocation. We show that this seemingly minor extension results in computational intractability barriers: computing a utilitarian or Nash-optimal allocation with item complements is NP-hard. However, when agents' complementary bundles have size at most $k$, there exist poly-time algorithms that compute $\frac1k$-$\texttt{maxUSW}$ allocations and approximate Nash-welfare-maximizing allocations. While PO+EF-1 allocations may not exist in the complementary preference setting, it is possible to compute $\frac1{k+1}$-approximately $\texttt{maxUSW}$ EF-X allocations in polynomial time; furthermore, these allocations offer each agent $i$ a utility of at least $\frac{\texttt{MMS}_i - k}{k+1 + \frac1n}$, where $\texttt{MMS}_i$ is agent $i$'s maximin share guarantee. While the standard dichotomous binary submodular setting admits simple sequential techniques for computing fair and efficient allocations, our results for the complements setting require more complex tools from combinatorial optimization.

cs.GT↗