Contracting for LLM Delegation: Moral Hazard in Technology and Effort Choice

Nanda Kishore Sreenivas; Kate Larson

cs.MAAug 18, 2026

Contracting for LLM Delegation: Moral Hazard in Technology and Effort Choice

Authors: Nanda Kishore Sreenivas, Kate Larson

Organizations: University of Waterloo

Abstract

We extend the standard Principal-Agent framework to scenarios where the Agent selects from a suite of technologies, each characterized by a distinct cost-capability profile. This framework is increasingly critical in the era of Large Language Models (LLMs), where Agents choose both a model and an associated effort level (e.g., token budget). We model the relationship between output quality and effort as a concave, saturating function, which depends on the Agent's hidden two-dimensional action choice balancing technology selection and effort allocation. We derive the optimal linear contract for the Principal, demonstrating that the Agent's best response is characterized by a threshold reward share that triggers technology switching. Finally, we calibrate our model using open-weight LLM pairings across the MATH and MMLUPro benchmarks. We show that both Principal and Agent, when employing bandit algorithms to navigate this environment, converge to strategies that closely align with our theoretical equilibrium. These results suggest that simple linear contracts can effectively incentivize complex, technology-aware delegation in agentic workflows.

Figures & tables

Panel of Figure 2 — Figure 2: Illustration of model utilities for Agent $U_{m}(\alpha)$ under both scenarios.

Figure 3: Accuracy vs. budget for Llama models on MATH .

Model	$M_{m}$	$k_{m}$	$b_{m}$	$R^{2}$	RMSE
MATH task domain
Llama-3.2-1B-Instruct	50	0.00529	134	0.998	0.772
Llama-3.2-3B-Instruct	82	0.00473	177	0.994	2.153
DS-R1-Distill-1.5B	75	0.00081	982	0.998	0.979
DS-R1-Distill-7B	92	0.00073	1009	0.997	1.373
Gemma-4-E2B-it	84	0.00159	430	0.999	0.952

Table 1: Model calibration and fitted params for both tasks.

Intra-Family Pairs
Model Pairing	$c_{H}$	$\theta_{0}$ (est.)	$\theta_{0}$ (learn)
Llama 3.2: 1B vs. 3B	0.0200	0.367	0.409
DeepSeek R1: 1.5B vs. 7B	0.0075	0.731	0.817
Gemma 4: E2B vs. E4B	0.0060	0.255	0.286
Inter-Family Pairs
Llama 1B vs. Gemma 4B	0.0100	0.419	0.388

Table 2: MATH Domain : Learned model choices

(\theta_{0})

for the LinUCB controller. We fix

c_{L}=0.005

for all configurations.

Figure 4: MATH: Llama 1B vs. Llama 3B

Figure 5: MMLUPro: DeepSeek 1.5B vs. Gemma 4B

Intra-Family Pairs
Model Pairing	$c_{H}$	$\theta_{0}$ (est.)	$\theta_{0}$ (learn)
Llama 3.2: 1B vs. 3B	0.0200	0.589	0.633
DeepSeek R1: 1.5B vs. 7B	0.0075	0.309	0.286
Gemma 4: E2B vs. E4B	0.0060	0.339	0.286
Inter-Family Pairs
Llama 1B vs. Gemma 4B	0.0200	0.520	0.592

Table 3: MMLUPro Domain : Learned model choices (determined by

\theta_{0}

). We fix

c_{L}=0.005

for all pairings.

Figure 6: Principal’s Learning for Llama 3.2: 1B vs. 3B

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

		( $x_{\min},x_{\max}$ )
Model Family	Hugging Face Repository ID	MATH	MMLU-Pro
Llama 3.2	meta-llama/Llama-3.2-1B-Instruct	$[100,1000]$	$[100,1000]$
	meta-llama/Llama-3.2-3B-Instruct	$[100,1000]$	$[100,1000]$
DeepSeek R1	deepseek-ai/DeepSeek-R1-Distill-Qwen-1.5B	$[1000,5000]$	$[400,5000]$
	deepseek-ai/DeepSeek-R1-Distill-Qwen-7B	$[1000,5000]$	$[400,5000]$
Gemma 4	google/gemma-4-E2B-it	$[400,3000]$	$[400,3000]$

Appendix

Table 4: Model identifiers and corresponding discretized token budget bounds (

x_{\min},x_{\max}

)

Panel of Figure 7 — Figure 7: Accuracy vs budget for all 3 model families and 2 task domains, along with the fitted curves.

Panel of Figure 8 — Figure 8: Learned policies of various model pairings in the MATH domain.

Panel of Figure 9 — Figure 9: Learned policies for the MMLU Pro domain.

Panel of Figure 10 — Figure 10: Principal’s Learning for different model pairings on the MATH task

Panel of Figure 11 — Figure 11: Agent using simple UCB in MATH task for two different pairings. The context $\alpha$ is discretized into 10 bins, and we use a standard UCB instead of LinUCB with handcrafted features. The Agent considers each bin to be independent, and therefore takes a longer time to converge, and these were trained for $5,000$ episodes.

Principal-Agent Theory

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Jul 29, 2026

When LLM Agents Negotiate: Private Information and Dynamic Bargaining in Supply Chains

As LLM agents move from decision support to autonomous procurement, firms need to know whether delegated negotiators create value, divide it predictably, and avoid money-losing contracts. We study this in a canonical supply chain bargaining problem: a buyer with private demand information negotiates a quantity-payment contract with an uninformed seller. We benchmark nine LLMs from OpenAI, Google, and Alibaba against a validated Perfect Bayesian Equilibrium across 9,840 LLM-to-LLM negotiations. First, capability governs value creation. Agents agree in 98.9% of negotiations and capture 95.4% of first-best surplus undiscounted, but average 2.98 rounds against the benchmark's 1.25, and this delay erodes 21-34% of surplus. Capability also governs reliability: baseline models accept individually irrational contracts in 19.2% of cases, versus 0.0-0.6% at mid-tier and flagship, making automated profit verification the binding guardrail below that threshold. Second, surplus capture is relational. Provider identity predicts who captures surplus better than capability rank: self-play buyer shares average 40% for OpenAI, 50% for Google, and 70% for Alibaba's Qwen, an ordering that survives restricted communication and no discounting. Reversing which provider sells moves the division by 7-18 percentage points, and the capable Qwen flagship is the weakest cross-family seller: vendor choice is a first-order distributional decision. Third, the prompt is a strategic lever. Delegation separates the principal's economic patience from the agent's prompted strategic patience, a free deployment choice that is the single strongest driver of surplus division (90% of explained variance). Together these establish an equilibrium-referenced audit of AI agents along three dimensions: discounted efficiency, distributional profile, and operational reliability.

Chen Liang, Fasheng Xu

School of Business, University of Connecticut

Multi-Agent Negotiation Automated Negotiation LLM Agent Evaluation Supply Chain Management LLM Agent Reliability

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Aug 24, 2026

Markets, Not Planners: Decentralized Orchestration of LLM Agents with Private Information

As LLM agents proliferate, built by different parties and with different capabilities and costs, orchestrating them is more like assembling labor across the economy than a computer calling a subroutine. Existing orchestration is typically centralized, with a single planner assigning every task, but this creates a bottleneck as agent pools grow, requires private information (e.g., agents' execution costs), and can easily be manipulated, such that a single inserted preference nearly doubles a favored agent's task share under a centralized LLM allocator. We introduce AgentLance, a repeated labor market in which agents bid on tasks using their private costs and self-maintained strategy notes, an allocator selects winners from bids and public reputation records, and a VCG-style payment rule rewards cost-aware bidding. Complex tasks are handled by hierarchical delegation: winning agents can decompose work and subcontract it through the same mechanism. Across mathematical reasoning, code generation, knowledge-intensive QA, and agentic tasks, AgentLance matches agents to their specializations, shifts work toward cheaper agents as cost sensitivity rises, and consistently outperforms single-model, centralized-orchestration, and market baselines. Diagnosing market failures, including inaccurate cost self-estimation and sub-optimal bidding, then correcting them in controlled experiments yields further gains, charting a path toward more efficient agent economies.

Xiao Liu, Haoyang Li, Songwei Li +4

Knowledge Lab, University of Chicago · University of Virginia · Tsinghua University +2

Multi-Agent Orchestration LLM Agent Orchestration Multi-Agent Resource Allocation Mechanism Design

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Mar 15, 2026

The Provenance Paradox in Multi-Agent LLM Routing: Delegation Contracts and Attested Identity in LDP

Multi-agent LLM systems delegate tasks across trust boundaries, but current protocols do not govern delegation under unverifiable quality claims. We show that when delegates can inflate self-reported quality scores, quality-based routing produces a provenance paradox: it systematically selects the worst delegates, performing worse than random. We extend the LLM Delegate Protocol (LDP) with delegation contracts that bound authority through explicit objectives, budgets, and failure policies; a claimed-vs-attested identity model that distinguishes self-reported from verified quality; and typed failure semantics enabling automated recovery. In controlled experiments with 10 simulated delegates and validated with real Claude models, routing by self-claimed quality scores performs worse than random selection (simulated: 0.55 vs. 0.68; real models: 8.90 vs. 9.30), while attested routing achieves near-optimal performance (d = 9.51, p < 0.001). Sensitivity analysis across 36 configurations confirms the paradox emerges reliably when dishonest delegates are present. All extensions are backward-compatible with sub-microsecond validation overhead.

Sunil Prakash

Indian School of Business, Hyderabad, India

LLM Agent Routing AI Agent Governance LLM Agent Reliability

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Abstract

Principal-Agent Theory

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