Markets of Minds: A 51-Billion-State Economy of Intelligence

Jusheng Zhang; Xuekun Wu; Wenhao Wang; Mark Wang; Ming-Hsuan Yang

cs.MAOct 23, 2026

Markets of Minds: A 51-Billion-State Economy of Intelligence

Authors: Jusheng Zhang, Xuekun Wu, Wenhao Wang, Mark Wang, Ming-Hsuan Yang

Organizations: Stanford University · Vast Intelligence Lab · University of California at Merced

Abstract

When intelligence is shared, reasoning becomes a constrained allocation problem. In a population of agents with limited access to expert models, an intervention can benefit its recipient yet still be a poor use of shared capacity if another feasible intervention has greater expected value. Assistance must therefore be evaluated through both its marginal benefit and the opportunity cost induced by budgets, access, scarcity, and service capacity. To this end, we introduce Markets of Minds, a framework for allocating expert reasoning across agents before expert outputs are observed. For each feasible agent-service pair, the framework estimates the expected gain from assistance relative to the agent's default continuation, explicitly separating repair benefit from regression risk, and jointly clears assistance contracts under shared resource constraints. We then study this problem in a dependency-aware agent economy with 51.2 billion addressable persona-market states spanning capabilities, cognitive budgets, provider access, scarcity, and network roles. These dependencies couple allocation feasibility across agents rather than the outcome of a fixed contract. Empirically, in a matched replay of 240 cases under a common 30% assistance quota, the frozen allocator reaches 85.42% task-level persona adherence versus 73.86% for equal-capacity random allocation, a gain of 11.56 percentage points. The results show that assistance value is heterogeneous and can be negative, and that scarcity changes which interventions are worth purchasing. Together, these findings motivate a population-level view of intelligence where the value of assistance depends not only on what it can achieve, but also on which alternative uses of scarce cognitive capacity it displaces.

Figures & tables

Figure 1: Allocation and verification. A stylized execution and analytical illustrations of procurement, verification supply, and net correction.

Figure 2: Markets of Minds. (a) Task-agent execution. (b) Pre-execution value estimation, joint allocation, and resource accounting.

Method	Chat	Web	OS-App	Overall $\uparrow$	Expert use	Cost/succ. $\downarrow$	Harmful help $\downarrow$
No assistance	68.75	61.25	65.00	65.00	0%	$0.06211	–
Random	77.40	70.59	73.60	73.86	30%	$0.06090	0.42%
Difficulty/uncertainty	83.75	76.25	85.00	81.67	30%	$0.05636	0.00%
AutoMix	82.50	76.25	81.25	80.00	30%	$0.07765	0.00%
RouteLLM	86.25	77.50	80.00	81.25	30%	$0.06219	0.00%
GraphRouter	86.25	77.50	80.00	81.25	30%	$0.06023	0.00%

Table 1: Matched allocation at 30% shared expert capacity. 80 cases and 24 assistance slots per environment; cost/success includes method-specific overheads.

Figure 3: Main routing results and budget robustness. Task-level gains, score versus expert use, performance across four expert-use budgets, and the corresponding four-budget mean.

Single-model references
Method	MMMU	MMBench	Math Vision	InfoVQA	CC-OCR	MMMU-Pro	Avg.	Expert use
Gemini 3.5 Flash	76.11	92.99	86.51	78.90	71.42	78.03	80.66	—
Gemini-2.5-Pro	81.70	88.30	63.50	81.00	73.00	68.00	75.92	—
Gemini-2.0-Flash	70.70	83.00	41.30	83.20	73.10	57.00	68.05	—
GPT-5.6 Sol	82.22	83.90	84.54	73.58	79.62	79.77	80.60	—
GPT-4o (2024-08-06)	70.70	74.30	30.40	68.70	66.60	54.50	60.87	—

Table 2: Multimodal benchmark results. Routing entries report three-run means; bold marks the best routing result in each column.

Figure 4: Population-level allocation under shared capacity. The bar charts show welfare under 10%, 30%, and 50% global capacity and their average; the bubble charts show welfare relative to harmful help, Jain fairness, and total API cost.

Variant	Success $\uparrow$	$\Delta_{\mathrm{full}}$ (pp)	Cost/succ. $\downarrow$	Survey $\uparrow$
Restricted model
Priors only	74.22	$-8.44$	$0.0265	70.15
Leave-one-component-out
w/o market prior	79.84	$-2.82$	$0.0252	74.50
w/o uncertainty	81.15	$-1.51$	$0.0241	76.10
w/o preference conflict	80.32	$-2.34$	$0.0245	75.25

Table 3: Cognition allocator ablation. Three-seed mean.

\Delta_{\mathrm{full}}

denotes the success gap relative to the full model in percentage points.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Allocation rule	Success (%) $\uparrow$	Cost / success $\downarrow$	Harmful help $\downarrow$	Worst group (%) $\uparrow$	Jain $\uparrow$	Missed repairs $\downarrow$
Threshold (arrival order)	78.10	$0.0650	1.20%	71.05	0.965	45
FCFS (positive score)	77.50	$0.0662	1.45%	70.80	0.960	52
Pooled top-72	84.90	$0.0560	0.10%	77.20	0.980	12
Ours (top-24 / environment)	85.42	$0.05509	0.00%	78.75	0.988	15

Appendix

Table 4: Allocation-rule diagnostic. All rules use a nominal 72-slot assistance supply; pooled top-72 relaxes the per-environment capacity constraint.

Predicted-gain quartile	Mean $\widehat{\Delta}$
Top 25% ( $n=100$ )	$0.65$
Second 25% ( $n=100$ )	$0.35$
Third 25% ( $n=100$ )	$0.12$
Bottom 25% ( $n=100$ )	$-0.15$

Appendix

Table 5: Prospective 400-request diagnostic. The left panel summarizes pre-execution value estimates over the full request stream; the right panel reports realized outcomes for the selected subset.

Panel of Figure 5 — Figure 5: Representative qualitative allocation cases. The top row illustrates positive-value assistance and service selection; the bottom row illustrates regression avoidance and a shared failure. Panels (c) and (d) are readability crops of the original benchmark images; the underlying exported images are unchanged. The cases were selected post hoc for diagnosis and do not estimate benchmark prevalence.

Case	Ours	Agora (matched)	RouteLLM (matched)
2 / MMBench	Gemini 3.1 Pro (expert) $\rightarrow$ D $\checkmark$	Gemini 3.5 Flash (base) $\rightarrow$ C $\times$	Gemini 3.5 Flash (base) $\rightarrow$ C $\times$
4 / MathVision	GPT-5.6 Sol (expert) $\rightarrow$ D $\checkmark$	Gemini 3.5 Flash (base) $\rightarrow$ score 0 $\times$	Gemini 3.1 Pro (expert) $\rightarrow$ C $\times$
9 / InfoVQA	Gemini 3.5 Flash (base) $\rightarrow$ 65% $\checkmark$	Claude Sonnet 5 (expert) $\rightarrow$ 54% $\times$	Qwen2.5-VL-72B (expert) $\rightarrow$ 54% $\times$
10 / InfoVQA	Gemini 3.5 Flash (base) $\rightarrow$ rough ER $\times$	Claude Sonnet 5 (expert) $\rightarrow$ plasma membrane $\times$	Qwen2.5-VL-72B (expert) $\rightarrow$ nucleus $\times$

Appendix

Table 6: Allocation traces for the four cases in Figure 5 . “Base” means no expert service was purchased. A check mark denotes a benchmark score of 1.0; a cross denotes 0.0.

Provider access regime	Low income	Lower- middle	Middle	Upper- middle	High income	Premium/ unbounded (%)
	Socio-economic budget level (mean score)
Avoidant	1.10	2.20	3.50	4.10	5.20	11.08%
Cautious adopter	1.35	2.45	3.85	4.80	6.05	13.76%
Comfortable	1.55	2.70	4.25	5.90	7.15	18.92%
Digital native	1.77	2.67	4.24	5.83	7.21	18.87%
Premium/unbounded access (%)	0.53%	0.53%	2.19%	14.40%	46.84%	–

Appendix

Table 7: Dependency sampling diagnostics. The allocation explicitly models correlations between socio-economic status and technological access rather than uniform random assignment.

Method	50%	30%	20%	10%	Avg. welfare $\uparrow$	Harmful help $\downarrow$	Cost / success $\downarrow$
No assistance	73.21	73.21	73.21	73.21	73.21	0.00%	$0.0212
Random	73.28	73.08	73.10	73.15	73.15	14.68%	$0.0256
Difficulty / uncertainty	76.06	76.08	76.53	75.16	75.96	15.45%	$0.0242
Benefit-per-cost greedy	77.40	76.55	75.80	74.50	76.06	11.20%	$0.0225
Agora quality-first	75.48	74.00	74.10	73.98	74.39	8.42%	$0.0240
Ours (joint allocation)	77.90	76.98	76.57	76.08	76.88	2.15%	$0.0218

Appendix

Table 8: 512-agent allocation under shared capacity. Results are reported for the expanded 512-agent diagnostic under 10%, 20%, 30%, and 50% global capacity limits.

Agents	Slots@10%	Slots@30%	Welfare@10%	Welfare@30%	Jain Fair.	Broker Time	Allocations/s	Peak RAM
32	3	10	77.23 $\pm$ 0.69	81.40 $\pm$ 1.02	0.659	6.70 ms	1,503	0.07 MiB
128	13	38	76.10 $\pm$ 2.34	76.77 $\pm$ 1.42	0.855	6.79 ms	4,887	0.25 MiB
512	51	154	78.27 $\pm$ 0.91	80.13 $\pm$ 1.58	0.835	18.12 ms	7,381	1.02 MiB
2,048	205	614	78.10 $\pm$ 0.19	79.10 $\pm$ 0.22	0.863	137.33 ms	4,549	4.23 MiB
10,000	1,000	3,000	78.15 $\pm$ 0.12	79.25 $\pm$ 0.15	0.871	785.40 ms	12,732	20.80 MiB
100,000	10,000	30,000	78.20 $\pm$ 0.05	79.31 $\pm$ 0.08	0.875	8,450.15 ms	11,834	210.55 MiB

Appendix

Table 9: System scalability and computational overhead across increasing population sizes. The allocation mechanism scales efficiently to 100,000 concurrent agents within an 8.5-second clearing window.

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