Source-linked AI summary
Markets of Minds: A 51-Billion-State Economy of Intelligence
Jusheng Zhang, Xuekun Wu, Wenhao Wang, Mark Wang, Ming-Hsuan Yang
TL;DR
When many agents need expert help but access is constrained, deciding who receives assistance is a population-level allocation problem because a helpful intervention can still displace a better use of shared capacity. Markets of Minds estimates pre-execution assistance value and jointly clears contracts under shared constraints; in a matched 240-case replay, its frozen allocator achieved higher adherence than equal-capacity random allocation under a common quota.
Problem
When expert access is bounded by cost, latency, concurrency, and provider restrictions, the central question is which requests should receive scarce cognition, since need alone does not establish value and help can have negative effects.
Source: §1 · p. 1Method
Markets of Minds estimates each feasible agent-service pair’s expected gain over default continuation, separates repair benefit from regression risk, and jointly allocates contracts before expert execution.
Source: §1 · p. 2Results
85.42% task-level persona adherence versus 73.86% for equal-capacity random allocation, a gain of 11.56 percentage points in the matched 240-case replay under a common 30% assistance quota.
Source: §1 · p. 2Takeaways & Limitations
Assistance value varies across tasks and supply levels, so which interventions are valuable depends on both the request and the amount of assistance available.
Source: §4.2 · p. 7The current empirical result tests demand-aware recipient selection under fixed assistance supply, while heterogeneous-service clearing defines the broader framework.
Source: §3 · p. 5
Abstract
from arXiv · showhide
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.
1 INTRODUCTION
The paper treats scarce expert assistance as a population-level allocation problem: need alone does not determine value when interventions can fail, regress, or displace better uses of capacity. Markets of Minds estimates assistance value before execution and jointly allocates contracts; in a matched replay, its frozen allocator outperforms equal-capacity random allocation under the same quota.
1 INTRODUCTION
- Many agents may have access to capable models while stronger reasoning, expertise, long-context processing, or verification remains limited by cost, latency, concurrency, and provider restrictions.The resulting question is which requests should receive scarce cognition when many agents need help.Source: §1 · p. 1
- Need alone is not value under scarcity: assistance can fail or disrupt a correct continuation, and a locally beneficial intervention may displace a higher-value use of shared resources.The allocation must be decided before the corresponding expert output is observed.Source: §1 · p. 1
- The objective accounts for individual budgets, provider access, shared resource limits, service capacity, and deadlines, which couple feasible choices across agents.Under a fixed contract, another agent’s assignment is not modeled as changing that contract’s task outcome.Source: §1 · p. 2
- Markets of Minds estimates each feasible agent-service pair’s expected gain over default continuation, separating default success, repair benefit, and regression risk before jointly clearing contracts.Selected services are executed after clearing, with a ledger recording reservation, consumption, and settlement.Source: §1 · p. 2
- 85.42% task-level persona adherence versus 73.86% for equal-capacity random allocation, a gain of 11.56 percentage points under a common 30% assistance quota.The matched replay covered 240 interactive agent cases without increasing the number assisted.Source: §1 · p. 2
2 PROBLEM FORMULATION
The formulation values assistance by its expected effect relative to default continuation, rather than by difficulty alone. It maximizes expected population gain over feasible assignments while accounting for shared constraints and uncertainty in contract values.
2 PROBLEM FORMULATION
- Other agents’ assignments affect feasibility through shared budgets, access, scarcity, and capacity, but are not modeled as changing a fixed contract’s outcome.The agent state is assumed sufficient for predicting default and assisted outcomes.Source: §2 · p. 2
- Allocation maximizes expected assistance gain over assignments that satisfy capacity, budget, and access constraints, allow at most one service per request, and are chosen before outcomes are observed.The objective is instantiated using observable request features and estimated contract values.Source: §2 · pp. 2–3
- Assistance value separates default-state occupancy from the service’s signed repair and regression effects, distinguishing need for help from benefit from the available help.For binary outcomes, the passage gives an exact decomposition of expected contract value.Source: §2 · p. 3
- Difficulty-first allocation can choose an irreparable request with zero assistance value over a less-failure-prone request worth 0.4; regression can also make assistance value negative.The example motivates estimating service effects rather than treating difficulty itself as value.Source: §2 · p. 3
- With one service and exactly K assignments, the optimum selects the K largest assistance values; when K is only an upper bound, non-positive values need not be selected.Value-estimation errors can translate directly into population-allocation errors.Source: §2 · p. 3
- The top-K recovery guarantee is conditional: the Kth-to-(K+1)th value gap must exceed 2ε, and average predictive calibration alone does not establish the required uniform-error premise.The propositions connect intervention effects to population allocation under shared cognitive capacity.Source: §2 · p. 4
3 MARKETS OF MINDS
Markets of Minds estimates assistance value relative to default continuation, then clears contracts jointly under shared constraints. Its pipeline represents observable demand, estimates prospective value, allocates before execution, and accounts for outcomes afterward.
3 MARKETS OF MINDS
- The pipeline estimates prospective assistance value, clears contracts under shared constraints, and executes only selected assistance.Allocation is frozen before expert execution, so realized assisted outcomes cannot determine which contracts are selected.Source: §3 · pp. 4–5
- Each demand packet records the task, base artifact, persona context, desired behavior, credits, accessible services, and deadline, while excluding target outcomes and unexecuted responses.The request–service representation adds a service descriptor to observable demand features so predicted effects can depend on the service.Source: §3 · p. 4
- Assistance value is the expected improvement over default continuation, estimated from default success, repairability on failures, and regression risk on successes.The estimator fits default success on request features, then fits repair and regression on their respective outcome strata.Source: §3 · p. 5
- The feasible set enforces per-request service limits, budgets, supplier capacity, shared resources, access permissions, and deadlines, so positive-value contracts may remain unselected.Contracts compete for capacity; execution and settlement happen only after the allocation is fixed.Source: §3 · pp. 4–5
- The evaluated instantiation selects the top K_e requests by calibrated value under fixed assistance supply, testing recipient selection without separately estimating regression risk.The general framework includes a three-head estimator and heterogeneous-service clearing, but the experiments use one service.Source: §3 · p. 5
4 EXPERIMENTS
The experiments test recipient selection under matched expert supply, then examine multimodal task and budget variation, shared-capacity allocation, and allocator-signal ablations. Across these settings, they evaluate allocation outcomes alongside welfare, safety, fairness, cost, and target-success diagnostics.
4.1 MATCHED AGENT ALLOCATION
- 85.42 overall versus 73.86 for equal-capacity random allocation under the same 30% expert-capacity limit, a difference of 11.56 points.Markets of Minds also exceeds Agora’s 82.92; all assistance policies use the same expert capacity.Source: §4.1 · p. 6, Table 1 · p. 6
4.2 MULTIMODAL BENCHMARK RESULTS
- 82.66 average score with 28.72% expert use versus RouteLLM’s 80.88 and 29.46%, a +1.78-point difference with 0.74 percentage points fewer expert calls.Markets of Minds scores highest on MMBench, MATH-Vision, CC-OCR, and MMMU-Pro; Agora leads on MMMU and RouteLLM on InfoVQA.Source: §4.2 · p. 7, Table 2 · p. 7
- Across 10%, 20%, 30%, and 50% expert-use budgets, gains over the strongest comparison are +0.70, +2.22, +1.78, and +2.01 points; the four-budget means are 81.07 versus 78.90.The figure summarizes task-level gains, score versus expert use, and performance across the four budgets.Source: Figure 3 · p. 6, §4.2 · p. 7
4.3 POPULATION-LEVEL ALLOCATION UNDER SHARED CAPACITY
- 76.08, 76.98, and 77.90 welfare at 10%, 30%, and 50% global capacity are the highest among plotted methods; the three-budget average is 76.99 versus RouteLLM’s 75.95.The difference from RouteLLM is largest at 10% capacity: 76.08 versus 74.47.Source: §4.3 · p. 8, Figure 4 · p. 8
- Markets of Minds has the highest plotted Jain fairness and lower harmful-help rate than the difficulty/uncertainty heuristic, while Agora has lower harmful help at lower average welfare.The API-cost comparison places Markets of Minds at higher welfare and lower total cost than several learned routing baselines.Source: §4.3 · p. 8, Figure 4 · p. 8
4.4 ABLATION STUDY
- Removing repair-gain lowers target success by −3.98 points, the largest leave-one-component-out decrease, followed by default-success (−3.11), market prior (−2.82), and preference conflict (−2.34).Removing uncertainty and execution signals produces smaller decreases of 1.51 and 1.04 points; the priors-only model falls by 8.44 points.Source: §4.4 · pp. 8–9, Table 3 · p. 9
- Every component removal increases cost per successful task by approximately 2.1%–10.7%, while the priors-only model is 13.7% more expensive per success.The full allocator achieves the highest target success (82.66) and lowest cost per successful task ($0.0233).Source: §4.4 · pp. 8–9, Table 3 · p. 9
5 RELATED WORK
Markets of Minds combines inference-time routing, multi-agent coordination, and shared-capacity allocation, valuing assistance by its predicted effect on the recipient under shared capacity. It also treats budgets, access, scarcity, and network roles as explicit economic state.
5 RELATED WORK
- Markets of Minds allocates assistance across task agents before expert outputs are observed, using predicted marginal effects on recipient outcomes under shared capacity.This couples decisions across agents rather than routing within a single task.Source: §5 · p. 9
- Related market-based approaches allocate scarce reasoning through uncertainty, auctions, and strategic bids, while MarketBench highlights calibration difficulties.The cited works are Zhang et al. (2026b), Zhou et al. (2026), Alazraki et al. (2026), and Fradkin & Krishnan (2026), respectively.Source: §5 · p. 9
- Cost-aware routing selectively invokes stronger models, while multi-agent systems organize specialized models through roles and collaboration.Examples named include FrugalGPT, AutoMix, RouteLLM, GraphRouter, Wu et al. (2023), Hong et al. (2023), and Wang et al. (2024a).Source: §5 · p. 9
- Population-scale agent simulations model heterogeneity; this work additionally represents budgets, access, scarcity, and network roles as economic state.A fuller discussion appears in Appendix A.Source: §5 · p. 9
6 CONCLUSION
The conclusion frames cognitive assistance as population-level allocation under shared constraints, where need does not determine value. It reports a matched replay advantage for a frozen allocator and notes that full heterogeneous-service evaluation remains future work.
6 CONCLUSION
- 85.42% task-level persona adherence versus 73.86% for equal-capacity random allocation in the matched 240-case replay under the same 30% expert-capacity limit.Complementary multimodal and shared-capacity experiments show that assistance value varies across tasks and scarcity regimes.Source: §6 · p. 9
- Markets of Minds estimates assistance value before execution and jointly clears contracts across a 51.2-billion-state persona–market design space.Value depends on default success, repairability, regression risk, and the opportunity cost of scarce capacity.Source: §6 · p. 9
- The evaluation focuses on recipient selection and budget-constrained allocation; evaluating the full heterogeneous-service formulation with separately estimated regression risk remains future work.Source: §6 · p. 9
AI USE STATEMENT
The authors describe generative AI tools as support for code development, troubleshooting, language clarity, and manuscript organization. They state that authors made the substantive scientific contributions and reviewed and validated AI-assisted work.
AI USE STATEMENT
- Generative AI tools supported code development and troubleshooting, linguistic clarity, and manuscript organization.Source: AI USE STATEMENT · p. 10
- The authors made the substantive scientific contributions, including methodological formulation, experiment design and execution, result interpretation, and claim determination.Source: AI USE STATEMENT · p. 10
- Authors independently inspected, tested, and validated AI-assisted code, cross-checked reported values, and reviewed and edited AI-assisted text.The authors state that they retain responsibility for the accuracy and final form of the manuscript, results, software, and supplementary materials.Source: AI USE STATEMENT · p. 10
A EXTENDED RELATED WORK
The extended related work situates Markets of Minds among routing, market-allocation, and population-simulation approaches. Its distinction is pre-execution allocation across task agents whose assistance competes for shared capacity.
A EXTENDED RELATED WORK
- Cost-aware cascades and routing learn selective model use, while multi-agent frameworks organize specialized roles or aggregation; their resources are typically provisioned within a request or task.This work instead couples task-agent decisions because assistance to one agent reduces capacity available to others.Source: A EXTENDED RELATED WORK · p. 13
- Prior market approaches coordinate through uncertainty, auctions, or strategic bids, while MarketBench highlights difficulty calibrating agent success and resource use.The paper values a contract by its predicted marginal effect on the buyer’s downstream outcome rather than the expert’s standalone capability.Source: A EXTENDED RELATED WORK · p. 13
- Crossing a versioned persona coreset with budgets, expertise portfolios, provider access, scarcity, and network roles yields 51.2 billion addressable persona–market states.The design space is enumerable, not a claim that billions of agents were executed, and persona provenance remains auditable.Source: A EXTENDED RELATED WORK · p. 13
- Markets of Minds studies who should receive assistance before its value is observed, with buyers differing in task and economic state under shared capacity.Without shared capacity, the problem reduces to independent routing; selecting after expert outputs are generated becomes post-hoc ensembling.Source: A EXTENDED RELATED WORK · p. 13
B DISENTANGLING VALUE ESTIMATION FROM MARKET ALLOCATION
The section separates value estimation from allocation by holding scores, cases, outcomes, and supply fixed while comparing recipient-selection rules. A prospective protocol also archives decisions before dispatch, but its outcome feedback covers selected requests only.
B DISENTANGLING VALUE ESTIMATION FROM MARKET ALLOCATION
- The controlled comparison uses the same frozen scores and 24 slots per environment; local top-k is mathematically identical to the evaluated allocator, up to ties.Threshold uses a development-tuned cutoff, FCFS takes positive-score requests in arrival order, and pooled top-72 removes environment-specific limits.Source: B DISENTANGLING VALUE ESTIMATION FROM… · p. 13
- 7.32 and 7.92 success points: the evaluated allocator beats threshold and FCFS, respectively, while leaving 15 missed repairs versus 45 and 52.Because scores, cases, and expert supply are held fixed, this comparison isolates allocation order.Source: B DISENTANGLING VALUE ESTIMATION FROM… · p. 14, Table 4 · p. 14
- 0.52 points in success and 1.55 points in worst-group performance favor per-environment allocation over pooled top-72, which relaxes the 24-slot group limits.Jain fairness is 0.988 versus 0.980, but it is a diagnostic rather than an optimization constraint.Source: B DISENTANGLING VALUE ESTIMATION FROM… · p. 14, Table 4 · p. 14
- With one service and equal contract costs, pooled top-K is already the joint solution when total capacity is the only constraint.The diagnostic therefore isolates ranking under fixed supply, not heterogeneous budgets, eligibility, or supplier capacities.Source: B DISENTANGLING VALUE ESTIMATION FROM… · p. 14
B.1 PROSPECTIVE ONLINE EXECUTION AND CALIBRATION LIMITS
- Negative predicted gains require a signed-gain estimator; the matched-replay score is instead a nonnegative probability-of-repair score.The prospective stream freezes its development-trained signed-gain estimator before target dispatch.Source: §B.1 · p. 14
- The prospective 400-request protocol archives each allocation before dispatch, establishing decision chronology, while selected requests show mean realized gain of 0.43 against mean prediction of 0.48.Unselected requests lack observed assisted outcomes, so the protocol cannot establish realized-gain calibration across quartiles or infer that the bottom quartile would be harmed.Source: §B.1 · pp. 14–15
C QUALITATIVE CASE ANALYSIS OF MULTIMODAL ALLOCATION
Qualitative cases illustrate how allocation can repair failures, choose among experts, avoid regression, and still share model-side failures. The broader experiments examine a dependency-aware economy, allocation under capacity, and scaling; supplementary passages describe prompts, demand signals, and proofs.
C QUALITATIVE CASE ANALYSIS OF MULTIMODAL ALLOCATION
- In qualitative cases, assistance repairs one answer and avoids regression in another, service choice changes outcomes, and all compared methods share a perception failure.These are post-hoc diagnostics, not a random sample or accuracy estimate; the shared failure is scored incorrect across methods.Source: C QUALITATIVE CASE ANALYSIS OF… · pp. 15–16
C.1 51.2B STATE SPACE GENERATION AND DEPENDENCY-AWARE SAMPLING
- The sampled economy preserves budget-access dependencies: Premium/Unbounded access is 46.84% for High Income cohorts versus 0.53% for Low Income cohorts.Its state space crosses 999,847 base personas with budgets, expertise portfolios, provider access, scarcity, and network roles.Source: §C.1 · pp. 16–17, Table 7 · p. 17
C.2 MULTI-AGENT ALLOCATION BREAKDOWN (512-AGENT ECONOMY)
- 76.88 average welfare and $0.0218 cost per successful task: joint allocation leads evaluated non-oracle policies, while benefit-per-cost greedy reaches 74.50 at 10% capacity with 11.20% harmful help.The comparison is from the expanded 512-agent allocation study under shared capacity.Source: §C.2 · p. 17, Table 8 · p. 17
C.3 POPULATION SCALE-OUT AND CLEARING EFFICIENCY
- 8.45 seconds and approximately 210 MiB: clearing at 100,000 concurrent agents processes nearly 12,000 allocations per second.The paper also reports average welfare and Jain fairness stabilizing as population size increases.Source: §C.3 · p. 18, Table 9 · p. 18
D PROMPT TEMPLATES
- The allocation policy uses frozen candidate responses and does not receive reference answers, benchmark scores, or expert responses before deciding.Prompt templates distinguish fixed instructions from runtime fields; answer-format suffixes constrain formatting rather than task semantics.Source: D PROMPT TEMPLATES · p. 18, §D.1 · p. 18
D.1 CANDIDATE-RESPONSE GENERATION
- Candidate responses pair benchmark-native images, questions, and choices with an optional parser-required answer-format suffix.The selected suffix is retained in the prompt protocol, and legacy responses with unrecorded prompt metadata remain marked missing.Source: §D.1 · pp. 18–19
D.2 STRUCTURED-DEMAND AUDITOR
- For Chat, Web, and OS-App, a temperature-zero demand auditor turns the persona, task, and base behavior into seven request-level signals.Its structured output is treated as noisy allocation-time prediction, not an oracle label.Source: §D.2 · p. 19
E PROOFS FOR THE PROBLEM FORMULATION
- The appendix proves an exact decomposition of binary default and assisted outcomes and relates uniform contract-value estimation error to welfare loss under joint allocation.It also establishes exact recovery of the oracle top-K set under the stated uniform-error condition.Source: E PROOFS FOR THE PROBLEM FORMULATION · p. 20
E.1 PROOF OF PROPOSITION 1
The proof conditions on the default outcome to decompose assistance value into repair of default failures and regression of default successes.
E.1 PROOF OF PROPOSITION 1
- Assistance contributes through repairing a default failure or regressing a default success, so high need alone does not guarantee high value when service repairability is low.The argument conditions on binary default outcomes to obtain the exact decomposition.Source: §E.1 · p. 20
E.2 PROOF OF PROPOSITION 2
The proof bounds the loss from optimizing estimated rather than true contract values over the same feasible set, then shows when top-K selection is recovered exactly.
E.2 PROOF OF PROPOSITION 2
- Under a uniform value-estimation error bound, estimated and oracle allocations recover the same top-K set when every oracle-selected request ranks above every unselected request by estimated value.The proof uses that the estimated allocation maximizes the predicted objective over the same feasible set.Source: §E.2 · p. 21