Price-setting designs
The 30 studies in which prices respond to the LLM agents’ own decisions, audited on the 12 components of the five conditions (Table 5 and Online Resource 1). Select a design for its profile, or a component for its definition.
Designs by component
The codes as recorded in Online Resource 1.
| Design | 1. Interaction | 2. Heterogeneity | 3. Information | 4. Institutions | 5. Validation | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
Interaction | Heterogeneity stated | Dispersion vs humans | Dependence measured | No real episode | Familiarity checked | Mechanism varied | Non-LLM baseline | Same-design humans | Repeated markets | Configuration documented | Wording tested | |
| Documented (yes) | 30 | 29 | 3 | 5 | 21 | 1 | 4 | 4 | 6 | 19 | 8 | 2 |
- Documented
- Partly documented
- Not documented
- Unknown
- Not applicable
- Dashed outline: value changed by the selected scenario
The audit checks documentation rather than certifying validity: a reported test may fail, a published prompt may fail to recover a retired model, and an unreported run count does not establish more than one run. Section 8
“Not documented” means not established in the material examined. Note to Table 5
From the review
Table 5 Conditions for credible aggregation and their documentation among the 30 price-setting designs
| Condition | Requirement | Documented among the 30 designs (unknown in parentheses) | Illustrative designs |
|---|---|---|---|
| 1. Interaction | Aggregate outcomes arise from agents’ interaction through prices, payoffs, or networks | 30 of 271 primary studies (4 of them also elicit decisions independently); 215 elicit decisions independently | Henning et al. (2025); Chupilkin (2026); Saxena et al. (2026) |
| 2. Heterogeneity | Sources of heterogeneity stated; heterogeneity validated for the claimed role; dependence reported; effective agent count when averaging assumptions apply | 3 compare between-agent dispersion with human markets of the same design (2 unknown), 1 finding similar dispersion; 1 initializes traits from investor records; 14 homogeneous by design; 5 measure dependence (2 unknown; errors in 2, action correlation or overlap in 2, holdings and common buying in 1) | Begin et al. (2026); Saxena et al. (2026); outside the 30: Feng et al. (2025) |
| 3. Information | Information structure stated; shared inputs identified; remembered outcomes excluded | 5 feed agents real news or replay real episodes (2 unknown); none of the 28 read in full measures the effect of remembered outcomes on prices; 1 of 9 replications checks whether models know the original design (2 designs unknown) | Gao et al. (2024); Lin (2025); Galanis (2026) |
| 4. Institutions | Institution varied or justified; non-LLM baseline under the same rules when the LLM’s explanatory contribution is claimed | 4 vary the auction or trading mechanism (2 unknown); 4 include non-LLM agents under the same rules (2 unknown); 20 compare with a theoretical or equilibrium prediction | Shah et al. (2025b); Chupilkin (2026); outside the 30: Ruano and Rajan (2026) |
| 5. Validation | Human benchmark matched to the claim; market as the unit of replication; dated configuration, prompts, and raw outputs | 1 runs same-design human markets; 5 compare with published same-design human evidence, including summary statistics (2 unknown); 19 report repeated markets or runs (10 unknown, 1 not applicable); of the 28 read in full, 12 name a dated identifier for at least one model and 17 state that full prompts are published (documentation indicators) | Henning et al. (2025); Galanis (2026); outside the 30: Coqueret et al. (2026) |
Note: Counts describe the 30 price-setting designs, unless another denominator is stated. “Not documented” means not established in the material examined. A dispersion comparison is counted regardless of its result; dependence measures need not be error correlations. Non-LLM baselines require agents to operate under the same rules. A same-design human comparison sets agents’ outcomes against quantitative human outcomes under the same core task, institution, and payoffs; published summary statistics are distinguished from analysis of the original data. Dispersion comparisons concern dispersion between agents, not pooled response frequencies, and mechanism variation includes whether a market maker updates its price. Online Resources 1 and 2 provide the study membership, definitions, locators, and audit qualifications. Illustrative studies need not satisfy every criterion. Treating uncertain absences as unknown lowers no positive count (by construction), and admitting the four boundary readings adds at most two to any count (Online Resource 1, sheet “Coverage sensitivity”). The repeated-run count includes T. Gao et al. (2026), whose ten run-level results do not document independent resets or seeds; this code remains uncertain. Row 1 counts price-setting designs only; the interaction through payoffs or networks is discussed in Section 6.3.
Table 4 Selected studies in which LLM agents’ decisions set prices
| Study | Institution | Agent population | Heterogeneity | Benchmark | Main aggregate result |
|---|---|---|---|---|---|
| Henning et al. (2025) | Call market with a constant fundamental value | 20 identical agents per market, six models; mixed markets of 24 agents | Across single-model markets and mixed markets | 19 human markets under the same design | Several LLM populations price near the fundamental; none approaches the human bubble magnitudes; final portfolio values are less dispersed than humans’; in mixed markets, two of three near the fundamental and one modest bubble |
| Ouyang and Sui (2026) | Call market with a constant fundamental value (adapted from Smith et al. (1988)) | 20 agents per single-model market, 14 models; mixed markets | Across models | Historical experiment literature; fundamental value | Hump-shaped average price path; mispricing (MSE) from 0.0012 to 113.83 across models; several two-model markets between their members’ single-model levels |
| Saxena et al. (2026) | Learning-to-forecast market of Hommes et al. (2008) | Six agents per market, 15 models; a six-model mixed market; one frontier model among five bubble-forming agents | Across models and reasoning modes | Published human markets; rational-expectations paths | From bubbles larger than humans’ to pricing at or near the fundamental; in bubble-forming markets, agent-level dispersion similar to humans’; the mixed market bubbles in about half of 50 runs; two frontier models among bubble-forming agents switch to trend following |
| del Rio-Chanona et al. (2025) | Positive- and negative-feedback markets of Heemeijer et al. (2009) | Six agents per market, GPT-3.5 or GPT-4 | Temperature | Published human markets | Human feedback contrast was reproduced with three or five periods of retained reasoning; full price histories were always shown. Higher temperature helps; forecasting rules less dispersed than humans’ |
| Struski et al. (2026) | Continuous double auction with a persistent order book | 11 buyers and 11 sellers, one model per market | Endowments | Smith (1962) human markets; competitive equilibrium | No population converges fully; the smallest model is the most efficient |
| Chupilkin (2026) | Call market, posted offer, posted bid, double auction, bilateral bargaining | Four buyers and four sellers, one model family per market | Endowments; model family | Competitive equilibrium | Efficiency from 88.6% (call market) to 56.4% (bargaining); model rankings reverse across institutions |
| Shah et al. (2025b) | Sealed-bid, clock, common-value, and online auction formats | Three GPT-4 bidders in most auctions | Private values and signals | Equilibrium bids; published human data | Clock formats move bids toward value, as for humans; sealed second-price bids fall below value, unlike humans’ |
| Tolety (2025) | Repeated procurement clock auction | One to seven bidders of the same model | None (homogeneous) | Subgame-perfect equilibrium with a maximum cartel size | Two of four models sustain supracompetitive prices with two to four bidders; median prices near the competitive level with five or more |
| Agrawal et al. (2025) | Double auction with seller messaging and oversight | Five buyers and five sellers; GPT-4.1 and Claude-3.7-Sonnet | Across models | Competitive equilibrium price of 90 | Communication raises average prices from 87.71 to 90.52 (overlapping intervals); an urgency message pushes them to about 96 |
| Galanis (2026) | Prediction markets with a logarithmic market scoring rule | Three agents per market; 16 teams drawn from 11 models | Private signals; team composition | Full aggregation predicted by Ostrovsky (2012) | Median price of the winning security 0.91 overall, 0.73 and 0.5 in the two hardest structures (1,772 first-wave markets) |
| Begin et al. (2026) | Prediction market with a scoring-rule market maker | Ten agents per market; LLM judgments with rule-based betting | Model family; post-training | Single agent; independence benchmark | Pooled honest-agent error correlation 0.696 (about 1.4 effective agents under a variance proxy); a separate ten-agent scaling condition provides no demonstrated accuracy gain |
| Yang et al. (2025) | Daily call auction with price limits and a social network | 100 GPT-4o investors with personas | Personas, beliefs, information, network position | Real 2023 index data; two rule-based models | In the headline run, stylized facts closer to the data than rule-based models; lost without heterogeneity; and rumors double the sell-to-buy ratio |
| Ross et al. (2026) | Market maker with linear price impact; noise traders | LLM share varied among noise traders; one model family per market | Across models | Noise-only market | Accurate shared signals improve price discovery; at a 100% LLM share, a misleading narrative raises tracking error to five to seven times the noise-only baseline |
| Barton et al. (2026b) | Real-capital automated-market-maker tournament; perpetual futures traded mostly on paper at live prices | Thousands of user-configured production agents | User configuration | Matched retail traders on the same venue (second fleet) | Common buying and converging portfolios in the real-capital fleet; in the trailing week ending August 15, 2026, 15% of week-active second-fleet accounts had positive net ROI versus 53% in the retail comparison |
Note: Selected from the 30 studies in the synthesis set in which prices respond to the LLM agents’ own decisions: orders or forecasts that enter a price equation in the learning-to-forecast designs (del Rio-Chanona et al., 2025; Saxena et al., 2026). MSE is the mean squared error of prices relative to the fundamental value.