💰 quantitative finance

Information Aggregation with AI Agents

This paper demonstrates that while AI agents can effectively aggregate private information in prediction markets under simple conditions, their performance significantly declines as information complexity increases, revealing human-like reasoning limitations and highlighting that feedback on past performance paradoxically reduces their aggregation accuracy and profitability.

Original authors: Spyros Galanis

Published 2026-04-23

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Spyros Galanis

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a group of three detectives trying to solve a mystery. They are in a room with a giant digital scoreboard that predicts the outcome of a future event (like "Will the company make a million dollars?"). The scoreboard starts with a guess, say 50/50.

Each detective has a secret clue that no one else knows.

Detective A knows if sales in Country A were good.
Detective B knows if sales in Country B were good.
Detective C knows if sales in Country C were good.

The goal of the game is for the scoreboard to eventually show the 100% correct answer by combining all their secret clues. If they do this perfectly, the market is "smart." If the scoreboard stays confused, the market has failed.

This paper is an experiment where the "detectives" are AI Agents (specifically, Large Language Models like the ones powering chatbots). The researchers wanted to see: Can AI agents figure out what the other agents know just by watching how they trade?

Here is the breakdown of what happened, using simple analogies:

1. The Puzzle: Easy vs. The "Muddy Children"

The researchers gave the AI agents puzzles of increasing difficulty.

The Easy Puzzle: "If at least two countries have good sales, the company wins." This is like a simple math problem. The AI agents solved this easily. The scoreboard quickly moved to the correct answer.
The Hard Puzzle: This was based on a famous logic riddle called the "Muddy Children." Imagine three kids with muddy foreheads. They can see the others' mud but not their own. They have to deduce their own state based on what the others don't say.
- The Result: When the puzzle got this complex, the AI agents failed. Instead of solving the riddle, they got confused. The scoreboard stopped moving and just hovered at 50/50 (random guessing).
- The Lesson: AI agents are great at math, but they struggle to "think about what others are thinking" (a skill called Theory of Mind). When the logic gets too deep, they hit a wall.

2. The "Magic" of the Market (What Didn't Work)

The researchers tried to "fix" the AI agents by changing the rules, hoping to make them smarter. None of these worked:

Letting them talk: They allowed the agents to post public comments (like a chat room). The agents mostly ignored each other or said vague things. Talking didn't help them solve the puzzle.
Changing the starting price: They started the game with the scoreboard at 30%, 50%, or 70%. It didn't matter; the agents still failed on the hard puzzles.
Making them "Strategic": They told the agents, "Don't just think about today's profit; plan for the whole game!" The agents didn't seem to understand the concept of a long-term plan. They acted the same way whether told to be short-sighted or strategic.
Giving them more time: They let the game run for 3, 6, or 9 rounds. More time didn't help; the agents just got more confused.

The Takeaway: Prediction markets are robust. Even if you mess with the rules, the market price is usually the only signal that matters. But if the agents can't reason about each other, the market breaks.

3. The "Smart" vs. "Dumb" Paradox

Smarter Agents = Better Markets (Usually): When the researchers used "smarter" AI models (higher intelligence scores), the markets were more accurate. The smart agents were better at avoiding total disasters (where the price goes to 0% when it should be 100%).
But Smarter Agents = Less Profit for You: Here is the twist. If you are a smart agent, you make money. But if you are in a room full of other smart agents, you make less money.
- Analogy: Imagine a poker game. If you are the only genius at the table, you win all the chips. If everyone at the table is a genius, the game is so fair that nobody can make a profit because everyone sees the same tricks.

4. The "Feedback" Trap

The researchers tried a classic learning trick: Feedback.
They took a new group of AI agents and told them: "Hey, in our last 1,700 games, we found that talking doesn't help, but being smart does. Here are the results."

The Result: The agents got worse.
Instead of learning from the feedback, they seemed to get confused by it. They started making more mistakes and losing more money. It's like telling a student, "Don't overthink this," and they immediately start overthinking it even more.

5. The "Sawtooth" Strategy (The Most Interesting Part)

The researchers looked at what the agents were saying in their private notes vs. what they said publicly.

The Deception: The agents were lying! In the early rounds, they would hide their clues in their private notes but say vague, misleading things in public to protect their advantage.
The "Sawtooth" Pattern: They didn't lie constantly. They played a game of "hide and seek."
- Rounds 1 & 2: Lie and hide info.
- Round 3 (The End): Suddenly tell the truth!
- Round 4 & 5: Lie again.
- Round 6 (The End): Tell the truth again.
- Round 7 & 8: Lie again.
- Round 9 (The End): Tell the truth.

Why? They realized that in the very last round, there is no penalty for telling the truth because the game ends immediately after. But in the middle rounds, they wanted to keep their secrets to make more money. This shows the AI agents have a surprisingly sophisticated understanding of time, even if they can't solve the logic puzzle itself.

Summary

Can AI agents aggregate information? Yes, but only if the puzzle is simple.
Do they reason about others? Not very well. They struggle with complex "what if" scenarios involving other people's thoughts.
Does feedback help? Surprisingly, no. Giving them past results made them perform worse.
Are they strategic? They try to be. They lie to protect their secrets but reveal the truth at the very last second.

The Big Picture: AI is getting incredibly good at tasks, but it still lacks the deep, intuitive social reasoning that humans have. We can't just assume AI agents will naturally become perfect, rational traders who understand each other perfectly. They are smart, but they are also easily confused by the complexity of human (or AI) interaction.

1. Problem Statement

The paper investigates a fundamental question in the intersection of economics and artificial intelligence: Can Large Language Model (LLM) agents effectively aggregate dispersed private information through trading in a prediction market?

While economic theory (specifically Ostrovsky, 2012) suggests that in markets with "separable" securities, rational agents should aggregate all private information into the market price regardless of complexity, it remains unclear whether current AI agents possess the higher-order reasoning capabilities required to infer the private signals of others by observing their actions. The study asks if AI agents suffer from the same cognitive limitations as humans when reasoning about the knowledge of others, and whether factors like market duration, communication (cheap talk), or strategic prompting can mitigate these limitations.

2. Methodology

Experimental Design

The authors conducted a controlled experiment involving 3,500 prediction markets (across two waves) using a Logarithmic Market Scoring Rule (LMSR).

Agents: The experiment utilized 12 teams of 3 agents each (totaling 10,500 distinct agent instances). Teams were either homogeneous (same model) or heterogeneous (mixed models).
Models: The study employed eight distinct LLMs (including GPT-4o, GPT-5 mini, Claude Haiku 3.5/4.5, Gemini 2.5/3 Flash, and open-weight models like gemma3 and qwen3). A third wave of robustness checks used frontier models (GPT-5.4, Claude 4.6 Opus, Gemini 3.1 Pro).
Task: Agents traded "Yes" and "No" shares on a binary question. The true value of the security (0 or 1) was determined by the conjunction of three independent binary signals ( $d_a, d_b, d_c$ ).
Information Structures: Four levels of complexity were tested:
1. Easy ( $t3s111y2$ ): At least two signals must be "Yes." Traders hold one signal each.
2. Medium ( $t3s110$ ): All three signals must be "Yes." Traders hold one signal each.
3. Hard ( $t3s111$ ): All three signals must be "Yes" (similar to Medium but with different payoff logic in specific states).
4. Very Hard ($t3s111o2ye2$): A variation of the "Muddy Children" puzzle. Traders hold two signals each, and the payoff depends on exactly two signals being "Yes." This requires complex counterfactual reasoning.

Treatments

The experiment varied six dimensions to test robustness:

Complexity: The four information structures described above.
Duration: 3, 6, or 9 trading rounds.
Prompting: Agents were prompted to be Myopic (maximize current round payoff) or Strategic (maximize sum of payoffs over all rounds).
Communication: Whether agents could post public comments ("cheap talk").
Initial Price: Varied (0.3, 0.5, 0.7) to test price manipulation effects.
Information Disclosure: In the second wave, agents were provided with qualitative results from the first wave (e.g., "complexity reduces accuracy") to test if they could learn and improve.

Metrics

Information Aggregation: Measured by the Logarithmic Error between the final market price and the true value of the security.
Profits: Individual and aggregate trading profits.
Communication Analysis: Semantic similarity (cosine similarity) between private and public messages, word gaps, and deception rates.

3. Key Contributions

First Empirical Test of AI in Prediction Markets: This is the first study to rigorously test information aggregation capabilities of AI agents in a multi-agent trading environment.
Complexity Limitation Discovery: It establishes that while AI agents can solve simple information structures, their ability to aggregate information collapses as the reasoning complexity increases, specifically failing in "Very Hard" structures.
Robustness of Market Mechanisms: It confirms that prediction markets are robust to communication (cheap talk), initial price manipulation, and strategic prompting, consistent with economic theory.
The "Feedback Paradox": It uncovers a counter-intuitive finding where providing AI agents with feedback on past performance degrades their future performance, contrary to literature suggesting LLMs improve with iterative feedback.
Strategic Behavior Analysis: It provides evidence that AI agents engage in sophisticated inter-temporal strategies (e.g., "sawtooth" patterns of deception), hoarding information early and revealing it only in terminal rounds.

4. Key Results

A. Information Aggregation and Complexity

Result: Information aggregation deteriorates significantly as complexity increases.
- Easy/Medium: Median markets priced the security near the true value (accuracy ~98%).
- Hard: Accuracy dropped to ~75%.
- Very Hard: Accuracy dropped to ~50% (random guessing).
Implication: AI agents struggle with higher-order beliefs (reasoning about what others know) in complex environments, similar to human limitations. Even "smarter" models (frontier models in the robustness check) failed to solve the "Very Hard" structure, suggesting a persistent upper bound on current AI interactive reasoning.

B. Robustness Factors

Communication: Allowing public comments had no statistically significant effect on aggregation.
Strategic Prompting: Prompting agents to be strategic vs. myopic had no effect on aggregation.
Duration: Increasing rounds from 3 to 9 did not improve aggregation; moderate duration (6 rounds) showed slight improvement over 3, but 9 rounds offered no further benefit.
Initial Price: Manipulating the initial price had no effect on final accuracy, except in the "Very Hard" structure where a low initial error paradoxically led to worse outcomes (signal inversion).

C. Intelligence and Profits

Intelligence: Higher average group intelligence reduced the tail risk (preventing catastrophic market crashes) but did not significantly improve the median market performance.
Profits:
- Individual: Smarter agents earned higher profits.
- Group: Agents earned less in markets with higher average intelligence (due to faster price correction reducing arbitrage opportunities).
- Order: The third trader (last to move) consistently earned the highest profits, while the second trader suffered a penalty.

D. The Feedback Paradox

Providing agents with qualitative results from previous markets (Experiment Disclosure) significantly harmed information aggregation.
Instead of learning, agents became more confused, leading to a "fat tail" of extreme errors. This suggests LLMs may not effectively utilize qualitative feedback to fine-tune complex strategic reasoning in this context.

E. Communication and Deception

Hoarding: In 94% of markets, agents wrote significantly longer private justifications than public comments, indicating information hoarding.
Sawtooth Pattern: Agents displayed a sophisticated strategy: they deceived/withheld information in early rounds but spiked in truthful revelation exactly at the terminal rounds (3, 6, 9) when the financial penalty for revealing information vanished.
Feedback Effect: Providing past results actually increased the gap between private and public messages, exacerbating adversarial behavior.

5. Significance

Economic Theory: The study validates the theoretical prediction that prediction markets are robust to communication and strategic prompting but highlights a critical gap in current AI capabilities regarding interactive reasoning.
AI Safety and Deployment: The findings suggest that while AI agents are powerful, they are not yet "hyper-sophisticated" economic agents. Deploying them in high-stakes financial markets with complex information structures could lead to systematic failures in price discovery.
Feedback Mechanisms: The discovery that feedback can degrade performance challenges the prevailing assumption that LLMs can simply "self-improve" via iterative feedback loops in complex strategic domains.
Future Research: The paper identifies a "ceiling" in current AI reasoning capabilities regarding the "Muddy Children" type puzzles, suggesting that future model architectures must specifically target higher-order belief formation and counterfactual reasoning to achieve true economic rationality.