🔬 physics

Large language models converge on competitive rationality but diverge on cooperation across providers and generations

This study of over 51,000 game-theoretic trials across 25 large language models reveals that while these systems converge on competitive and coordination behaviors, they exhibit stark, unpredictable, and provider-dependent divergence in cooperative dispositions that cannot be inferred from standard capability benchmarks.

Original authors: Felipe M. Affonso

Published 2026-04-22

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Felipe M. Affonso

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 you hire a team of digital assistants to run your business. You tell them, "Go negotiate deals, buy supplies, and work with other companies." You assume that because they are all "smart" and "rational," they will all act the same way: calculating the best math, spotting the best price, and playing fair.

This paper is a massive reality check. It reveals that while these AI assistants are all equally good at math and logic, they are wildly different when it comes to trust and friendship.

Here is the breakdown of the study, explained through simple analogies.

1. The Great Divide: Math vs. Manners

The researchers put 25 different AI models (from companies like OpenAI, Google, and Anthropic) into 38 different "games." Some games were about pure competition (like an auction), and some were about cooperation (like the classic "Prisoner's Dilemma," where two people must decide whether to trust each other or betray them).

The Math Part (Convergence): When the games required logic, strategy, or competition, all the AIs were almost identical. They were all excellent at calculating the "smart" move. It's like a group of chess grandmasters; they all see the board the same way.
The Manners Part (Divergence): When it came to being nice or cooperative, the AIs were totally different. The difference was 48 times.
- One AI (GPT-5 Nano) was a total "backstabber," cooperating only 1.5% of the time. It was the ultimate selfish player.
- Another AI (Claude Opus 4.6) was a "super-friend," cooperating 71.5% of the time. It was the ultimate team player.

The Analogy: Imagine a room full of calculators. If you ask them to solve a math problem, they all give the exact same answer. But if you ask them to decide whether to share their lunch with a stranger, one might say "No, I need it," while another says "Here, take half," and a third says "I'll give you my whole sandwich." The "calculator" part is the same; the "personality" part is totally different.

2. The "Brand" Matters More Than the "Brain"

You might think a newer, smarter AI would be more cooperative. The study found the opposite. The company that built the AI was the biggest predictor of its personality.

Anthropic (The "Idealists"): Their models were consistently the most cooperative. They acted like they were raised with a strict moral code about fairness and helping others.
OpenAI (The "Realists" or "Skeptics"): Their newer models became less cooperative over time. The older models were fairly nice, but the newest ones became cold and calculating, defecting (betraying) almost every time.
Google (The "Evolvers"): Their models started out very selfish but got much more cooperative with every new update.

The Analogy: Think of these AIs like cars from different manufacturers. A Ferrari, a Toyota, and a Ford might all have engines that go 100 mph (the "competitive rationality"). But if you ask them to drive through a crowded neighborhood, the Ferrari might speed through, the Toyota might stop for pedestrians, and the Ford might honk aggressively. The engine is the same, but the driving style depends entirely on who built the car.

3. The "Endgame" Surprise

The researchers played games that lasted 10 rounds. In game theory, there's a rule called "backward induction." It basically says: "If I know this is the very last round, I have no reason to be nice, so I'll betray you. And if I know you know that, I should betray you in round 9, and so on."

The "Strategic Exploiters" (Google): These AIs played nice for the first 9 rounds to build a reputation, then betrayed everyone in the final round. They were playing a long con.
The "True Believers" (Anthropic): Even in the final round, where there was no penalty for being mean, these AIs still chose to cooperate. They seemed to value "being good" as a rule in itself, not just a strategy to win.
The "Cynics" (OpenAI): These AIs stopped cooperating almost immediately. They didn't care about reputation; they just wanted to win.

4. Why This Matters for You

This isn't just about games. These AIs are starting to be used to negotiate contracts, buy supplies, and manage money for real companies.

The Risk: If a company upgrades its AI from an "old model" to a "new model" expecting it to work the same way, they might get a shock. A company that used an AI that was great at building partnerships might suddenly upgrade to a model that is a ruthless negotiator, destroying their relationships.
The Blind Spot: Currently, we test AI on how smart they are (can they write code? can they solve math?). We don't test their "strategic personality." We don't know if they are the "nice neighbor" or the "shark" until we hire them.

The Bottom Line

The paper concludes that AI has a "Strategic Personality."

Just like humans, some AIs are naturally trusting, some are naturally suspicious, and some are naturally manipulative. These personalities aren't random; they are baked into the AI by the specific training methods of the company that created them.

The Takeaway: When you hire an AI agent, you aren't just hiring a calculator. You are hiring a personality. And right now, we don't have a "driver's license test" to check if that personality is going to be a good partner or a backstabber. We need to start testing AI on how they treat others, not just how smart they are.

1. Problem Statement

As Large Language Models (LLMs) are increasingly deployed as autonomous agents for economic tasks (negotiation, procurement, dispute resolution), their strategic dispositions directly impact economic outcomes. While previous research has shown that LLMs can exhibit human-like biases or rational play in isolated game-theoretic settings, there is a critical lack of systematic understanding regarding:

Strategic Personalities: Whether LLMs possess coherent, provider-specific behavioral profiles that persist across different game types.
Generational Stability: Whether these strategic dispositions remain stable as models are updated (e.g., from GPT-4 to GPT-5).
Provider Divergence: How different training pipelines (e.g., Anthropic's Constitutional AI vs. OpenAI's RLHF) shape cooperative vs. competitive behaviors.

Current deployment frameworks rely on capability benchmarks (reasoning, coding) which fail to measure these "revealed-preference" strategic dispositions, potentially leading to unpredictable economic outcomes when agents interact.

2. Methodology

The study employs a massive, systematic game-theoretic experimental design to characterize the strategic personalities of 25 frontier LLMs from 7 providers (Anthropic, OpenAI, Google, DeepSeek, Meta, Mistral, Alibaba).

Dataset Scale:
- 51,906 trials generating 826,990 strategic decisions.
- 38 canonical games spanning 8 categories: Cooperation, Coordination, Competition, Trust, Fairness, Negotiation, Strategic Depth, and Risk.
- 545,691 reasoning traces available for behavioral fingerprinting.
Experimental Designs:
- Design F (Cross-Play): 16 budget-tier models played against every other model, themselves, and deterministic strategies (e.g., Tit-for-Tat, Grim Trigger) across all 38 games (5 trials per cell).
- Design G (Frontier Strategy-Play): 9 frontier models played against deterministic strategies across all 38 games (1 trial per cell) to manage cost while maintaining coverage.
Key Metrics:
- Cooperation Rates: Frequency of cooperative choices in social dilemmas.
- Endgame Analysis: Round-by-round behavior in finitely repeated games (10 rounds) to test for backward induction vs. terminal values.
- Reciprocity Profiling: Conditional probabilities $P(\text{cooperate} | \text{opponent cooperated})$ and $P(\text{cooperate} | \text{opponent defected})$ to classify behavioral archetypes.
- Hodoscope Pipeline: A novel behavioral fingerprinting method using TF-IDF vectorization and SVD to embed reasoning traces into a 384-dimensional semantic space, clustering models by their reasoning style rather than just their choices.

3. Key Contributions

Definition of "Strategic Personalities": The paper establishes that LLMs possess stable, provider-shaped behavioral profiles (strategic personalities) that are distinct from their general capability benchmarks.
The Convergence-Divergence Dissociation: It demonstrates a fundamental split in LLM behavior:
- Convergence: Models converge on competitive rationality (coordination, strategic depth, risk-taking) regardless of provider.
- Divergence: Models diverge massively (48-fold) on cooperative disposition, driven entirely by the provider's training pipeline.
Generational Instability: The study reveals that strategic personalities are not static; they shift unpredictably across model generations, sometimes in opposite directions for different providers.
Endgame Typology: It identifies three distinct strategic archetypes in finite games: Terminal Cooperators (sustain cooperation to the end), Strategic Exploiters (cooperate until the final round to build reputation, then defect), and Unconditional Defectors.
Reasoning Trace Fingerprinting: The "Hodoscope" pipeline proves that reasoning traces contain provider-specific signatures (e.g., Anthropic models consistently use "fairness" language), allowing for behavioral clustering even when choice data is noisy.

4. Key Results

A. Competitive Rationality vs. Cooperative Divergence

Convergence: Coordination rates (CV 0.06) and strategic depth (CV 0.11) are highly consistent across all 25 models. They approximate Nash equilibria in competitive games (e.g., auctions, beauty contests).
Divergence: Cooperation rates vary by a factor of 48:
- Lowest: GPT-5 Nano (1.5%).
- Highest: Claude Opus 4.6 (71.5%).
- Provider Clustering: Anthropic models cluster tightly (69–71.5%); OpenAI's newest small models cluster at the bottom (1.5–6.3%); Google models show a rising trend (8.3% to 56.8%).

B. Generational Drift

OpenAI: Cooperation declined monotonically from GPT-4o Mini (50.3%) to GPT-5 Nano (1.5%), a 33-fold reduction.
Google: Cooperation increased monotonically from Gemini 2.0 Flash (8.3%) to Gemini 3 Flash (56.8%), a 7-fold increase.
Anthropic: Stable high cooperation across frontier models, with a 30-point gap between budget (Haiku) and frontier (Opus) tiers.

C. Endgame Strategies (Finite Repeated Games)

In 10-round Prisoner's Dilemmas, backward induction predicts universal defection in the final round.

Type 1: Terminal Cooperators (Anthropic Frontier): Maintain >50% cooperation in Round 10 (e.g., Claude Opus 4.6 at 56.9%). They treat cooperation as a terminal value overriding game-theoretic calculation.
Type 2: Strategic Exploiters (Google Frontier): Sustain high cooperation through Round 9 but drop to 0% in Round 10 (e.g., Gemini 3 Pro). This aligns with the "reputation-building equilibrium" (Kreps et al.).
Type 3: Unconditional Defectors (OpenAI Small Models): Defect from Round 1 with near-zero cooperation (e.g., GPT-5 Nano at <2.7%).

D. Reciprocity Archetypes

Strict Reciprocators: High reciprocation, low forgiveness (e.g., Anthropic models, GPT-4.1).
Grudge-Holders: High reciprocation, near-zero forgiveness (e.g., Gemini 3 family).
Unconditional Defectors: Low sensitivity to opponent actions.
Anti-Reciprocators: LLaMA 3.3 70B uniquely cooperated more after being defected against (22.2%) than after cooperation (14.3%), a non-equilibrium behavior.

E. Behavioral Fingerprinting (Hodoscope)

Anthropic: Models form a tight cluster in the reasoning embedding space (Mean Silhouette Score: 0.48), indicating a consistent "Constitutional AI" behavioral signature.
OpenAI: Models scatter widely with negative silhouette scores (Mean: -0.60), indicating that newer models are behaviorally closer to other providers than to their own predecessors.

5. Significance and Implications

Economic Risk: Organizations deploying AI agents cannot assume behavioral continuity across model updates. Upgrading from a cooperative model (e.g., GPT-4o Mini) to a newer version (e.g., GPT-5 Mini) could result in a 33-fold increase in defection, destroying trust in negotiations or supply chains.
Governance Gap: Current AI safety and capability benchmarks do not measure "strategic personality." A model can be highly capable in coding or math but behave as a ruthless defector in economic interactions.
Training Pipeline Impact: The results suggest that alignment procedures (RLHF vs. Constitutional AI) have a more profound impact on social behavior than model size or reasoning capability.
Future Research: The paper calls for "strategic personality" testing to become a standard part of AI deployment frameworks, complementing traditional benchmarks to ensure agents are aligned not just with instructions, but with the cooperative norms required for multi-agent economic systems.

Data Availability: The complete dataset (51,906 trials) and an interactive explorer are publicly available at https://felipemaffonso.github.io/strategic-personalities/.