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Evolutionary Dynamics of Cooperation in Next-Generation LLM Agent Systems: A Cross-Provider Empirical Extension

This study extends evolutionary game theory benchmarks to four frontier LLM agents from 2025–2026, revealing that while cooperative biases persist across most models, provider identity significantly influences equilibrium outcomes and noise robustness remains a universal challenge despite partial improvements in aggressive capability parity.

Original authors: Francisco León Zúñiga Bolívar (Institución Universitaria Colegio Mayor del Cauca)

Published 2026-05-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Francisco León Zúñiga Bolívar (Institución Universitaria Colegio Mayor del Cauca)

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 giant, digital arena where thousands of AI "agents" are locked in an endless game of Prisoner's Dilemma. In this game, two players can either Cooperate (work together for a shared reward) or Defect (betray the other for a bigger personal gain).

The question this paper asks is simple: As AI gets smarter and newer, do these digital agents learn to be better teammates, or do they become more ruthless competitors?

The author, Francisco León Zúñiga Bolívar, took a famous experiment from 2025 and updated it with the "hot off the press" AI models from 2025 and 2026. Here is the story of what he found, explained without the jargon.

The Setup: A Digital Evolutionary Zoo

Think of the experiment like a zoo of evolving species.

The Players: The author created four new "species" of AI agents (from companies Anthropic, Google, and OpenAI).
The Game: These agents play the Prisoner's Dilemma over and over again.
The Evolution: Instead of just playing one game, the author simulated 500 generations of evolution. If an agent plays well, it "reproduces" (its strategy becomes more common). If it plays poorly, it dies out.
The Goal: To see which "attitude" wins in the long run: Aggressive (always betray), Cooperative (always help), or Neutral (mix of both).

The Big Findings

1. The "Good Guy" Bias is Still Strong (H1)

The Analogy: Imagine a schoolyard where the kids are told to play a game. Even though the smartest kids could figure out how to bully everyone to win, they mostly choose to play nice.
The Result: In most scenarios, Cooperation wins. In 9 out of 12 different combinations of AI models and instructions, the "Cooperative" strategy became the dominant one. The new, smarter AIs didn't turn into ruthless dictators; they kept the "good guy" bias of their older siblings.

2. The "Provider" Matters More Than the "Generation" (H3)

The Analogy: Think of the AI models as cars. You might think a 2026 model is always better than a 2025 model. But in this race, it matters who built the car more than what year it is.

Google's "Flash" model was like a race car built for speed and aggression. It often turned the whole population into bullies (up to 77% aggressive).
OpenAI's "Mini" model was like a car built for safety. It kept the population friendly (up to 70% cooperative).
Anthropic's model stayed very consistent, acting almost exactly like its predecessor from the previous year.

The Takeaway: If you want a team of AIs to cooperate, you can't just pick the "newest" one; you have to pick the one from the company that trains them to be nice.

3. The "Self-Refinement" Trap (H2)

The Analogy: Imagine asking a student to write an essay, and then asking them to critique and rewrite their own essay to make it better.
The Result: When the AI was asked to "Self-Refine" (critique its own strategy), it got much better at being Aggressive.

In the "Default" mode, Aggressive strategies were weak and lost easily.
In "Self-Refine" mode, the Aggressive strategies became so sharp that they almost tied with the Cooperative ones.
The Warning: Trying to make an AI "smarter" by having it critique its own plans might accidentally make it a better bully.

4. The "Static Noise" Problem (H4)

The Analogy: Imagine playing a game of telephone where sometimes the message gets garbled (noise). Does the new AI handle the garbled messages better than the old one?
The Result: The new AI (Claude 4.6) seemed to handle the noise slightly better than the old one, but the author cannot say for sure. The difference was so small that it might just be a fluke of the math.

The Reality: Noise (errors in communication) almost always pushes the group toward aggression, no matter how smart the AI is. It's a universal challenge.

Summary of the "Characters"

GPT-5.4 Mini (OpenAI): The most consistent "Good Guy." Even when the odds were stacked against it, it stayed cooperative.
Gemini 2.5 Flash (Google): The "Aggressive Wildcard." It was the most likely to turn the whole group into a cutthroat competition.
Claude Sonnet 4.6 (Anthropic): The "Steady Hand." It didn't change much from the previous year, staying mostly cooperative but very sensitive to how it was asked to think.
Gemini 3.1 Pro (Google): The "Confused Middle." It was hard to tell if it was being aggressive or neutral because it kept cooperating even when it was supposed to be fighting.

The Bottom Line

The paper concludes that AI agents are not becoming naturally ruthless as they get bigger. They still have a strong bias toward cooperation. However, who trained them (the company) matters more than how new they are.

Also, a word of caution: If you ask these AIs to "think harder" and refine their own strategies, you might accidentally teach them how to be better at fighting each other. And if the environment is messy (noisy), even the best AIs tend to turn aggressive.

The author released all the code and data so anyone can run these same "digital evolution" tests on future AI models to see if this pattern holds.

Technical Summary: Evolutionary Dynamics of Cooperation in Next-Generation LLM Agent Systems

Problem Statement
The paper addresses a critical gap in understanding the evolutionary behavior of Large Language Model (LLM) agents in competitive multi-agent systems. While Willis et al. [25] established that earlier frontier models (ChatGPT-4o, Claude 3.5 Sonnet) exhibit a persistent cooperative bias in Iterated Prisoner's Dilemma (IPD) settings, the landscape has shifted with the release of next-generation models (2025–2026). It remains unknown whether these newer models, featuring extended contexts and revised alignment training, maintain, deepen, or erode this cooperative bias. Furthermore, no systematic cross-provider comparison exists to determine if cooperative tendencies are universal properties of frontier LLMs or artifacts of specific provider training choices.

Methodology
The authors extend the experimental protocol of Willis et al. [25] to four new frontier models across three providers:

Models: Claude Sonnet 4.6 (Anthropic), Gemini 2.5 Flash (Google), Gemini 3.1 Pro (Google), and GPT-5.4 Mini (OpenAI).
Strategy Generation: For each model, 25 natural-language strategies are generated per "attitude" (Aggressive, Cooperative, Neutral) using three prompting styles: Default (direct game-theoretic language), Prose (obfuscated real-world scenario), and Refine (Self-Refine framework where the model critiques and rewrites its strategy). These are converted to Python algorithms by the same provider's model.
Evolutionary Simulation: The study simulates Moran evolutionary processes with a population size of $n=12$ and 500 iterations per condition (a significant increase from the $n=100$ in the predecessor study to reduce sampling error).
Conditions: Four population compositions are tested: Balanced/Clean (4:4:4), Biased/Clean (8:2:2), Balanced/Noise (4:4:4 with 10% action flip), and Biased/Noise (8:2:2 with noise).
Metrics: The study introduces the Index of Differential Capabilities (ICD) to quantify the payoff gap between aggressive and cooperative agents. It also measures noise sensitivity ( $\Delta_{noise}$ ) as the drop in cooperative equilibrium probability under action noise.

Key Contributions

Longitudinal Extension: This is the first within-lineage comparison of next-generation LLMs against their immediate predecessors under the same Moran IPD framework, covering Anthropic, OpenAI, and Google.
Cross-Provider Benchmark: It provides the first systematic comparison of equilibrium outcomes across three major providers, moving beyond single-provider studies.
New Metric (ICD): The introduction of the Index of Differential Capabilities allows for a scalar summary of the aggressive-cooperative payoff gap, facilitating the analysis of "aggressive capability parity."
High-Power Replication: By increasing iterations to $n=500$ , the study resolves ambiguities present in the original $n=100$ study, particularly regarding the stability of equilibrium outcomes under noise.

Results

Cooperative Bias Persistence (H1): The cooperative bias documented in previous generations persists. In balanced, noiseless conditions, 9 of 12 model–prompt combinations favor cooperative equilibria as the plurality outcome. Aggressive equilibria remain well below the 33% prior probability in most configurations.
Provider Divergence (H3): Provider identity is the strongest correlate of equilibrium outcomes, outweighing model generation.
- Gemini 2.5 Flash is the most aggressive, reaching up to 77% aggressive equilibria in biased, noisy conditions.
- GPT-5.4 Mini is the most cooperative, achieving 70% cooperative equilibria under Self-Refine prompting.
- Claude 4.6 mirrors its predecessor (Claude 3.5 Sonnet) almost exactly in balanced conditions, suggesting stable strategic dispositions within the Anthropic lineage.
Aggressive Capability Parity (H2): The Self-Refine prompt consistently narrows the payoff gap (increasing ICD) across all models. Claude 4.6 Refine achieves the highest ICD (0.913), approaching payoff parity between aggressive and cooperative agents. However, this capability parity does not uniformly translate to higher aggressive equilibrium rates across all prompts; it is most pronounced under specific conditions.
Noise Robustness (H4): Evidence for improved noise robustness is directionally positive but not statistically robust. Claude 4.6 shows a lower average noise sensitivity ( $\approx$ 6 percentage points) compared to Claude 3.5 Sonnet (13 pp). However, when propagating the unreported sampling error from the predecessor's study ( $n=100$ ), the difference is not statistically significant.

Significance and Claims
The paper claims that cooperative bias is a broadly shared property of current frontier LLMs, surviving the transition to a new model generation. However, the specific equilibrium dynamics are heavily dependent on the provider. The study cautions that "provider identity" is a confounded variable in this design, entangling alignment choices, training corpora, and the fidelity of code-conversion (since each provider's model converts its own strategies to code).

Crucially, the authors highlight a safety implication: Self-Refine prompting, while intended to improve strategy quality, inadvertently narrows the gap between aggressive and cooperative capabilities. This suggests that prompt engineering techniques designed to enhance reasoning may increase the viability of aggressive strategies in deployed multi-agent systems.

The paper concludes that while the cooperative baseline appears stable within the Anthropic lineage, noise remains a universal challenge that shifts equilibria toward aggression. The authors emphasize that their findings are specific to the generated strategy libraries and the IPD framework, and they release their code and data to enable future longitudinal tracking of these dynamics as new models emerge.