🎯 GameTheory-Formulator-Model

Phase 3 of the Alogotron Game Theory AI Pipeline — A QLoRA adapter that teaches language models to translate real-world scenarios into formal game theory formulations.

Overview

The Alogotron Game Theory Pipeline

This model is part of a 3-phase training pipeline:

What This Model Does

Given a real-world scenario (business competition, political negotiation, security analysis, etc.), this model:

1. 📋 Formulation Steps — Walks through the reasoning to identify the game structure
2. 🎮 Formal Game Model — Identifies players, strategies, payoffs, information structure, and solution concept
3. 🧮 Solution — Solves the formulated game (Nash equilibrium, dominant strategies, etc.)
4. 🌍 Real-World Interpretation — Translates the mathematical solution back to actionable insights

Training Details

QLoRA Configuration

Training Hyperparameters

Training Metrics

Evaluation Results

Tested on 20 held-out examples across 6 domains and 3 difficulty levels:

By Domain

By Difficulty

Usage

With PEFT + Transformers

from transformers import AutoModelForCausalLM, AutoTokenizer, BitsAndBytesConfig
from peft import PeftModel
import torch

# Load base model in 4-bit
bnb_config = BitsAndBytesConfig(
    load_in_4bit=True,
    bnb_4bit_quant_type="nf4",
    bnb_4bit_compute_dtype=torch.bfloat16,
    bnb_4bit_use_double_quant=True,
)

base_model = AutoModelForCausalLM.from_pretrained(
    "Qwen/Qwen2.5-7B-Instruct",
    quantization_config=bnb_config,
    device_map="auto",
)
tokenizer = AutoTokenizer.from_pretrained("Qwen/Qwen2.5-7B-Instruct")

# Load the Formulator adapter
model = PeftModel.from_pretrained(base_model, "Alogotron/GameTheory-Formulator-Model")
model.eval()

# Create a prompt
messages = [
    {"role": "system", "content": "You are a game theory expert. Given a real-world scenario, formulate it as a formal game theory model. Identify the players, strategies, payoffs, and information structure. Then solve the game and interpret the results."},
    {"role": "user", "content": "Two coffee shops on the same street must decide whether to offer a loyalty program. If both offer it, they split customers evenly but incur costs. If neither offers it, they split evenly with no extra cost. If only one offers it, that shop attracts 70% of customers."}
]

text = tokenizer.apply_chat_template(messages, tokenize=False, add_generation_prompt=True)
inputs = tokenizer(text, return_tensors="pt").to(model.device)

with torch.no_grad():
    outputs = model.generate(**inputs, max_new_tokens=1024, temperature=0.3, top_p=0.9)

response = tokenizer.decode(outputs[0][inputs["input_ids"].shape[1]:], skip_special_tokens=True)
print(response)

Example Output

Input Scenario:

Two airline companies, Stellar and Haven, each control roughly half the market. They are independently deciding their pricing for the upcoming quarter...

Model Output:

Formulation Steps

Step 1 - Stellar and Haven are each making pricing decisions that directly affect each other's profits...

Step 2 - Players: Stellar and Haven...

Step 3 - Strategies: Each firm can either 'Maintain Prices' or 'Cut Prices'...

Formal Game Model

Game Type: Simultaneous Players: Stellar, Haven Strategies: Maintain Prices, Cut Prices Payoffs: Both Maintain: (54, 54), Both Cut: (18, 18)... Solution Concept: Nash Equilibrium

Solution

Both firms will cut prices. Cutting is a dominant strategy for each...

Real-World Interpretation

This is a classic Prisoner's Dilemma. Both companies rationally choose to cut prices, resulting in lower profits than cooperation would yield...

Dataset

Trained on Alogotron/GameTheory-Formulator — 1,215 expert-crafted formulation problems across 6 domains:

• Business (290): Pricing, market entry, production, R&D, supply chain
• Security (230): Cybersecurity, threat modeling, defense allocation
• Politics (195): Elections, negotiations, voting, international relations
• Social (190): Social dilemmas, public goods, coordination, trust
• Technology (165): Platform competition, standards, adoption, innovation
• Auctions (145): First-price, second-price, common value, combinatorial

Related Models & Datasets

Limitations

• Trained on synthetic formulation data; may not handle all real-world edge cases
• Formulation quality depends on scenario clarity and completeness
• Best suited for classical game theory formulations (simultaneous, sequential, auctions)
• Does not cover cooperative game theory or mechanism design (yet)

Citation

@misc{alogotron-formulator-2025,
  title={GameTheory-Formulator-Model: Real-World Scenario to Game Theory Formulation},
  author={Alogotron},
  year={2025},
  publisher={HuggingFace},
  url={https://huggingface.co/Alogotron/GameTheory-Formulator-Model}
}

---

📚 Related Work

• "Game Theory Meets Large Language Models: A Systematic Survey" — IJCAI 2025 (arxiv:2502.09053) — The definitive survey on game theory × LLMs, covering RLHF alignment, multi-agent interactions, and strategic reasoning.
• DeepMind SHOR-PSRO (April 2026) — LLM-driven rewriting of game theory algorithms that outperformed hand-designed baselines (MarkTechPost).
• GT-HarmBench — Game-theoretic framing for AI safety benchmarking (arxiv:2602.12316).

📄 Citation

@model{alogotron_gametheory_formulator_model_2026,
  author    = {Alogotron},
  title     = {GameTheory-Formulator-Model: Real-World Scenario to Formal Game Theory},
  year      = {2026},
  publisher = {Hugging Face},
  url       = {https://huggingface.co/Alogotron/GameTheory-Formulator-Model},
  note      = {Phase 3 formulation adapter achieving 100\% valid formulation rate}
}