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A Coopetitive-Compatible Data Generation Framework for Cross-silo Federated Learning

This paper proposes CoCoGen, a framework that leverages generative AI and potential game theory to optimize cross-silo federated learning by modeling inter-organizational competition and statistical heterogeneity to maximize social welfare.

Original authors: Thanh Linh Nguyen, Quoc-Viet Pham

Published 2026-06-24

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Thanh Linh Nguyen, Quoc-Viet Pham

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 rival bakeries in a city. Each bakery has its own secret recipe book (local data) and wants to bake the best possible cake. However, they are forbidden by law from sharing their actual recipe books with each other.

To solve this, they decide to work together in a "Cross-Silo Federated Learning" (CFL) club. Instead of sharing recipes, they each bake a small batch of cakes using their own secret ingredients, send the results (how the cake turned out) to a central judge, and the judge combines these results to create one "Master Cake Recipe" for everyone to use.

The Problem: Rivals and Uneven Skills
The paper identifies two big problems with this setup:

The Rivalry (Competition): Even though they are working together, these bakeries are still competitors. They are worried that if they help too much, they might lose their edge to the other bakeries. They are "coopetitors"—cooperating to learn, but competing to win.
The Unevenness (Heterogeneity): Some bakeries have huge, diverse recipe books (lots of data), while others have very small or weird ones (e.g., only chocolate cakes, no fruit). This makes it hard to bake a Master Recipe that tastes good for everyone.

If the bakeries are too scared to contribute, or if their data is too different, the Master Recipe will be terrible. Everyone loses money, and the whole system fails.

The Solution: CoCoGen (The "Magic Ingredient" Generator)
The authors, Thanh Linh Nguyen and Quoc-Viet Pham, propose a new framework called CoCoGen. Think of this as a smart system that helps the bakeries use Generative AI (GenAI) to create "fake" but realistic practice ingredients.

Here is how CoCoGen works in simple terms:

The Magic Ingredient (GenAI): Instead of just using their limited real recipes, the bakeries use AI to generate extra "practice dough." This helps the bakeries with small or weird recipe books catch up to the others. It fills in the gaps so the Master Recipe can be baked properly.
The Game of Give-and-Take (Game Theory): The authors realized that because the bakeries are rivals, they need a fair way to decide how much "practice dough" to make. They modeled this as a Weighted Potential Game.
- Imagine a seesaw. If one bakery makes too little dough, the seesaw tips, and the Master Recipe suffers. If they make too much, they waste energy.
- CoCoGen calculates the perfect balance. It tells each bakery exactly how much AI-generated data to create so that everyone benefits, even the rivals.
The Fair Paycheck (Payoff Redistribution): To make sure the rivals don't feel cheated, the system includes a rule: if one bakery works harder (makes more data) to help the group, the system ensures they get a bigger share of the rewards later. This stops the "free-rider" problem where some try to slack off while others do the work.

What They Found (The Results)
The researchers tested this idea using a digital dataset called Fashion-MNIST (which is like a collection of pictures of clothes, used to train AI to recognize items).

The More Rivalry, The More Work Needed: They found that when the bakeries were very competitive (high rivalry), they needed to generate more AI data to keep the system working. If they didn't, the system's overall success (Social Welfare) dropped.
The More Different, The More Work Needed: When the bakeries had very different types of data (high heterogeneity), they also needed to generate more AI data to fix the imbalance.
CoCoGen Wins: Compared to other methods (like doing nothing, or just randomly generating data), CoCoGen consistently produced the best results. It managed to keep the "Master Recipe" high-quality and ensured the bakeries stayed happy and profitable, even when they were fierce competitors.

In a Nutshell
CoCoGen is a smart rulebook that helps rival organizations work together. It uses AI to fill in data gaps and uses math to ensure everyone gets a fair deal. This way, even competitors can build a better shared AI model without worrying about losing their competitive edge or wasting resources.

Technical Summary: CoCoGen – A Coopetitive-Compatible Data Generation Framework for Cross-Silo Federated Learning

1. Problem Statement

Cross-silo Federated Learning (CFL) enables organizations (e.g., hospitals, banks) to collaboratively train AI models while preserving data privacy. However, existing approaches often overlook the dual challenge of statistical heterogeneity (non-IID data distributions across silos) and economic competition (coopetition).

In real-world scenarios, participating organizations are often market rivals. This creates a "coopetition" dynamic where:

Competition: Organizations hesitate to contribute resources due to fears of revealing competitive advantages or suffering utility losses (reduced net benefit) if the global model benefits their rivals.
Heterogeneity: Statistical differences in local data can cause the global model to diverge from optima, leading to poor generalization and low individual utility.
The Gap: Prior work has analyzed competition or heterogeneity in isolation. There is a lack of frameworks that explicitly model the interplay between these factors and their impact on organizational decision-making and system-wide social welfare. Furthermore, while Generative AI (GenAI) offers a solution for data augmentation, there is no established mechanism to optimize GenAI-based data generation strategies in competitive, heterogeneous CFL settings to maximize collective welfare.

2. Methodology: The CoCoGen Framework

The authors propose CoCoGen, a framework that integrates economic coopetition concepts with potential game theory to model and optimize CFL under these constraints.

A. System Model and Definitions

CFL Coopetition: Defined as a dual strategy where organizations cooperate to train a shared global model but compete to maximize their own downstream market revenue.
Data Strategy: Each organization $n$ utilizes a mixed dataset $D^{mix}_n = D^{loc}_n \cup D^{gen}_n$ , where $D^{gen}_n$ is data generated by GenAI. The strategy profile is the vector of generated data sizes $\mathbf{d}^{gen}$ .
Costs: The framework accounts for computational costs (energy consumption for data generation and training) and server fees. Communication costs are neglected.

B. Utility and Payoff Formulation

The utility $U_n$ for an organization is derived from a balance of gains and losses:

Gain from Cooperation: Revenue is proportional to the improvement in global model performance ( $\epsilon_0 - \epsilon(\mathbf{d}^{gen})$ ), where performance is modeled as an inverse power-law function of total data size.
Payoff Redistribution: To ensure fairness, organizations with lower contributions receive compensation from those with higher contributions. This is proportional to the marginal contribution gap and the competitive intensity ( $\gamma_{n,n'}$ ).
Coopetition Loss: Organizations incur a loss representing the revenue their competitors gain from their contributions, scaled by competitive intensity.
Constraints: The system operates under Individual Rationality (utility $\ge 0$ ) and Budget Balance (total monetary transfers sum to zero).

C. Game-Theoretic Analysis

The interaction is modeled as a Weighted Potential Game:

Players: Rational, self-interested organizations.
Strategies: The amount of GenAI data to generate.
Potential Function: The authors prove that the game possesses a weighted potential function $F(\mathbf{d}^{gen})$ . The Nash Equilibrium (NE) of the game corresponds to the minimization of this function.
Solution Mechanism: Since the optimization problem is non-convex, the authors relax the integer constraints on data size to a continuous interval. They derive the NE conditions using Karush–Kuhn–Tucker (KKT) conditions and solve for the optimal data generation strategy using a Fixed-Point Iteration (FPI) algorithm (Algorithm 1).

3. Key Contributions

Coopetitive-Compatible Framework: CoCoGen is the first framework to jointly model statistical heterogeneity and inter-organizational competition in CFL using learning performance and utility-based formulations.
Potential Game-Based Mechanism: The authors prove that each training round constitutes a weighted potential game. They derive a closed-form solution for the Nash Equilibrium, enabling organizations to determine optimal GenAI data generation strategies that maximize social welfare.
Empirical Validation: Extensive experiments on the Fashion-MNIST dataset demonstrate the framework's efficacy under varying levels of heterogeneity and competition.

4. Experimental Results

Experiments were conducted with $N=10$ organizations using the Fashion-MNIST dataset. Key findings include:

Impact of Heterogeneity and Competition: Increasing levels of statistical heterogeneity (lower Dirichlet parameter $\alpha_D$ ) and competitive intensity (higher $\bar{\gamma}$ ) significantly reduce social welfare. These conditions necessitate a larger volume of GenAI-generated data to maintain model convergence.
Performance vs. Baselines: CoCoGen consistently outperforms three baselines:
- Vanilla CFL (VCFL): No GenAI augmentation.
- Without Competition (WCO): Ignores competitive factors.
- Random Data Generation (RaDG): Randomly selects data generation amounts.
Quantitative Gains: Under high heterogeneity ( $\alpha_D = 0.1$ ), CoCoGen improved social welfare by approximately 50% over VCFL, 25.93% over WCO, and 16.89% over RaDG.
Mechanism Effectiveness: The embedded payoff redistribution mechanism effectively compensates high-contributing organizations, mitigating coopetition losses and sustaining participation incentives even in highly competitive environments.

5. Significance and Claims

The paper claims that CoCoGen provides a practical theoretical and algorithmic solution for sustaining CFL cooperation in realistic, competitive markets.

Theoretical Insight: It clarifies how the coexistence of heterogeneity and competition affects organizational behavior, showing that without specific incentives (like payoff redistribution and optimized data generation), social welfare degrades significantly.
Practical Utility: By leveraging GenAI to bridge data distribution gaps and using game theory to align individual incentives with collective welfare, CoCoGen enables organizations to benefit from collaboration despite being market rivals.
Scalability: The proposed FPI algorithm offers a computationally efficient method to derive optimal strategies, making the framework applicable to real-world CFL deployments.

The authors conclude that their work addresses the critical need to balance privacy, competition, and data heterogeneity, offering a pathway to more robust and socially optimal federated learning systems.