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arxiv: 2604.14886 · v1 · submitted 2026-04-16 · 💻 cs.AI · cs.DC· cs.GT

Recognition: unknown

Cooperate to Compete: Strategic Data Generation and Incentivization Framework for Coopetitive Cross-Silo Federated Learning

Thanh Linh Nguyen , Nguyen Van Huynh , Quoc-Viet Pham
Authors on Pith no claims yet

Pith reviewed 2026-05-10 11:29 UTC · model grok-4.3

classification 💻 cs.AI cs.DCcs.GT
keywords coopetitive federated learningsynthetic data generationpotential gameincentive mechanismcross-silo learningnon-IID datastrategic decision makingsocial welfare maximization
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The pith

Organizations in cross-silo federated learning strategically choose synthetic data volumes by modeling each round as a weighted potential game that balances model gains against competitive losses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Cross-silo federated learning lets organizations train shared models without exchanging raw data, yet participants also compete in downstream markets. When data are non-identical across sites, contributions that improve the global model can also strengthen rivals, creating a dilemma that standard incentive schemes ignore. CoCoGen+ treats the volume of synthetic data each organization generates as a strategic variable and frames every training round as a weighted potential game whose payoffs include learning improvements, generation costs, and utility losses inflicted on competitors. The framework supplies a tractable equilibrium characterization and generation strategies that maximize social welfare, then adds a payoff-redistribution mechanism to offset competition-induced losses and sustain long-term participation. Experiments across learning tasks show that the resulting strategies adapt to data heterogeneity and competition intensity while outperforming prior approaches in efficiency.

Core claim

CoCoGen+ formulates each training round as a weighted potential game in which organizations endogenously decide synthetic data generation volumes to optimize their individual utilities, incorporating performance gains from the improved global model, computational costs, and competition-caused utility degradation; the paper derives a tractable equilibrium characterization and implementable generation strategies that maximize social welfare, then integrates a payoff redistribution incentive to compensate organizations for both their contributions and the competitive harms they incur.

What carries the argument

The weighted potential game formulation that lets each organization treat synthetic data volume as a continuous strategic variable whose marginal effect on global model quality and rival utility determines equilibrium generation levels.

If this is right

  • Equilibrium data-generation levels are reached when each organization accounts for how its choices alter both the global model and competitors' downstream utilities.
  • Social welfare is increased by implementing the characterized equilibrium strategies rather than independent or uniform generation policies.
  • Payoff redistribution offsets the utility degradation organizations suffer from strengthening rivals, thereby supporting continued participation.
  • Asymmetric learning gains caused by non-IID data are mitigated through the joint optimization of generation volumes and incentives.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same game structure could be adapted to other settings where agents jointly improve a shared resource while still competing over its downstream uses, such as collaborative robotics or shared supply-chain optimization.
  • If organizations cannot reliably estimate rivals' utility losses, the equilibrium may need to be approximated through repeated interaction or partial information sharing.
  • Higher competition intensity is predicted to reduce synthetic data generation, which could slow global model convergence unless offset by stronger redistribution incentives.

Load-bearing premise

That organizations can accurately quantify the marginal impact of their synthetic data volume on both the shared model and rivals' utilities, and that the resulting game admits a tractable equilibrium that remains stable under realistic non-IID distributions and changing competition intensities.

What would settle it

A controlled deployment in which organizations follow the derived equilibrium strategies yet exhibit lower overall participation rates or reduced social welfare compared with non-strategic baselines when data heterogeneity and market competition are high.

Figures

Figures reproduced from arXiv: 2604.14886 by Nguyen Van Huynh, Quoc-Viet Pham, Thanh Linh Nguyen.

Figure 1
Figure 1. Figure 1: Coopetitive cross-silo federated learning setting with [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: CoCoGen+ architecture with workflow. B. GenAI-based Cross-silo Federated Learning Workflow CFL organizations collaboratively train the global model under the coordination of a central server using their private data. Each organization owns a local model architecture with the same dimension as the global model architecture [30]. The per-round CFL training process is as follows (see [PITH_FULL_IMAGE:figures… view at source ↗
Figure 3
Figure 3. Figure 3: 𝜖𝑛 with respect to the number of local training data using different datasets and deep neural network architectures. • Without Data Generation (WDG). In WDG, GenAI￾based data generation mechanisms are not applied, but payoff redistribution-based incentive solution is still used (i.e., 𝑑 gen 𝑛 = 0, 𝛾𝑛,𝑛′ ≠ 0,∀𝑛, 𝑛′ ∈ N, 𝑛′ ≠ 𝑛). • Random Data Generation (RaDG). In this RaDG scheme, organizations randomly ge… view at source ↗
Figure 4
Figure 4. Figure 4: Impact of 𝛾¯ and 𝛼𝐷 on the organization’s data generation strategy and the social welfare of CoCoGen+. three datasets with a fixed value4 of 𝜉 = 90. Under highly heterogeneous data conditions (e.g., 𝛼𝐷 = 0.1), increasing 𝛾¯ exacerbates the demand for substantial data augmentation volumes among organizations. This behavior is driven by the proposed payoff redistribution mechanism in Eq. (10), wherein compet… view at source ↗
Figure 5
Figure 5. Figure 5: Impacts of payoff redistribution rate 𝜉 on data contributions across organizations and social welfare over three datasets with 𝛼𝐷 = 0.1 and 𝛾¯ = 0.8956 in CoCoGen+. for rewards. As 𝛾¯ intensifies, the marginal utility gained from outperforming competitive organizations increases, effectively incentivizing a tournament dynamic [52] where organizations try to maximize their payoff defined in Eq. (11) through… view at source ↗
Figure 6
Figure 6. Figure 6: The utility of organization across different [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Efficiency of CoCoGen+ compared to baseline methods with (top) varying 𝛼𝐷 and 𝛾 = 0.4782 and (bottom) varying 𝛾 and 𝛼𝐷 = 0.5 for three datasets FMNIST, CIFAR-10, and CIFAR100 from left to right. can dominate, reducing social welfare. As 𝜉 increases toward 𝜉 ∗ , redistribution partially internalizes competitive externalities such as losses from exposing valuable data features, curbing excessive generation, … view at source ↗
read the original abstract

In data-sensitive domains such as healthcare, cross-silo federated learning (CFL) allows organizations to collaboratively train AI models without sharing raw data. However, practical CFL deployments are inherently coopetitive, in which organizations cooperate during model training while competing in downstream markets. In such settings, training contributions, including data volume, quality, and diversity, can improve the global model yet inadvertently strengthen rivals. This dilemma is amplified by non-IID data, which leads to asymmetric learning gains and undermines sustained participation. While existing competition-aware CFL and incentive-design approaches reward organizations based on marginal training contributions, they fail to account for the costs of strengthening competitors. In this paper, we introduce CoCoGen+, a coopetition-compatible data generation and incentivization framework that jointly models non-IID data and inter-organizational competition while endogenizing GenAI-based synthetic data generation as a strategic decision. Specifically, CoCoGen+ formulates each training round as a weighted potential game, where organizations strategically decide how much synthetic data to generate by balancing learning performance gains against computational costs and competition-caused utility losses. We then provide a tractable equilibrium characterization and derive implementable generation strategies to maximize social welfare. To promote long-term collaboration, we integrate a payoff redistribution-based incentive mechanism to compensate organizations for their contributions and competition-caused utility degradation. Experiments on varying learning tasks validate the feasibility of CoCoGen+. The results show how non-IID data, competition intensity, and incentives shape organizational strategies and social welfare, while CoCoGen+ outperforms baselines in efficiency.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces CoCoGen+, a coopetition-compatible framework for cross-silo federated learning that endogenizes GenAI-based synthetic data generation as a strategic decision. It formulates each training round as a weighted potential game in which organizations choose synthetic data volumes to balance global model performance gains against computational costs and competition-induced utility losses from strengthening rivals. The paper provides a tractable equilibrium characterization, derives implementable generation strategies that maximize social welfare, and integrates a payoff redistribution incentive mechanism to sustain long-term participation. Experiments on varying learning tasks are reported to validate feasibility, illustrate effects of non-IID data and competition intensity, and demonstrate outperformance over baselines.

Significance. If the weighted potential game property and equilibrium characterization hold for general non-IID distributions, the framework would offer a principled game-theoretic method for aligning individual incentives with collective welfare in competitive FL settings, addressing a key barrier to sustained participation in data-sensitive domains such as healthcare.

major comments (2)
  1. [Weighted potential game formulation and equilibrium characterization] The modeling section on the weighted potential game: the utilities (performance gain minus cost minus rival-utility loss) must satisfy the defining condition that there exists a potential function Φ and fixed weights w_i such that any unilateral change in an organization's synthetic data volume produces Δu_i = w_i ΔΦ. The competition-loss term depends on asymmetric model improvements under non-IID partitions, yet no explicit construction of Φ or proof that the differential condition holds for arbitrary competition intensities is provided; this assumption is load-bearing for the tractable equilibrium characterization and the derived welfare-maximizing strategies.
  2. [Experiments] The experimental validation section: no details are given on the steps used to derive or compute the equilibria, the specific numerical values or sensitivity ranges chosen for the free parameters (competition intensity coefficient, synthetic data cost weight, welfare redistribution weights), statistical significance of performance differences, or controls against post-hoc strategy tuning; without these, the claims of outperformance and welfare maximization cannot be independently verified.
minor comments (1)
  1. [Abstract] The abstract could more explicitly separate the theoretical claims (potential-game formulation and equilibrium derivation) from the empirical observations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and outline the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: The modeling section on the weighted potential game: the utilities (performance gain minus cost minus rival-utility loss) must satisfy the defining condition that there exists a potential function Φ and fixed weights w_i such that any unilateral change in an organization's synthetic data volume produces Δu_i = w_i ΔΦ. The competition-loss term depends on asymmetric model improvements under non-IID partitions, yet no explicit construction of Φ or proof that the differential condition holds for arbitrary competition intensities is provided; this assumption is load-bearing for the tractable equilibrium characterization and the derived welfare-maximizing strategies.

    Authors: We agree that an explicit construction of the potential function Φ and a rigorous proof of the weighted potential game property are required to substantiate the equilibrium characterization. The manuscript states that the utilities admit a weighted potential but omits the full derivation for space reasons. In the revision we will add the explicit form of Φ (a weighted sum of global performance, individual generation costs, and competition-induced losses) together with a complete proof that Δu_i = w_i ΔΦ holds for arbitrary non-IID partitions and competition intensities. This addition will be placed in the modeling section immediately after the utility definition. revision: yes

  2. Referee: no details are given on the steps used to derive or compute the equilibria, the specific numerical values or sensitivity ranges chosen for the free parameters (competition intensity coefficient, synthetic data cost weight, welfare redistribution weights), statistical significance of performance differences, or controls against post-hoc strategy tuning; without these, the claims of outperformance and welfare maximization cannot be independently verified.

    Authors: We acknowledge that the experimental section currently lacks the implementation details needed for reproducibility. In the revised manuscript we will expand the experimental setup subsection to describe: (i) the exact algorithm and convergence criteria used to compute the Nash equilibria of the weighted potential game; (ii) the concrete numerical values and tested ranges for the competition intensity coefficient, synthetic-data cost weight, and redistribution weights; (iii) statistical significance results (paired t-tests or Wilcoxon signed-rank tests with p-values) computed over at least ten independent runs with different random seeds; and (iv) the controls employed, including pre-specified parameter grids and ablation studies, to guard against post-hoc tuning. These additions will allow independent verification of the reported performance gains and welfare improvements. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper claims to formulate each training round as a weighted potential game and derive tractable equilibrium strategies from balancing performance gains, costs, and competition losses. No quoted equations or sections in the provided text reduce the equilibrium characterization or welfare-maximizing strategies to fitted parameters by construction, self-definition of utilities, or self-citation chains. The formulation is presented as an independent modeling choice, with experiments serving as validation rather than input to the derivation. The central claim remains self-contained against external game-theoretic benchmarks and does not exhibit the required reduction for circularity flags.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 1 invented entities

The framework rests on standard rational-agent assumptions from game theory plus paper-specific modeling choices for synthetic data as a controllable strategic variable and competition as a direct utility penalty; several free parameters for costs and weights are required to close the model.

free parameters (3)
  • competition intensity coefficient
    Scales the utility loss from strengthening rivals; appears as a tunable input in the potential game payoff.
  • synthetic data cost weight
    Balances computational cost of GenAI generation against learning gains; chosen or fitted per organization or task.
  • welfare redistribution weights
    Determine how payoffs are reallocated to compensate for contributions and competitive harm.
axioms (2)
  • domain assumption Organizations are rational utility maximizers who internalize both learning gains and competitor-strengthening losses.
    Invoked when modeling strategic synthetic data decisions in the weighted potential game.
  • ad hoc to paper Synthetic data volume can be treated as a continuous, costed decision variable whose marginal contribution to the global model is quantifiable.
    Required to endogenize GenAI generation inside the game; not standard in prior CFL literature.
invented entities (1)
  • CoCoGen+ weighted potential game formulation no independent evidence
    purpose: Jointly captures strategic synthetic data generation, non-IID effects, and competition costs.
    New modeling construct introduced to derive equilibrium strategies and welfare-maximizing incentives.

pith-pipeline@v0.9.0 · 5598 in / 1630 out tokens · 73477 ms · 2026-05-10T11:29:36.756293+00:00 · methodology

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