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Gaming and Cooperation in Federated Learning: What Can Happen and How to Monitor It

Dongseok Kim, Hyoungsun Choi, Mohamed Jismy Aashik Rasool, Gisung Oh

TL;DR

The paper reframes Federated Learning as a governed strategic system where evaluation, information disclosure, rewards, and audits shape participant incentives. It introduces a three-layer framework and three key indices—Manipulability M, Price of Gaming PoG, and Price of Cooperation PoC—to quantify how policy choices affect metric gaming and welfare, and how participation dynamics respond over time. Through stylized simulations and a Fashion-MNIST case study, it shows that high-metric, low-welfare equilibria can emerge under narrow metric focus, and that mixed public-private evaluation, targeted audits, and calibrated sanctions can curb gaming while preserving cooperation. The work provides a practical design toolkit—penalty calibration, mixed challenges, audit budgeting, and governance checklists—to guide FL platforms toward stable, high-welfare cooperation with reduced metric gaming.

Abstract

The success of federated learning (FL) ultimately depends on how strategic participants behave under partial observability, yet most formulations still treat FL as a static optimization problem. We instead view FL deployments as governed strategic systems and develop an analytical framework that separates welfare-improving behavior from metric gaming. Within this framework, we introduce indices that quantify manipulability, the price of gaming, and the price of cooperation, and we use them to study how rules, information disclosure, evaluation metrics, and aggregator-switching policies reshape incentives and cooperation patterns. We derive threshold conditions for deterring harmful gaming while preserving benign cooperation, and for triggering auto-switch rules when early-warning indicators become critical. Building on these results, we construct a design toolkit including a governance checklist and a simple audit-budget allocation algorithm with a provable performance guarantee. Simulations across diverse stylized environments and a federated learning case study consistently match the qualitative and quantitative patterns predicted by our framework. Taken together, our results provide design principles and operational guidelines for reducing metric gaming while sustaining stable, high-welfare cooperation in FL platforms.

Gaming and Cooperation in Federated Learning: What Can Happen and How to Monitor It

TL;DR

The paper reframes Federated Learning as a governed strategic system where evaluation, information disclosure, rewards, and audits shape participant incentives. It introduces a three-layer framework and three key indices—Manipulability M, Price of Gaming PoG, and Price of Cooperation PoC—to quantify how policy choices affect metric gaming and welfare, and how participation dynamics respond over time. Through stylized simulations and a Fashion-MNIST case study, it shows that high-metric, low-welfare equilibria can emerge under narrow metric focus, and that mixed public-private evaluation, targeted audits, and calibrated sanctions can curb gaming while preserving cooperation. The work provides a practical design toolkit—penalty calibration, mixed challenges, audit budgeting, and governance checklists—to guide FL platforms toward stable, high-welfare cooperation with reduced metric gaming.

Abstract

The success of federated learning (FL) ultimately depends on how strategic participants behave under partial observability, yet most formulations still treat FL as a static optimization problem. We instead view FL deployments as governed strategic systems and develop an analytical framework that separates welfare-improving behavior from metric gaming. Within this framework, we introduce indices that quantify manipulability, the price of gaming, and the price of cooperation, and we use them to study how rules, information disclosure, evaluation metrics, and aggregator-switching policies reshape incentives and cooperation patterns. We derive threshold conditions for deterring harmful gaming while preserving benign cooperation, and for triggering auto-switch rules when early-warning indicators become critical. Building on these results, we construct a design toolkit including a governance checklist and a simple audit-budget allocation algorithm with a provable performance guarantee. Simulations across diverse stylized environments and a federated learning case study consistently match the qualitative and quantitative patterns predicted by our framework. Taken together, our results provide design principles and operational guidelines for reducing metric gaming while sustaining stable, high-welfare cooperation in FL platforms.

Paper Structure

This paper contains 90 sections, 8 theorems, 82 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Motivation
  3. Contributions
  4. Related Work
  5. FL Attacks, Defenses, and Robust Aggregation
  6. Incentive Design and Differential Client Contribution
  7. Game Theory of Federated Learning and Participation Dynamics
  8. Metric Gaming and the Goodhart Phenomenon
  9. Design of Evaluation Information, Audits, and Sanctions
  10. Trade-offs Between Privacy and Incentives
  11. Federated Learning as a Strategic System: Setup and Notation
  12. Federated environment and timing
  13. Actions, outcomes, metrics, and welfare
  14. True outcomes and welfare.
  15. Metrics and proxy performance.
  16. ...and 75 more sections

Key Result

Proposition 4.5

Suppose that for a design policy $\pi$ and reference class $\Sigma^\mathrm{ref}$ we have $\mathcal{M}(\pi) = 0$. Then for every $\sigma \in \Sigma^\mathrm{ref}$, every client $i$, and every deviation $\sigma_i' \in \mathcal{A}_i$, In particular, there are no metric-gaming deviations at any profile in $\Sigma^\mathrm{ref}$.

Figures (2)

  • Figure 1: Effect of sanction strength $\alpha_{\mathrm{penalty}}$ on gaming scenarios (steady-state averages), showing welfare $\overline{W}_{\mathrm{game}}$, participation $\overline{x}_{\mathrm{game}}$, and Price of Gaming (PoG) as a function of $\alpha_{\mathrm{penalty}}$.
  • Figure 2: Effect of public-metric weight $\rho_{\mathrm{pub}}$ on gaming scenarios (steady-state averages), showing welfare $\overline{W}_{\mathrm{game}}$, participation $\overline{x}_{\mathrm{game}}$, PoG, the public metric level $\overline{M}_{\mathrm{game}}$, and the metric--welfare gap $\overline{M}_{\mathrm{game}} - \overline{W}_{\mathrm{game}}$ as functions of $\rho_{\mathrm{pub}}$.

Theorems & Definitions (44)

  • Definition 3.1: Federated strategic system
  • Definition 4.1: Local welfare and metric responses
  • Definition 4.2: Metric-gaming deviation
  • Definition 4.3: Local manipulability at a profile
  • Definition 4.4: Manipulability index of a design policy
  • Proposition 4.5: Zero manipulability and local alignment
  • Remark 4.6
  • Definition 4.7: Price of Gaming
  • Proposition 4.8: Manipulability and Price of Gaming
  • Definition 4.9: Price of Cooperation
  • ...and 34 more