[Paper Review] Incentive Mechanism Design for Federated Learning: Hedonic Game Approach

Cengis Hasan|arXiv (Cornell University)|Jan 24, 2021

Auction Theory and Applications20 references4 citations

TL;DR

This paper proposes a hedonic game-based incentive mechanism for federated learning to ensure stable coalition formation among self-interested agents. By modeling agent clustering as a hedonic game and introducing the Nash-stable set, the authors prove that additively separable and symmetric gain allocations guarantee Nash-stable partitions, and demonstrate that the resulting non-cooperative game is a potential game, ensuring convergence to a stable decentralized clustering solution.

ABSTRACT

Incentive mechanism design is crucial for enabling federated learning. We deal with clustering problem of agents contributing to federated learning setting. Assuming agents behave selfishly, we model their interaction as a stable coalition partition problem using hedonic games where agents and clusters are the players and coalitions, respectively. We address the following question: is there a family of hedonic games ensuring a Nash-stable coalition partition? We propose the Nash-stable set which determines the family of hedonic games possessing at least one Nash-stable partition, and analyze the conditions of non-emptiness of the Nash-stable set. Besides, we deal with the decentralized clustering. We formulate the problem as a non-cooperative game and prove the existence of a potential game.

Motivation & Objective

• To address the challenge of incentivizing self-interested agents to form stable coalitions in federated learning.
• To model agent clustering as a hedonic game where preferences depend only on coalition members.
• To identify conditions under which Nash-stable coalition partitions exist in federated learning settings.
• To design a decentralized incentive mechanism ensuring stable, scalable clustering without central coordination.
• To prove the existence of a potential game in the decentralized clustering formulation, enabling convergence to stable equilibria.

Proposed method

• Formalizes federated learning clustering as a hedonic coalition formation game where agents' preferences depend only on their coalition members.
• Introduces the Nash-stable set as the family of hedonic games that admit at least one Nash-stable partition.
• Proves that additively separable and symmetric gain allocation mechanisms ensure Nash stability.
• Models the decentralized clustering process as a non-cooperative game with individual strategy choices.
• Defines a potential function $ P_{\mathbf{v}}(\bm{\sigma}) = \sum_{S\in\Pi(\bm{\sigma})} \sum_{(i,j)\in\mathcal{V}(S)} v(i,j) $ that captures total coalition gains and ensures game convergence.
• Demonstrates that any strategy improvement by an agent corresponds to an increase in the potential function, confirming the game is a potential game.

Experimental results

Research questions

• RQ1 Under what conditions does a Nash-stable coalition partition exist in a federated learning setting with self-interested agents?
• RQ2 Which gain allocation mechanisms ensure the existence of a Nash-stable partition in hedonic games?
• RQ3 Can decentralized clustering in federated learning be modeled as a potential game to guarantee convergence to stable equilibria?
• RQ4 How do additively separable and symmetric gain functions contribute to Nash stability in coalition formation?
• RQ5 What is the role of the potential function in ensuring stability and convergence in the decentralized non-cooperative game formulation?

Key findings

• The Nash-stable set is non-empty when gain allocations are additively separable and symmetric, ensuring the existence of at least one Nash-stable coalition partition.
• Additively separable and symmetric gain functions result in a potential game, guaranteeing the existence of a Nash equilibrium that corresponds to a Nash-stable partition.
• The potential function $ P_{\mathbf{v}}(\bm{\sigma}) $ captures the total value of all coalitions and ensures that any unilateral strategy improvement by an agent increases the potential, leading to convergence.
• The decentralized clustering game is a potential game, implying that best-response dynamics converge to a Nash equilibrium, which corresponds to a stable coalition structure.
• The proposed mechanism ensures that no agent can unilaterally improve its utility by switching coalitions, thus achieving Nash stability under the specified gain allocation rules.
• The theoretical framework provides a foundation for designing incentive mechanisms that promote stable, scalable, and privacy-preserving federated learning systems.