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<p>The paper introduces an analytical framework for decomposing finite strategic games within the multi-potential game (MPG) paradigm. Specifically, it partitions the finite non-cooperative game space into multi-potential subspace and multi-harmonic subspace, uncovering the common interests and conflicts of player subsets. Additionally, this approach provides a systematic methodology for calculating potential functions within MPGs. Within the MPG framework, a finite non-cooperative game characterized by its minimal potential index <i>q</i><sub><i>G</i></sub> can be considered as a <i>q</i><sub><i>G</i></sub>-person non-cooperative game. Furthermore, the Nash equilibrium of this <i>q</i><sub><i>G</i></sub>-person non-cooperative game is examined. This analysis substantially enhances our comprehension of Nash equilibrium in finite non-cooperative games in terms of group welfare. Finally, an illustrative example is presented to demonstrate the theoretical results.</p>

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Decomposition and equilibrium analysis of multi-potential games: aligning individual interest with group welfare

  • 期刊论文

  • 发表日期：

    2025年6月6日

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  • Aixin Liu,
  • Haitao Li,
  • Lin Wang

摘要

The paper introduces an analytical framework for decomposing finite strategic games within the multi-potential game (MPG) paradigm. Specifically, it partitions the finite non-cooperative game space into multi-potential subspace and multi-harmonic subspace, uncovering the common interests and conflicts of player subsets. Additionally, this approach provides a systematic methodology for calculating potential functions within MPGs. Within the MPG framework, a finite non-cooperative game characterized by its minimal potential index qG can be considered as a qG-person non-cooperative game. Furthermore, the Nash equilibrium of this qG-person non-cooperative game is examined. This analysis substantially enhances our comprehension of Nash equilibrium in finite non-cooperative games in terms of group welfare. Finally, an illustrative example is presented to demonstrate the theoretical results.