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分布惯性在线游戏算法用于跟踪概括的纳什平衡
Haomin Bai1, Wenying Xu1, Shaofu Yang2
1School of Mathematics, Southeast University, Nanjing 211189, China.
Chaos (Woodbury, N.Y.)
|October 13, 2023
概括
本研究介绍了一种分布式惯性在线游戏 (D-IOG) 算法,用于跟踪动态非合作游戏中的通用纳什平衡 (GNE). 该算法有效地管理时间变化的成本和约束,实现线下遗憾界限.
科学领域:
- 分布式优化 分布式优化
- 游戏理论 游戏理论
- 非合作游戏 非合作游戏
- 动态系统 动态系统
背景情况:
- 在具有时变函数的动态环境中跟踪泛纳什平衡 (GNE) 的挑战.
- 需要分布式算法,可以处理代理人在决策后披露信息.
- 现有方法在解决合约束和时间变化通信方面的局限性.
研究的目的:
- 开发一种分布式算法来跟踪非合作游戏中的GNE,这些游戏具有动态成本和合约束函数.
- 在遗憾和约束违规方面分析拟议算法的性能.
- 调查惯性和信息传输模式对算法效率的影响.
主要方法:
- 基于镜像下降的分布式惯性在线游戏 (D-IOG) 算法的建议,用于在没有合约束的情况下进行GNE跟踪.
- 修改D-IOG算法,使用初级-双元和镜像下降方法,以结合时间变化的合约束.
- 对遗憾和约束违规行为的上限的推导.
主要成果:
- D-IOG算法成功地追踪了Nash平衡 (NE) 在时间变化的通信图表上.
- 后悔的亚线性增长是在步骤大小和惯性参数的特定条件下实现的.
- 经过修改的D-IOG算法在跟踪GNE中表现出有效性,使用结合约束,并以衍生边界为支持.
结论:
- 拟议的D-IOG算法在动态非合作游戏中有效用于分布式GNE跟踪.
- 这些算法为低平均遗憾和可管理的约束违规提供了潜力.
- 模拟示例验证了开发算法的实际适用性和性能.
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