Utility design for two-player normal-form games
Utility design for two-player normal-form games
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DOI：
10.1109/ascc.2017.8287495
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发表时间：
2017-12
期刊：
影响因子：
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通讯作者：
Koji Kitagawa;M. Guo;K. Kogiso;Hideaki Hata
中科院分区：
文献类型：
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作者：
Koji Kitagawa;M. Guo;K. Kogiso;Hideaki Hata
这项研究为两人正常形式游戏制定了实用性设计问题，并提出了一种新的计算算法来解决该问题。这项研究提出了一种用于计算实用程序矩阵作为实用程序（收益）的自动和系统的算法，该算法能够达到所需的NASH平衡（NE）。这项研究的主要贡献是实用程序计算算法，可以使用控制系统设计框架构建。 NE和相应的实用程序矩阵之间相关性的非线性动力学以离散时间，非线性，自主动力学系统表示，该系统源自Karush-Kuhn-Tucker条件。从理论上讲，该模型是稳定的，并产生NE和相应实用程序矩阵的更新。分析结果使得可以设计跟踪控制系统，该系统继续自动调整NE中的位移量。此外，数值示例证实了实用程序设计问题可以通过提出的算法解决。
This study formulates a utility design problem for two-player normal-form games and proposes a novel computational algorithm to solve the problem. This study proposes an automatic and systematic algorithm for calculating a utility matrix, as a utility (payoff), that enables to achieve the desired Nash equilibrium (NE). The main contribution of this study is the utility calculation algorithm, which can be constructed using a control system design framework. The nonlinear dynamics of the correlation between an NE and a corresponding utility matrix is expressed in a discrete-time, nonlinear, autonomous dynamical system, which is derived from the Karush-Kuhn-Tucker condition. The model is theoretically guaranteed to be stable and to yield updates of the NE and the corresponding utility matrix. The analysis result enables to design the tracking control system that continues to automatically adjust the amount of displacement in the NE. Besides, numerical examples confirm that the utility design problem can be solved by the proposed algorithm.