Distributed Nash Equilibrium Seeking by a Consensus Based Approach
Distributed Nash Equilibrium Seeking by a Consensus Based Approach
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DOI：
10.1109/tac.2017.2688452
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发表时间：
2016-02
影响因子：
6.8
通讯作者：
Maojiao Ye;G. Hu
中科院分区：
文献类型：
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作者：
Maojiao Ye;G. Hu
在本文中，考虑了玩家网络之间的纳什均衡寻求。与许多现有的非合作博弈中纳什均衡寻求的著作不同，本文考虑的参与者无法直接观察不是其邻居的参与者的行为。相反，玩家应该能够通过无向且连接的通信图相互通信。通过综合领导者跟随共识协议和梯度博弈，提出了一种针对非合作博弈的分布式纳什均衡寻求策略。通过李雅普诺夫稳定性分析，对参与者的行为收敛到纳什均衡进行了分析。对于非二次方收益的博弈，博弈中可能同时存在多个孤立的纳什均衡，在一定条件下会得到局部收敛结果。然后，提供更强的条件来导出非二次博弈的非局部收敛结果。对于二次博弈，结果表明，所提出的寻求策略使玩家的行为在给定条件下能够全局收敛到纳什均衡。提供数值例子来验证所提出的搜索策略的有效性。
In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in noncooperative games, the players considered in this paper cannot directly observe the actions of the players who are not their neighbors. Instead, the players are supposed to be capable of communicating with each other via an undirected and connected communication graph. By a synthesis of a leader-following consensus protocol and the gradient play, a distributed Nash equilibrium seeking strategy is proposed for the noncooperative games. Analytical analysis on the convergence of the players’ actions to the Nash equilibrium is conducted via Lyapunov stability analysis. For games with nonquadratic payoffs, where multiple isolated Nash equilibria may coexist in the game, a local convergence result is derived under certain conditions. Then, a stronger condition is provided to derive a nonlocal convergence result for the nonquadratic games. For quadratic games, it is shown that the proposed seeking strategy enables the players’ actions to converge to the Nash equilibrium globally under the given conditions. Numerical examples are provided to verify the effectiveness of the proposed seeking strategy.