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Distributed Nash Equilibrium Seeking by a Consensus Based Approach

机译：基于共识的方法的分布式纳什均衡寻求

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摘要

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.
机译：本文考虑了参与者网络之间的纳什均衡寻求。与许多现有的关于非合作博弈中纳什均衡寻求的著作不同，本文考虑的参与者不能直接观察非邻居参与者的行为。取而代之的是，玩家应该能够通过无方向和连接的通信图彼此通信。通过对领导者遵循共识协议和梯度博弈的综合，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Lyapunov稳定性分析对参与者的行为收敛到纳什均衡进行了分析。对于具有非二次收益的游戏，其中多个孤立的纳什均衡可能共存于游戏中，则在某些条件下会得出局部收敛结果。然后，提供了更强的条件来导出非二次博弈的非局部收敛结果。对于二次游戏，证明了所提出的寻求策略能够使玩家的行为在给定条件下全局收敛到纳什均衡。提供了数字示例，以验证所提出的搜索策略的有效性。

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