On the uniqueness and stability of equilibria of network games
On the uniqueness and stability of equilibria of network games
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论网络博弈均衡的唯一性和稳定性
DOI：
10.1109/allerton.2017.8262749
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
M. Liu
中科院分区：
文献类型：
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作者：
Parinaz Naghizadeh Ardabili;M. Liu
我们研究了一类在具有一般（非线性）最佳响应函数的网络上玩的游戏。具体来说，我们让每个智能体的收益取决于通过非线性交互函数的邻居行为的线性加权和。我们确定了博弈背后的网络结构条件，其中（i）博弈的纳什均衡是唯一的，并且（ii）纳什均衡在模型参数的扰动下是稳定的。我们发现纳什均衡的唯一性和稳定性都与适当定义的矩阵的最低特征值有关，该矩阵由网络的邻接矩阵以及交互函数的斜率决定。我们表明，我们的唯一性结果概括了线性最佳响应游戏与一般最佳响应函数的游戏的现有唯一性条件。我们进一步确定了有助于在网络上传播冲击的代理类别。特别是，对于小冲击，我们表明，在给定均衡下严格不活跃的主体可以被排除在均衡的稳定性分析之外，无论其网络位置或链接如何。
We study a class of games played on networks with general (non-linear) best-response functions. Specifically, we let each agent's payoff depend on a linearly weighted sum of her neighbors' actions through a non-linear interaction function. We identify conditions on the network structure underlying the game given which (i) the Nash equilibrium of the game is unique, and (ii) the Nash equilibria are stable under perturbations in the model's parameters. We find that both the uniqueness and stability of the Nash equilibria are related to the lowest eigenvalue of suitably defined matrices, which are determined by the network's adjacency matrix, as well as the slopes of the interaction functions. We show that our uniqueness result generalizes an existing uniqueness condition for games of linear best-responses to games with general best-response functions. We further identify the classes of agents that are instrumental in the spread of shocks over the network. In particular, for small shocks, we show that agents that are strictly inactive at a given equilibrium can be precluded from the equilibrium's stability analysis, irrespective of their network position or links.