论文标题
拥塞游戏中不可预测的动态:记忆力丧失可以防止混乱
Unpredictable dynamics in congestion games: memory loss can prevent chaos
论文作者
论文摘要
我们研究了具有两个资源的简单拥堵游戏的动力学,其中代理的连续体根据经验加权的吸引力(EWA)算法的形式行为。动力学的特征是两个参数:选择的(人口)强度$ a> 0 $捕获代理总人口的经济合理性和[0,1]中的折扣因子$σ\ in [0,1] $捕获一种记忆损失类型,而过去的现象却比最近的成果较小。最后,我们的系统添加了(0,1)$中的第三个参数$ b \,该参数捕获了两个资源的成本功能的不对称性。它是使用NASH平衡的第一个资源的代理的比例,$ b = 1/2 $捕获对称网络。 在这个简单的框架内,我们显示了许多分叉现象,其中行为动力学从全局融合到平衡,以限制周期,甚至(正式证明)混乱,这是参数$ a $ a $,$ b $和$ $σ$的函数。具体来说,我们表明,对于任何折扣因子$σ$,该系统将不稳定,因为$ a $ a $ a $ a。尽管对于折扣系数,$σ= 0 $几乎总是(即$ b \ neq 1/2 $),系统将变得混乱,因为$σ$增加了混乱的态度将为吸引周期时期2的周期性轨道提供位置。因此,内存损失可以简化游戏动态并使系统可预测。我们通过模拟和几个分叉图对我们的理论分析进行了补充,这些图表即使在最简单的潜在游戏中,也展示了人口动态的不屈不挠的复杂性(例如,吸引了不同长度的周期性轨道)。
We study the dynamics of simple congestion games with two resources where a continuum of agents behaves according to a version of Experience-Weighted Attraction (EWA) algorithm. The dynamics is characterized by two parameters: the (population) intensity of choice $a>0$ capturing the economic rationality of the total population of agents and a discount factor $σ\in [0,1]$ capturing a type of memory loss where past outcomes matter exponentially less than the recent ones. Finally, our system adds a third parameter $b \in (0,1)$, which captures the asymmetry of the cost functions of the two resources. It is the proportion of the agents using the first resource at Nash equilibrium, with $b=1/2$ capturing a symmetric network. Within this simple framework, we show a plethora of bifurcation phenomena where behavioral dynamics destabilize from global convergence to equilibrium, to limit cycles or even (formally proven) chaos as a function of the parameters $a$, $b$ and $σ$. Specifically, we show that for any discount factor $σ$ the system will be destabilized for a sufficiently large intensity of choice $a$. Although for discount factor $σ=0$ almost always (i.e., $b \neq 1/2$) the system will become chaotic, as $σ$ increases the chaotic regime will give place to the attracting periodic orbit of period 2. Therefore, memory loss can simplify game dynamics and make the system predictable. We complement our theoretical analysis with simulations and several bifurcation diagrams that showcase the unyielding complexity of the population dynamics (e.g., attracting periodic orbits of different lengths) even in the simplest possible potential games.