非原子路由博弈中的社会学习
Social Learning in Nonatomic Routing Games
摘要：
考虑了一个需求可变、费用不确定的离散时间非原子路由博弈问题。给定一个单起点和单终点的路由网络，每条边的代价函数依赖于某个不确定的持久状态参数。在每个周期，一个随机的交通需求是通过网络根据Wardrop均衡路由。已实现成本是公开观测的，并且关于状态参数的公共贝叶斯信念被更新。我们说，当信念收敛于真理时，存在强学习，而当平衡流收敛于完整信息流时，存在弱学习。我们描述了学习发生的网络。我们证明了这些网络具有串并联结构，并提供了一个反例来表明，学习可能会失败，在非串并联网络。
英文摘要：
We consider a discrete-time nonatomic routing game with variable demand and uncertain costs. Given a routing network with single origin and destination, the cost function of each edge depends on some uncertain persistent state parameter. At every period, a random traffic demand is routed through the network according to a Wardrop equilibrium. The realized costs are publicly observed and the public Bayesian belief about the state parameter is updated. We say that there is strong learning when beliefs converge to the truth and weak learning when the equilibrium flow converges to the complete-information flow. We characterize the networks for which learning occurs. We prove that these networks have a series-parallel structure and provide a counterexample to show that learning may fail in non-series-parallel networks.
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