论文标题
原子路由游戏中的成本设计
Cost Design in Atomic Routing Games
论文作者
论文摘要
原子路由游戏是有向图上的多人游戏。游戏中的每个玩家都选择一条路径 - 将其原始节点连接到其目标节点的链路序列 - 成本最低，每个链接的成本都是所有玩家选择的函数。我们开发了一种新颖的数值方法来设计原子路由游戏中的链接成本功能，以使玩家在NASH均衡中的选择最小化给定的平滑性能功能。该方法首先近似于非平滑NASH平衡条件的光滑条件，然后迭代通过隐式分化来改善链接成本函数。我们演示了这种方法在网格世界中导航的非合作代理建模的原子路由游戏中的应用。
An atomic routing game is a multiplayer game on a directed graph. Each player in the game chooses a path -- a sequence of links that connect its origin node to its destination node -- with the lowest cost, where the cost of each link is a function of all players' choices. We develop a novel numerical method to design the link cost function in atomic routing games such that the players' choices at the Nash equilibrium minimize a given smooth performance function. This method first approximates the nonsmooth Nash equilibrium conditions with smooth ones, then iteratively improves the link cost function via implicit differentiation. We demonstrate the application of this method to atomic routing games that model noncooperative agents navigating in grid worlds.
