Cost Design in Atomic Routing Games

TL;DR

This paper introduces a numerical method to design link cost functions in atomic routing games, enabling the Nash equilibrium to optimize a specified performance metric, with applications demonstrated in grid world navigation.

Contribution

A novel numerical approach for designing link costs in atomic routing games to steer Nash equilibria towards desired performance outcomes.

Findings

Method effectively approximates Nash equilibria with smooth functions.

Iterative improvement via implicit differentiation enhances cost design.

Application to grid worlds shows practical utility.

Abstract

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.