The Complexity of Sequential Routing Games

TL;DR

This paper analyzes the computational complexity of sequential routing games with congestion, showing that finding optimal strategies and equilibria is PSPACE-hard or complete, highlighting the intrinsic difficulty of such problems.

Contribution

It establishes the PSPACE-hardness of approximating strategies and computing equilibria in sequential routing games with congestion.

Findings

Approximating a winning strategy within n^{1-ε} is PSPACE-hard.

Computing a subgame perfect equilibrium under perfect information is PSPACE-hard and in FPSPACE.

Deciding SPE existence under imperfect information is PSPACE-complete.

Abstract

We study routing games where every agent sequentially decides her next edge when she obtains the green light at each vertex. Because every edge only has capacity to let out one agent per round, an edge acts as a FIFO waiting queue that causes congestion on agents who enter. Given $n$ agents over $|V|$ vertices, we show that for one agent, approximating a winning strategy within $n^{1-\varepsilon}$ of the optimum for any $\varepsilon>0$, or within any polynomial of $|V|$, are PSPACE-hard. Under perfect information, computing a subgame perfect equilibrium (SPE) is PSPACE-hard and in FPSPACE. Under imperfect information, deciding SPE existence is PSPACE-complete.