Dynamic network congestion games

TL;DR

This paper introduces dynamic network congestion games where players choose routes synchronously and costs depend on simultaneous usage, analyzing their complexity and equilibrium existence.

Contribution

It defines dynamic NCGs, studies their equilibrium properties, and establishes complexity bounds for finding and verifying equilibria with bounded social costs.

Findings

Pure Nash equilibria always exist in dynamic NCGs.

Deciding the existence of bounded-cost Nash equilibria is computationally hard.

Strategies for equilibria can be computed within high exponential time bounds.

Abstract

Congestion games are a classical type of games studied in game theory, in which n players choose a resource, and their individual cost increases with the number of other players choosing the same resource. In network congestion games (NCGs), the resources correspond to simple paths in a graph, e.g. representing routing options from a source to a target. In this paper, we introduce a variant of NCGs, referred to as dynamic NCGs: in this setting, players take transitions synchronously, they select their next transitions dynamically, and they are charged a cost that depends on the number of players simultaneously using the same transition. We study, from a complexity perspective, standard concepts of game theory in dynamic NCGs: social optima, Nash equilibria, and subgame perfect equilibria. Our contributions are the following: the existence of a strategy profile with social cost bounded by a constant is in PSPACE and NP-hard. (Pure) Nash equilibria always exist in dynamic NCGs; the existence of a Nash equilibrium with bounded cost can be decided in EXPSPACE, and computing a witnessing strategy profile can be done in doubly-exponential time. The existence of a subgame perfect equilibrium with bounded cost can be decided in 2EXPSPACE, and a witnessing strategy profile can be computed in triply-exponential time.