Price of Anarchy in Stochastic Atomic Congestion Games with Affine Costs

Abstract

We consider an atomic congestion game with stochastic demand in which each player participates in the game with probability $p$, and incurs no cost with probability $1-p$. We assume that $p$ is common knowledge among all players and that players are independent. For congestion games with affine costs, we provide an analytic expression for the price of anarchy as a function of $p$, which is monotonically increasing and converges to the well-known bound of ${5}/{2}$ as $p\to 1$. On the other extreme, for $p\leq {1}/{4}$ the bound is constant and equal to ${4}/{3}$ independently of the game structure and the number of players. We show that these bounds are tight and are attained on routing games with purely linear costs. Additionally, we also obtain tight bounds for the price of stability for all values of $p$.