On the Price of Anarchy of Highly Congested Nonatomic Network Games

We consider nonatomic network games with one source and one destination. We examine the asymptotic behavior of the price of anarchy as the inflow increases. In accordance with some empirical observations, we show that, under suitable conditions, the price of anarchy is asymptotic to one. We show with some counterexamples that this is not always the case. The counterexamples occur in very simple parallel graphs.Comment: 26 pages, 6 figure

Price of Anarchy in Bernoulli Congestion Games with Affine Costs

We consider an atomic congestion game in which each player participates in the game with an exogenous and known probability $p_{i}\in[0,1]$, independently of everybody else, or stays out and incurs no cost. We first prove that the resulting game is potential. Then, we compute the parameterized price of anarchy to characterize the impact of demand uncertainty on the efficiency of selfish behavior. It turns out that the price of anarchy as a function of the maximum participation probability $p=\max_{i} p_{i}$ is a nondecreasing function. The worst case is attained when players have the same participation probabilities $p_{i}\equiv p$. For the case of affine costs, we provide an analytic expression for the parameterized price of anarchy as a function of $p$. This function is continuous on $(0,1]$, is equal to $4/3$ for $0<p\leq 1/4$, and increases towards $5/2$ when $p\to 1$. Our work can be interpreted as providing a continuous transition between the price of anarchy of nonatomic and atomic games, which are the extremes of the price of anarchy function we characterize. We show that these bounds are tight and are attained on routing games -- as opposed to general congestion games -- with purely linear costs (i.e., with no constant terms).Comment: 29 pages, 6 figure

Interplay between security providers, consumers, and attackers: a weighted congestion game approach

Network users can choose among different security solutions to protect their data. Those solutions are offered by competing providers, with possibly different performance and price levels. In this paper, we model the interactions among users as a noncooperative game, with a negative externality coming from the fact that attackers target popular systems to maximize their expected gain. Using a nonatomic weighted congestion game model for user interactions, we prove the existence and uniqueness of a user equilibrium, compute the corresponding Price of Anarchy, that is the loss of efficiency due to user selfishness, and investigate some consequences for the (higher-level) pricing game played by security providers.Game theory;Weighted games; Security