arXiv - CS - Computer Science and Game Theory Pub Date : 2019-03-08 , DOI: arxiv-1903.03309
Roberto Cominetti; Marco Scarsini; Marc Schröder; Nicolás Stier-Moses

Since demand in transportation networks is uncertain, commuters need to anticipate different traffic conditions. We capture this uncertainty by assuming that each commuter may make the trip or not with a fixed probability, creating an atomic congestion game with Bernoulli demands. Each commuter participates with an exogenous probability $p_i\in[0,1]$, which is common knowledge, independently of everybody else, or does not travel 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 the transportation network. 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 commuters 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

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