Abstract
In this paper, we present a new model of congestion games with finite and random number of players, and an analytical method to compute the random path and link flows. We study the equilibrium condition, reformulate it as an equivalent variational inequality problem, and establish the existence and non-uniqueness of the equilibria. We also upper bound the price of anarchy with affine cost functions to characterize the quality of the equilibria. The upper bound is tight in some special cases, including the case of deterministic players. Finally a general lower bound is also provided.
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