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We study the repeated, non-atomic routing game, in which selfish players make a sequence of routing decisions. We consider a model in which players use regret-minimizing algorithms as the learning mechanism, and study the resulting dynamics. We are concerned in particular with the convergence to the set of Nash equilibria of the routing game. No-regret… (More)

We study the repeated congestion game, in which multiple populations of players share resources, and make, at each iteration, a decentralized decision on which resources to utilize. We investigate the following question: given a model of how individual players update their strategies, does the resulting dynamics of strategy profiles converge to the set of… (More)

- Walid Krichene, Benjamin Drighès, Alexandre Bayen
- 2014

Lemma 1. Let (γ τ) τ ∈N be a non-summable sequence of positive weights. If a real sequence (u (τ)) τ ∈N converges absolutely to u in the sense of Cesàro means w.r.t. (γ τ) τ , that is lim T →∞ τ ≤T γτ |u (τ) −u| τ ≤T γτ = 0, then there exists a subset of indexes T of density one such that the subsequence (u (τ)) τ ∈T converges to u.

— We consider the single commodity non-atomic congestion game, in which the player population is assumed to obey the replicator dynamics. We study the resulting rest points, and relate them to the Nash equilibria of the one-shot congestion game. The rest points of the replicator dynamics, also called evolutionary stable points, are known to coincide with a… (More)

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