The complexity of approximate Nash equilibrium in congestion games with negative delays

Details The complexity of approximate Nash equilibrium in congestion games with negative delays The complexity of approximate Nash equilibrium in congestion games with negative delays

2011-02-06

arxiv.org/abs/1102.1161v1

Computer Science

Computer Science and Game Theory

Scientific paper

We extend the study of the complexity of finding an $\eps$-approximate Nash equilibrium in congestion games from the case of positive delay functions to delays of arbitrary sign. We first prove that in symmetric games with $\alpha$-bounded jump the $\eps$-Nash dynamic converges in polynomial time when all delay functions are negative, similarly to the case of positive delays. We then establish a hardness result for symmetric games with $\alpha$-bounded jump and with arbitrary delay functions: in that case finding an $\eps$-Nash equilibrium becomes $\PLS$-complete.

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