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Pré-Publication, Document De Travail Année : 2019

On approximate pure Nash equilibria in weighted congestion games with polynomial latencies

Résumé

We consider the problem of the existence of natural improvement dynamics leading to approximate pure Nash equilibria, with a reasonable small approximation, and the problem of bounding the efficiency of such equilibria in the fundamental framework of weighted congestion game with polynomial latencies of degree at most $\d \geq 1$.\\ In this work, by exploiting a simple technique, we firstly show that the game always admits a $\d$-approximate potential function. This implies that every sequence of $\d$-approximate improvement moves by the players always leads the game to a $\d$-approximate pure Nash equilibrium. As a corollary, we also obtain that, under mild assumptions on the structure of the players' strategies, the game always admits a constant approximate potential function. Secondly, by using a simple potential function argument, we are able to show that in the game there always exists a $(\d+\delta)$-approximate pure Nash equilibrium, with $\delta\in [0,1]$, whose cost is $2/(1+\delta)$ times the cost of any optimal state.

Dates et versions

hal-02089351 , version 1 (03-04-2019)

Identifiants

Citer

Ioannis Caragiannis, Angelo Fanelli. On approximate pure Nash equilibria in weighted congestion games with polynomial latencies. 2019. ⟨hal-02089351⟩
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