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Communication Dans Un Congrès Année : 2019

On Approximate Pure Nash Equilibria in Weighted Congestion Games with Polynomial Latencies

Ioannis Caragiannis
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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 ≥ 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 + δ)-approximate pure Nash equilibrium, with δ ∈ [0, 1], whose cost is 2/(1 + δ) times the cost of an optimal state.
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Dates et versions

hal-02431939 , version 1 (08-01-2020)

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Ioannis Caragiannis, Angelo Fanelli. On Approximate Pure Nash Equilibria in Weighted Congestion Games with Polynomial Latencies. 46th International Colloquium on Automata, Languages and Programming, Jul 2019, Patras, Greece. ⟨10.4230/LIPIcs.ICALP.2019.133⟩. ⟨hal-02431939⟩
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