Nash Dynamics in Constant Player and Bounded Jump Congestion Games

We study the convergence time of Nash dynamics in two classes of congestion games – constant player congestion games and bounded jump congestion games. It was shown by Ackermann and Skopalik [2] that even 3-player congestion games are PLS-complete. We design an FPTAS for congestion games with constant number of players. In particular, for any > 0, we establish a stronger result, namely, any sequence of (1 + )-greedy improvement steps converges to a (1 + )-approximate equilibrium in a number of steps that is polynomial in −1 and the size of the input. As the number of strategies of a player can be exponential in the size of the input, our FPTAS result assumes that a (1+ )-greedy improvement step, if it exists, can be computed in polynomial time. This assumption holds in previously studied models of congestion games, including network congestion games [9] and restricted network congestion