  We study bottleneck routing games where the social cost is determined by the
worst congestion on any edge in the network. Bottleneck games have been studied
in the literature by having the player's utility costs to be determined by the
worst congested edge in their paths. However, the Nash equilibria of such games
are inefficient since the price of anarchy can be very high with respect to the
parameters of the game. In order to obtain smaller price of anarchy we explore
{\em exponential bottleneck games} where the utility costs of the players are
exponential functions on the congestion of the edges in their paths. We find
that exponential bottleneck games are very efficient giving a poly-log bound on
the price of anarchy: O(log L log |E|), where L is the largest path length in
the players strategy sets and E is the set of edges in the graph.
