  Two important metrics for measuring the quality of routing paths are the
maximum edge congestion $C$ and maximum path length $D$. Here, we study
bicriteria in routing games where each player $i$ selfishly selects a path that
simultaneously minimizes its maximum edge congestion $C_i$ and path length
$D_i$. We study the stability and price of anarchy of two bicriteria games:
  - {\em Max games}, where the social cost is $\max(C,D)$ and the player cost
is $\max(C_i, D_i)$. We prove that max games are stable and convergent under
best-response dynamics, and that the price of anarchy is bounded above by the
maximum path length in the players' strategy sets. We also show that this bound
is tight in worst-case scenarios.
  - {\em Sum games}, where the social cost is $C+D$ and the player cost is
$C_i+D_i$. For sum games, we first show the negative result that there are game
instances that have no Nash-equilibria. Therefore, we examine an approximate
game called the {\em sum-bucket game} that is always convergent (and therefore
stable). We show that the price of anarchy in sum-bucket games is bounded above
by $C^* \cdot D^* / (C^* + D^*)$ (with a poly-log factor), where $C^*$ and
$D^*$ are the optimal coordinated congestion and path length. Thus, the
sum-bucket game has typically superior price of anarchy bounds than the max
game. In fact, when either $C^*$ or $D^*$ is small (e.g. constant) the social
cost of the Nash-equilibria is very close to the coordinated optimal $C^* +
D^*$ (within a poly-log factor). We also show that the price of anarchy bound
is tight for cases where both $C^*$ and $D^*$ are large.
