  The robustness of multiagent systems can be affected by mistakes or
behavioral biases (e.g., risk-aversion, altruism, toll-sensitivity), with some
agents playing the "wrong game." This can change the set of equilibria, and may
in turn harm or improve the social welfare of agents in the system. We are
interested in bounding what we call the biased price of anarchy (BPoA) in
populations with diverse agent behaviors, which is the ratio between welfare in
the "wrong" equilibrium and optimal welfare.
  We study nonatomic routing games, and derive an externality bound that
depends on a key topological parameter of the underlying network.
  We then prove two general BPoA bounds for games with diverse populations: one
that relies on the network structure and the average bias of all agents in the
population, and one that is independent of the structure but depends on the
maximal bias. Both types of bounds can be combined with known results to derive
concrete BPoA bounds for a variety of specific behaviors (e.g., varied levels
of risk-aversion).
