  Recent work has considered theoretical models for the behavior of agents with
specific behavioral biases: rather than making decisions that optimize a given
payoff function, the agent behaves inefficiently because its decisions suffer
from an underlying bias. These approaches have generally considered an agent
who experiences a single behavioral bias, studying the effect of this bias on
the outcome.
  In general, however, decision-making can and will be affected by multiple
biases operating at the same time. How do multiple biases interact to produce
the overall outcome? Here we consider decisions in the presence of a pair of
biases exhibiting an intuitively natural interaction: present bias -- the
tendency to value costs incurred in the present too highly -- and sunk-cost
bias -- the tendency to incorporate costs experienced in the past into one's
plans for the future.
  We propose a theoretical model for planning with this pair of biases, and we
show how certain natural behavioral phenomena can arise in our model only when
agents exhibit both biases. As part of our model we differentiate between
agents that are aware of their biases (sophisticated) and agents that are
unaware of them (naive). Interestingly, we show that the interaction between
the two biases is quite complex: in some cases, they mitigate each other's
effects while in other cases they might amplify each other. We obtain a number
of further results as well, including the fact that the planning problem in our
model for an agent experiencing and aware of both biases is computationally
hard in general, though tractable under more relaxed assumptions.
