  An algorithmic decision-maker incentivizes people to act in certain ways to
receive better decisions. These incentives can dramatically influence subjects'
behaviors and lives, and it is important that both decision-makers and
decision-recipients have clarity on which actions are incentivized by the
chosen model. While for linear functions, the changes a subject is incentivized
to make may be clear, we prove that for many non-linear functions (e.g. neural
networks, random forests), classical methods for interpreting the behavior of
models (e.g. input gradients) provide poor advice to individuals on which
actions they should take. In this work, we propose a mathematical framework for
understanding algorithmic incentives as the challenge of solving a Markov
Decision Process, where the state includes the set of input features, and the
reward is a function of the model's output. We can then leverage the many
toolkits for solving MDPs (e.g. tree-based planning, reinforcement learning) to
identify the optimal actions each individual is incentivized to take to improve
their decision under a given model. We demonstrate the utility of our method by
estimating the maximally-incentivized actions in two real-world settings: a
recidivism risk predictor we train using ProPublica's COMPAS dataset, and an
online credit scoring tool published by the Fair Isaac Corporation (FICO).
