  We consider the problem of using logged data to make predictions about what
would happen if we changed the `rules of the game' in a multi-agent system.
This task is difficult because in many cases we observe actions individuals
take but not their private information or their full reward functions. In
addition, agents are strategic, so when the rules change, they will also change
their actions. Existing methods (e.g. structural estimation, inverse
reinforcement learning) make counterfactual predictions by constructing a model
of the game, adding the assumption that agents' behavior comes from optimizing
given some goals, and then inverting observed actions to learn agent's
underlying utility function (a.k.a. type). Once the agent types are known,
making counterfactual predictions amounts to solving for the equilibrium of the
counterfactual environment. This approach imposes heavy assumptions such as
rationality of the agents being observed, correctness of the analyst's model of
the environment/parametric form of the agents' utility functions, and various
other conditions to make point identification possible. We propose a method for
analyzing the sensitivity of counterfactual conclusions to violations of these
assumptions. We refer to this method as robust multi-agent counterfactual
prediction (RMAC). We apply our technique to investigating the robustness of
counterfactual claims for classic environments in market design: auctions,
school choice, and social choice. Importantly, we show RMAC can be used in
regimes where point identification is impossible (e.g. those which have
multiple equilibria or non-injective maps from type distributions to outcomes).
