  The standard game-theoretic solution concept, Nash equilibrium, assumes that
all players behave rationally. If we follow a Nash equilibrium and opponents
are irrational (or follow strategies from a different Nash equilibrium), then
we may obtain an extremely low payoff. On the other hand, a maximin strategy
assumes that all opposing agents are playing to minimize our payoff (even if it
is not in their best interest), and ensures the maximal possible worst-case
payoff, but results in exceedingly conservative play. We propose a new solution
concept called safe equilibrium that models opponents as behaving rationally
with a specified probability and behaving potentially arbitrarily with the
remaining probability. We prove that a safe equilibrium exists in all
strategic-form games (for all possible values of the rationality parameters),
and prove that its computation is PPAD-hard. We present exact algorithms for
computing a safe equilibrium in both 2 and $n$-player games, as well as
scalable approximation algorithms.
