  While Nash equilibrium has emerged as the central game-theoretic solution
concept, many important games contain several Nash equilibria and we must
determine how to select between them in order to create real strategic agents.
Several Nash equilibrium refinement concepts have been proposed and studied for
sequential imperfect-information games, the most prominent being trembling-hand
perfect equilibrium, quasi-perfect equilibrium, and recently one-sided
quasi-perfect equilibrium. These concepts are robust to certain arbitrarily
small mistakes, and are guaranteed to always exist; however, we argue that
neither of these is the correct concept for developing strong agents in
sequential games of imperfect information. We define a new equilibrium
refinement concept for extensive-form games called observable perfect
equilibrium in which the solution is robust over trembles in
publicly-observable action probabilities (not necessarily over all action
probabilities that may not be observable by opposing players). Observable
perfect equilibrium correctly captures the assumption that the opponent is
playing as rationally as possible given mistakes that have been observed (while
previous solution concepts do not). We prove that observable perfect
equilibrium is always guaranteed to exist, and demonstrate that it leads to a
different solution than the prior extensive-form refinements in no-limit poker.
We expect observable perfect equilibrium to be a useful equilibrium refinement
concept for modeling many important imperfect-information games of interest in
artificial intelligence.
