  The bounded rationality plays a vital role in the collective behavior of the
evacuation process. Also investigating human behavior in such an extreme
situation is a continuing concern within social psychology. In this paper, we
construct a cellular automaton (CA) model for the escape dynamics, and the
bounded rational behavior induced by heterogeneous information is introduced.
The non-trivial behavior shows in the replicator dynamics method with mean
field approximation, where people's perception of the distribution of
population and velocity is reduced to an average value in a certain direction.
Analyzing the escape efficiency shows that under the premise of rationality,
the bounded rational strategy can get higher performance. Interestingly, a
quantifiable meta-stable state appears in the escape process, and the escape
time is power-law dependent on system size.
