information sets encompasses players’ beliefs regarding probability distributions over infor-
mation sets. Accordingly, the perfect Bayesian equilibrium and the sequential equilibrium
require the players’ beliefs to be part of these solution concepts themselves. Note that these
solution concepts embody players’ rationalities in games. Therefore, the perfect Bayesian
equilibrium and the sequential equilibrium propose conditions for rational beliefs as they
propose sequential rationality, which is the condition for rational strategies.
In general games, however, those conditions for rational beliefs might cause problems
with these solution concepts. The perfect Bayesian equilibrium and the sequential equi-
librium propose reasonability and consistency, respectively, as their conditions for rational
beliefs. These conditions are defined based on Bayes’ rule. However, Bayes’ rule has limited
application in practice and this limited application could result in these solution concepts
being incapable of satisfying the criteria of rational solution concepts in general games. In
this paper, we propose two criteria of rational solution concepts in general games, namely,
weak consistency and the subgame perfect Nash equilibrium condition. Therefore, the lim-
ited application of Bayes’ rule might mean that these solution concepts are unable to satisfy
the weak consistency and the subgame perfect Nash equilibrium condition in general games.
The weak consistency is a criterion of the rational beliefs that places restrictions only on
the beliefs on the equilibrium path. This condition for weak consistency is a requirement for
all criteria related to rational beliefs. Thus, it is a necessary condition for rational beliefs.
However, it is weak in that it does not locate any restriction on the beliefs off the equilibrium
path. The subgame perfect Nash equilibrium condition, on the other hand, is a criterion