Perfect Regular Equilibrium

of the rational strategies. It places restrictions on all actions on the equilibrium path.
Moreover, it sets restrictions on some of the actions off the equilibrium path, and in this way
it can indirectly inspect some of the beliefs off the equilibrium path. Consequently, it can
compensate for the weakness of the weak consistency, and therefore these two conditions can
serve as the criteria of the rational solution concepts. In fact, the sequential rationality is also
known as an important criterion of the rational solution concepts in multi-period games. This
condition, however, is a requirement for the perfect Bayesian equilibrium and the sequential
equilibrium. Furthermore, it is a requirement for our solution concept, namely, the perfect
regular equilibrium. So these solution concepts always satisfy the sequential rationality, and
thus we do not use this criterion to evaluate the rationality of these solution concepts.

Perfect regular equilibrium satisfies the weak consistency and the subgame perfect Nash
equilibrium condition in general games, and thus it solves the incapability problem with the
perfect Bayesian equilibrium and the sequential equilibrium. The perfect regular equilibrium
is defined as a pair of beliefs and strategies such that the beliefs are updated from period to
period according to the regular conditional probability and taking the beliefs as given, no
player prefers to change its strategy at any of its information sets. So, the perfect regular
equilibrium still breaks a whole game into information sets and searches strategies that satisfy
sequential rationality at each of the information sets just as those two solution concepts do.
However, this solution concept defines its condition for rational beliefs as not being based
on Bayes’ rule, but rather on a regular version of the conditional probability. This regular
conditional probability does not have a limited application. Hence, the perfect regular

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