Perfect Regular Equilibrium

Perfect Bayesian equilibrium and sequential equilibrium introduced by Kreps and Wilson
(1982) improved the subgame perfect Nash equilibrium. These solution concepts break a
whole game into information sets and search strategies that satisfy sequential rationality at
each information set. The sequential rationality is a condition for the strategies of rational
players and requires that each strategy be the best response to the other strategies at each
of the information sets. This sequential rationality, therefore, inherits the spirit of the Nash
equilibrium condition. As units of analysis in multi-period games, information sets are small
enough to catch each of the players’ incentives separately. Consequently, these solution
concepts could reflect different incentives in different periods in multi-period games, and thus
they could exclude incredible threats. Particularly in finite games, these solution concepts
can exclude all of the incredible threats. In general games that allow a continuum of types
and strategies, however, these solution concepts might cause more serious problems than
including incredible threats because of their new approaches through information sets.

Information sets can be regarded as the smallest units of analysis. In games, players
cannot distinguish decision points in a common information set. So, whatever action they
choose, the same action must be applied to all decision points in a common information
set. That is, players can choose only one action at each of their information sets. Hence,
information sets would be the smallest units used to analyze players’ rational behavior.

These smallest units of analysis, however, might be smaller than complete units of analy-
sis. For this reason, we might need more information to find rational strategies at each
information set. In games, sufficient information to find rational strategies at each of the

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