was defined in strategic form games in which all players chose their strategies once and
simultaneously. Hence, this solution concept might not properly predict players’ behavior in
multi-period games where players choose their actions in each period after observing actions
taken before. In multi-period games, players could also have different incentives in different
periods. Since the Nash equilibrium requires all players to decide what actions they should
take once and simultaneously, it might not reflect these changes in incentives in multi-period
games. As a result, a Nash equilibrium could include incredible threats.
The subgame perfect Nash equilibrium by Selten (1975) improved the Nash equilibrium.
The basic idea behind this solution concept was to break a whole game into subgames
and to find Nash equilibria in every subgame. When we analyze each of the subgames
separately, we are able to consider players’ incentives within those subgames. Thus, if
situations in different periods lead to the formation of different subgames, then the subgame
perfect Nash equilibrium could reflect different incentives in different periods in multi-period
games. As a result, it could exclude incredible threats1 . Here, subgames can be regarded
as complete units in the analysis of games in that we can find Nash equilibria, which reflect
players’ rational behavior, within subgames without referring to any information outside
those subgames. In games with incomplete information, however, these complete units of
analysis are too large to catch each of the players’ incentives separately. So, the subgame
perfect Nash equilibrium might fail to reflect players’ incentives in different periods.
1 To find a subgame perfect Nash equilibrium in practice, it is convenient to analyze subgames from back
to front. This is because, by analyzing backward, we can naturally consider players’ future incentives in any
period. In this sense, we may think the subgame perfect Nash equilibrium is a combination of the Nash
equilibrium and backward induction.