The Concept of Subgame Perfection: Some Discontents
In mainstream game theory, the prominent solution concept for dynamic games is the “subgame perfect Nash equilibrium”. This concept combines the mathematical method of backward induction with the assumption of common knowledge of rationality. Whereas backward induction on its own is an indisputable mathematical method, there might be problems when it is paired with the common knowledge of rationality assumption. After presenting the concept of subgame perfection, this chapter explains why several acclaimed game theorists believe that using the concept of subgame perfection might be philosophically incoherent and likely to lead to paradoxical results. On a different level, it may be argued that subgame perfection is not necessarily the unique way to approach a dynamic game, as other concepts (such as a combination of forward induction with common knowledge of rationality) might be equally, if not more, plausible. This chapter illustrates this view with a comprehensive example. Finally, as another discontent against subgame perfection, it is shown that rational players might prefer to deviate from what subgame perfection instructs them to do, as long as one of the players holds (even very small) doubts about another player’s rationality.