Backwards Forward Induction

In this paper we isolate a particular refinement of the notion of Nash equilibrium that is characterized by (i) the fact that it provides a unified framework for both backwards and forward induction; and (ii) by the fact that it is mechanically computable. We provide an effective procedure, whose definition embodies certain given principles of rationality. Such a procedure allows us, given a representation of an extensve form game, to compute a set of paths through the tree corresponding to what we call "reasonable equilibria." The reasonable equilibria are all shown to be Nash equilibria. Further, such a notion of reasonable equilibrium agrees with backwards induction in the case of extensive form games of perfect information, and with forward induction in the case of extensive form games of imperfect information. This allows us to model the players' reasoning process by giving a theory (with which each player is supposed to be endowed), from which statements characterizing the players' behavior are deducible. Such a theory is not yet complete, in that it cannot handle true (irrational) deviations. We point at directions for future work by showing how such a theory can be made complete provided we re-interpret some of its axioms as defeasible inference rules.