Forward induction

In this paper we isolate a particular refinement of the notion of Nash equilibrium that is characterized by two properties: (i) it provides a unified framework for both backwards and forward induction; and (it) it is mechanically computable. We provide an effective procedure that allows players, given the extensive-form representation of a game, to compute a set of "reasonable paths" through the tree. The set of reasonable paths corresponds to the set of strategies that survive iterated elimination of (weakly) dominated strategies in the strategic form. We prove that whenever our procedure identifies a unique path, that path corresponds to a Nash equilibrium. Moreover, our procedure rules out all Nash equilibria that contain (weakly) dominated strategies. Further, our notion of "reasonable" paths leads to the backwards induction solution in the case of games of perfect information, and to forward induction in the case of games of imperfect information. We 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 reinterpret some of its axioms as defeasible inference rules.