Forward Induction

Abstract

In this chapter we present different forward induction criteria which restrict the way in which players should revise their conjectures during the game. Although there does not exist a unique definition of forward induction in the literature, its main idea can be described as follows. Suppose that a player’s initial conjecture about the opponents’ behavior has been contradicted by the play of the game. In this case, this player is required to form an alternative conjecture compatible with the current situation in the game. In other words, the player should study all possible scenarios that could have led to this situation, and form some subjective belief about these scenarios. Roughly speaking, a forward induction criterion requires the player to make a distinction between “more plausible” and “less plausible” scenarios, and to assign positive probability only to the “more plausible” scenarios. The various criteria presented in this chapter differ in the formalization of “more plausible” and “less plausible” scenarios. The forward induction criteria discussed in this chapter are iterated weak dominance, stable sets of equilibria, forward induction equilibrium, justifiable sequential equilibrium and stable sets of beliefs. The idea of forward induction is particularly succesful in eliminating “implausible” sequential equilibria in signaling games. For this class of games, which is relevant due to many applications to information economics, several forward induction criteria have been developed that exploit the specific structure of signaling games.