Sequentiality

Abstract

One major problem in the theory of extensive games is the following: How should a player react when he finds himself at an information set that contradicts his previous belief about the opponent’s strategy choice? Different approaches have been proposed to this problem. As mentioned in Chapter 2, Ben-Porath (1997) and Reny (1992) have formulated ra- tionalizability and equilibrium notions based on weak sequentially, in which a player is allowed to believe, in this situation, that his opponent will no longer choose rationally. Battigalli and Siniscalchi (2002) have shown that Pearce’s (1984) extensive form rationalizability can be characterized by assuming that a player, in such a situation, should look for the highest degree of “strategic sophistication” that is compatible with the event of reaching this information set, and stick to this degree until it is contradicted later on in the game. Perea (2002, 2003) suggests that the player, in such a situation, may revise his conjecture about the opponent’s utility function in order to rationalize her “surprising” move, while maintaining common belief of rational choice at all information sets. The most prominent position, however, is that the player should still believe that his opponent will choose rationally in the remainder of the game; this underlies concepts that promote backward induction. Such concepts will be presented in this and the next chapter, which reproduce joint work with Andrés Perea, cf. Asheim and Perea (2005).