Eco514-Game Theory Lecture 10: Extensive Games with(Almost) Perfect Information Marciano siniscalchi October 19. 1999 Introduction Beginning with this lecture, we focus our attention on dynamic games. The majority of games of economic interest feature some dynamic component, and most often payoff uncertainty as The analysis of extensive games is challenging in several ways. At the most basic level describing the possible sequences of events(choices) which define a particular game form is not problematic per se; yet, different formal definitions have been proposed, each with its Representing the players information as the play unfolds is nontrivial: to some extent research on this topic may still be said to be in progress The focus of this course will be on solution concepts; in this area, subtle and unexpected difficulties arise, even in simple games. The very representation of players'beliefs as the play unfolds is problematic, at least in games with three or more players. There has been a fierce debate on the right" notion of rationality for extensive games, but no consensus seems to have emerged among theorists We shall investigate these issues in due course. Today we begin by analyzing a particu- larly simple class of games, characterized by a natural multistage structure. I should point out that, perhaps partly due to its simplicity, this class encompasses the vast majority of extensive games of economic interest, especially if one allows for payoff uncertainty. We shall return to this point in the next lecture Games with Perfect Information Following OR, we begin with the simplest possible extensive-form game. The basic idea is as follows: play proceeds in stages, and at each stage one(and only one) player chooses anEco514—Game Theory Lecture 10: Extensive Games with (Almost) Perfect Information Marciano Siniscalchi October 19, 1999 Introduction Beginning with this lecture, we focus our attention on dynamic games. The majority of games of economic interest feature some dynamic component, and most often payoff uncertainty as well. The analysis of extensive games is challenging in several ways. At the most basic level, describing the possible sequences of events (choices) which define a particular game form is not problematic per se; yet, different formal definitions have been proposed, each with its pros and cons. Representing the players’ information as the play unfolds is nontrivial: to some extent, research on this topic may still be said to be in progress. The focus of this course will be on solution concepts; in this area, subtle and unexpected difficulties arise, even in simple games. The very representation of players’ beliefs as the play unfolds is problematic, at least in games with three or more players. There has been a fierce debate on the “right” notion of rationality for extensive games, but no consensus seems to have emerged among theorists. We shall investigate these issues in due course. Today we begin by analyzing a particu￾larly simple class of games, characterized by a natural multistage structure. I should point out that, perhaps partly due to its simplicity, this class encompasses the vast majority of extensive games of economic interest, especially if one allows for payoff uncertainty. We shall return to this point in the next lecture. Games with Perfect Information Following OR, we begin with the simplest possible extensive-form game. The basic idea is as follows: play proceeds in stages, and at each stage one (and only one) player chooses an 1