Nash equilibrium has undoubtedly proved to be the most influential idea in game theory. enabled fundamental breakthroughs in economics and the social sciences. Its development was a major intellectual achievement; what is perhaps more important, it Recent foundational research has emphasized the subtleties in the interpretation of Nash equilibrium. This lecture deals with the technical details of equilibrium analysis, but also with these interpretational issues. However, a more precise appraisal of the situation must

This lecture, as well as the next, exemplify applications of the framework and techniques developed so far to problems of economic interest. Neither lecture attempts to cover the example applications in any generality, of course; you may however find these topics of sufficient interest to warrant further study

This lecture continues our analysis of games with payoff uncertainty. The three main objec- tives are: (1) to illustrate the flexibility of the Harsanyi framework (or our version thereof); (2)to highlight the assumptions implicit in the conventional usage of the framework, and the possible departures; (3) to discuss its potential problems, as well as some solutions to the latter

One of the merits of the notion of sequential equilibrium is the emphasis on out-of- equilibrium beliefs-that is, on beliefs (about past and future play)at information sets that should not be reached if given equilibrium is played. The key insight of extensive-form analysis is that out-of-equilibrium beliefs deter. mine equilibrium behavior. For instance, consider the simple two-stage entry deter- rence game in which potential entrant decides whether to enter a market or stay out, and the incumbent decides whether to fight or acquiesce after the entrant's move

Signaling games are used to model the following situation: Player 1, the Sender, receives some private information and sends a message m E M to Player 2, the Receiver. The latter, in turn, observes m but not 0, and chooses response r E R. Players'payoffs depend on 0, m and r. What could be simpler? Yet, there is a huge number of economically interesting games that fit nicely within this framework: Spence's job market signaling model is the leading example, but applications abound in IO (limit pricing, disclosure...) finance (security design) and political economics

This lecture continues the analysis of normal-form games. We analyze general, non-zeros ames, emphasizing the informalequation Rational Behavior Assumptions about Beliefs= Solution Concepts Before we tackle the new material. let us review what we have learned about zerosum games in light of this \equation\. Rational behavior in the context of normal-form games

The theory of extensive games is built upon a key notion, that of sequential rationality, and a key insight, the centrality of off-equilibrium beliefs. The definition of sequential equilibrium brings both to the fore in a straightforward manner, and emphasizes their interrelation. From subgame perfection to sequential rationality

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

Class: Tue-Thu 10: 40-12: 10 [?] Room 317, Bendheim. OH, by appointment. The Big Picture Most of you will already have used some of the tools of GT in your core courses. You will probably be familiar with the notions of simultaneous us. extensive-form game, perfect vs. imperfect information, complete us. incomplete information, Nash

The notion of subgame perfection is the cornerstone of the theory of extensive games. It embodies its key intuitions-and provides a vivid example of the difficulties inherent in such a theor But, above all, it has proved to be extremely profitable in a variety of applications. More- over, it has spawned a huge theoretical literature which has attempted(often successfully