Eco514 Game Theory Problem Set 4: Due Tuesday, November 9 1. Machines Extend Proposition 151.1 (the Perfect Folk Theorem with discounting) to arbitrary mixtures of payoff profiles of the original game G =(, (A Ui) ) Allow for both rational and real weights on the set of profiles {u(a): a E A}; note that the statement of the result will involve an approximation of the payoff profile

Eco514 Game Theory Problem Set 2: Due Thursday, October 14 Recall the following definitions: in any model M=(, (Ti, a: )eN), Ri is the event \Player i is rational\; R ien. Also, (E) is the event \Player i is certain that E is true\ and(E) NieN B (). This is as in Lecture 7

Eco514 Game Theory The Trembling Hand: Normal-Form Analysis and Extensive-Form Implications Marciano Siniscalchi January 10, 2000 Introduction: Invariance In their seminal contribution, Von Neumann and Morgenstern argue that the normal form of a game contains all \strategically relevant\ information. This view, note well, does not invalidate or trivialize extensive-form analysis; rather, it leads those who embrace it to be suspicious of extensive-form solution concepts which yield different predictions in distinct

Eco514 Game Theory Forward Induction Marciano Siniscalchi January 10, 2000 Introduction 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

Eco514 Game Theory Lecture 8.5: More on Auctions; PS#1 Marciano Siniscalchi October 14, 1999 Introduction These notes essentially tie up a few loose ends in Lecture 8; in particular, I exhibit examples of inefficiencies in first-and second-price auctions I would also like to briefly comment on Questions 1 and 2 in Problem Set 2

Eco514 Game Theory Lecture 6: Interactive Epistemology(1) Marciano Siniscalchi October 5, 1999 Introduction This lecture focuses on the interpretation of solution concepts for normal-form games. You will recall that, when we introduced Nash equilibrium and Rationalizability, we mentioned numerous reasons why these solution concepts could be regarded as yielding plausible restric- tions on rational play, or perhaps providing a consistency check for our predictions about

Eco514 Game Theory Lecture 4: Games with Payoff Uncertainty(1) Marciano Siniscalchi September 28, 1999 Introduction The vast majority of games of interest in economics, finance, political economy etc. involve some form of payoff uncertainty. A simple but interesting example is provided by auctions: an object is offered for sale, and individuals are required to submit their bids in sealed

Eco514 Game Theory Lecture 16: Applications of Sequential and Perfect Bayesian Equilibrium Marciano Siniscalchi November 16, 1999 Introduction The purpose of this lecture is to help you familiarize with the workings of sequential equi- librium and \sequential equilibrium lite, i.e. perfect Bayesian equilibrium. The main focus is the \reputation\ result of Kreps and Wilson(1982). You should refer

Eco514 Game Theory Lecture 14: General Extensive Games Marciano Siniscalchi November 10, 1999 Introduction [By and large, I will follow OR, Chapters 11 and 12, so I will keep these notes to a minimum.] Games with observed actions and payoff uncertainty Not all dynamic models of strategic interaction fit within the category of games with observed actions we have developed in the previous lectures. In particular, no allowance was made

Eco514 Game Theory Lecture 12: Repeated Games(1) Marciano Siniscalchi October 26, 1999 Introduction [By and large, I will follow OR, Chap. 8, so I will keep these notes to a minimum.] The theory of repeated games is double-edged sword. On one hand, it indicates how payoff profiles that are not consistent with Nash equilibrium in a simultaneous-move game might be achieved when the latter is played repeatedly, in a manner consistent with Nash or