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 3: Due Thursday, October 28 1. Asymmetric Auctions Consider an interdependent-values auction with two bidders, each of whom observes an i.i.d uniform signal E [0, 1]. Bidder i's valuation for the object is equal to vi

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 Problem Set 1: Due Friday, September 30 oTE: On the“ethics”of problem sets Some of the theoretical exercise I will assign are actually well-known results; in other cases, you may be able to find the answer in the literature. This is certainly the case for the current problem set. My position on this issue is that, basically, if you look up the answer somewhere, it's your problem. After all, you can buy answer keys to most textbooks... The fact is, you will not

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 Signaling Games Marciano Siniscalchi January 10, 2000 Introduction 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

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 Lecture8: Applications(1)Simultaneous Auctions Marciano Siniscalchi October 12, 1999 Introduction 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

Eco514 Game Theory Lecture 7: Interactive Epistemology(2) Marciano Siniscalchi October 7, 1999 Introduction This lecture presents the two main contributions of \interactive epistemology\ to the the- ory of normal-form games: a characterization of Nash equilibrium beliefs, and a full (i.e. behavioral)characterization of rationalizability