1. Asymmetric auctions Consider an interdependent-values auction with two bidders, each of whom observes an i.i.d uniform signal s; E [ 0, 1]. Bidder i' s valuation for the object is equal to
1. Machines Extend Proposition 151. 1(the Perfect Folk Theorem with discounting)to arbitrary mixtures of payoff profiles of the original game G=(N, (Ai, lilieN Allow for both rational and real weights on the set of profiles u(a): aE A]; note that the statement of the result will involve an approximation of the payoff profile Construct a machine that implements the strategies in your proof
Player i is rational\;R=nieN Ri. Also, Bi(E) is the event \Player i is certain that E is true\ and B(E)=neN Bi(E). This is as in Lecture 7. Let me introduce the following notation for iterated mutual certainty: B()(E)=E B()(E)=B(B-I)(E)). Then the definition of Bk in Lecture 7 can be rewritten as Bk
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 uspicious of extensive-form solution concepts which yield different predictions in distinct