1. Under the assumption that each bidders density fi is continuous and strictly
positive and that each vi 1Fi(vi) fi(vi) is strictly increasing.
(a) Show that the optimal selling mechanism entails the
(Principal-Agent Problem with Hidden Information) Consider a principal-agent
problem with hidden information in which the principal faces the problem of
designing an optimal (i.e., payoff maximising)
(Stochastic Dominance) Consider an N-bidder first-price auction with
independent private values. Let b be the symmetric equilibrium bidding
strategy when each bidders value is distributed according to
Consider direct mechanisms that can be derived from the first- and secondprice auctions. (a) Use the equilibrium of the second-price, sealed-bid auction
to construct an incentivecompatible direct sell
In this problem, you shall explore the consequences of risk aversion on the
part of bidders. There are N bidders participating in a first-price auction. Each
bidders value is independently drawn from
Consider the second-price, sealed-bid auction. Show that bidding ones value
is weakly dominant for bidders with independent private values (you may
show that either bidding higher or bidding lower tha
Show that the equilibrium bidding strategy of a first-price auction b(v) = 1 F
N1 (v) Z v 0 xdF N1 (x) (as derived in class) is strictly increasing. Also show
that b(v) < v for any finite number N of
2. (Optimal Auction) There is a single object for sale and there are two
potential buyers. The value assigned by buyer 1 to the object V1 is uniformly
drawn from the interval [0, 1 + k] whereas the va
[Dana & Spier (1994), Designing a private industry: Government auctions
with endogenous market structure, Journal of Public Economics] Two firms, j
= 1, 2, compete for the right to produce in a given
Microeconomics
Midterm Examination
March 24, 2014
1. Consider the following chicken game.
A2
B2
A1
2, 2
0, 3
B1
3, 0
-1, -1
(i) Find the all Nash equilibria (including that in mixed-strategy). (5%)
(i