Econ521b Spring2009
Problem Set 6. Bandit Problem
Suggested Answer
1 (a) According to the martingale property, we know that the evolution of
(t)
=
1
)
dt + (1
(t)
(t) follows:
dt) (t + dt)
(t + dt) =
(1
(t + dt) dt:
Dividing dt on both sides and letting d
Econ521b Spring2009
Problem Set 5. Information Aggregation and Information Acquisition
Suggested Answer
1 (a) Let the report be v = (v1 ; v2 ; v3 ) 2 f0; 1g3 . Each player is required to report their
X
7
valuation and the bridge is built i
vi 4 and not bu
Econ521b Spring2009
Problem Set 4. Implementation
Suggested Answer
1 (a) Suppose a 2 F P O (R): 8b 2 A, 9 an individual, say j , suth that aRj b. If we replace
0
0
R with R0 such that for 8i, aRi b ) aRi b, then it must be aRj b. Hence, according to denit
Econ521b Spring2009
Problem Set 3. Optimal Auctions and Implementation
Suggested Answer
23.D.2. in MGW. Suppose agent 1 is the seller and 2 is the buyer. Trade occurs i
so the decision rule is
8
<1
; if
k ( 1; 2) =
:0
and thus:
v1 (k;
1; 2)
= (1
k)
1
1
2
Econ521b Spring2009
Problem Set 2. Nonlinear Pricing and Optimal Auctions
Suggested Answer
1. (1)In the mechanism hM; g i, which is composed of a correspondence M :
determining the admissible messages and an outcome function g :
g
:
!
g
();
A social choic
Econ521b Spring2009
Problem Set 1. Revelation Principle
Suggested Answer
1. (a) Typically, there are I players in the game: agent i 2 I = f1; 2; : : : ; I g. Agent i has
private information (or type):
prole by
= ( 1;
= ( 1; : : : ;
i
i
j 2Infig
2; : : : ;
Suggested Solutions for PS 1
Question 2
Assume that there are two alternative technologies for reducing pollution.
Each is owned by a separate rm i 2 f1; 2g: The technologies are convex and
they depend on an privately known parameter
i:
For simplicity, we