Clarke-Groves Mechanism!

Hi all,
I'd appreciate if you could provide a solution to these questions as
I'm unfamilar with this concept. If possible could you provide an
explanation also? Thanks.

QUESTION 1:

Suppose we have a society consisting of three individuals and two
public projects, A and B. The following data gives the benefit derived
by each person from each project(that is, the benefit net of the taxes
assessed in order to command the resources to construct the project).

1 2 3

Project A 15 25 37
Project B 20 15 45

(1) What project would be undertaken if the Clarke-Groves Mechanism
were employed and individuals reported the above benefit figures
truthfully?

(2) Show that none of the three individuals has an incentive to
misrepresent his benefit schedule in part (1). What does it mean to
say that truthful revelation of preferences is a dominant strategy in
this case?

(3) What is the size of the government budget surplus associated with
the answer to part (1)?

(4) Suppose now that the government budget surplus would be returned
to the community by giving each individual an equal share. Show that
truthful revelation is no longer a dominant strategy in the case of
the Clarke-Groves mechanism.

(5) Using a specific numerical example, show that although a single
individual can not manipulate the Clarke-Groves mechanism, it is
vunerable to manipulation by a coalition of individuals acting in
concert.

QUESTION 2:

Exact same question as above with the following data:

1 2 3

Project A 30 46 70
Project B 40 30 90

.