41-310 Assignment 2 Due on Nov. 16 (Monday), 2:30pm. (Please turn it

41-310 Assignment 2 Due on Nov. 16 (Monday), 2:30pm. (Please turn it
in at the beginning of the class.)
1.
Player 2
Left
Right
Player 1
Top
4,4
0,6
Bottom
6,0
1,1
For the game as shown above,
a. which strategy is the dominant strategy for P1
b. Write down the dominant strategy equilibrium.
c. The dominant strategy equilibrium payos (1,1) are not optimal. Is
it possible to change the game with a transfer (or penalty) between the two
players so that the dominant strategy equilibrium of the new game becomes
ecient Find the transfer and represent the new game after the transfer.
2. (GHG) There are 40 identical countries in the world. Facing a deci-
sion making problem of maintaining a steady economic growth and reduc-
ing GHGs, each has two choices: Reduce GHGs (R) and Not to reduce
GHGs(NR). If a country chooses NR, then the economy grows faster, and
the faster growth generates an additional estimated economic value of 20
billion dollars. But it increases the level of GHGs in the atmosphere, and its
negative impact imposes the cost of $1 billion
on each and every country
in the world
. If a country selects R, then its economy grows slower, the
slower growth generates an additional estimated economic value of only 5
billion dollars. In this case, there is no increase in GHGs in the atmosphere,
and hence no negative impact.
(a) Show that R is dominated by NR for a country.
(b) Find the total (social) maximum surplus and the minimum surplus
(or maximum loss).
(c) Explain the reason why the minimum surplus, not the total maximum
surplus, is likely to be the outcome these countries collectively select.
3. Two countries, country 1 and country 2, select either Abate or Pollute.
Each country has two types of individuals, Ninenine and Topone. Individuals
receive two types of gains(or losses); economic gain and non-economic gain.
Assume that Ninenines only receive non-economic gain and Topones only
receive economic gain.
If there are no Topones and only Ninenines in both countries, then the
game is represented as shown below.
1
Country 2
Abate
Pollute
Country 1
Abate
0.5, 0.5
0.4, 0
Pollute
0, 0.4
-0.1,-0.1
If there are only Topones without Ninenines in both countries, then the
game is represented as shown below.
Country 2
Abate
Pollute
Country 1
Abate
-8, -8
-9, 12
Pollute
12, -9
10, 10
a. Suppose that there are 50 Ninenines and 1 Topone. Find or represent
the game that the two countries are playing. And nd the dominant strategy
equilibrium of the game.
b. If the non-economic gains are ignored in each country, what will be
the expected choices made by the countries Explain why it is suboptimal.
c. Is the prisoners’ dilemma game an appropriate game that describes
the problem faced by the two countries here Explain.
4. Individuals A and B both enjoy
owers (public good). The MWTP curves
of
owers are given by
M W T P
(
A
) = 60