coalitional game and matching markets, Game Theory

Assignment Help:
1. This question and the next is based on the following description.
Consider the coalitional game (referred to as Game 1) given by: N = {1,2,3,4};
v(N) = 3, v{i} = 0, i = 1,...,4, v{j,4} = 0, j = 1,2,3,
v(S) = 1 for all other coalitions S.
In Game 1,
a) players 1, 3 and 4 are substitutes.
b) players 2 is a dummy player.
c) players 1, 2 and 3 are substitutes.
d) player 4 is a dummy player.
e) None of the above.
2. In Game 1, player 1’s Shapley value is
a) 5/6.
b) 11/12.
c) 1/6.
d) 1/4.
e) None of the above.
3. In Game 1, player 4’s Shapley value is
a) 1/4.
b) 1/2.
c) 1/6.
d) 5/6.
e) None of the above.
4. Consider the two-sided matching model in which a set of three men M = {m1,m2,m3} and a set of three women W = {w1,w2,w3} have strict preferences over members of the opposite sex, given by
m1 : w2,w1,w3; w1 : m1,m3,m2
m2 : w1,w2,w3; w2 : m3,m1,m2
m3 : w1,w2,w3; w3 : m1,m2,m3.
The men ?nd all the women acceptable and the women ?nd all the men acceptable.
a) The men-proposing (M-proposing) and the women-proposing (W-proposing) Deferred Ac-ceptance Algorithms (DAAs) lead to the same core-stable matching for this example.
b) The M-proposing DAA matches m2 with w2 while the the W-proposing DAA matches m2 with w3.
c) Each of m1 and m2 strictly prefers his M-proposing match to his W-proposing match.
d) Each of w1, w2 and w3 strictly prefers her W-proposing match to her M-proposing match.
e) None of the above.
5. Consider the problem of matching a set of four students {i1,i2,i3,i4} to a set of three schools {s1,s2,s3}, where school s1 has a quota (or capacity) of 2 students each and schools s2 and s3 have a quota of 1 student each. Each student has a strict preference ranking over the schools and each school has a priority order for the students that is determined by a central authority. Each student’s preference and each school’s (strict) priority order for each student are given below
i1 : s3, s1, s2 s1 : i1, i2, i3, i4
i2 : s2, s1, s3 s2 : i1, i2, i3, i4
i3 : s1, s3, s2 s3 : i3, i1, i2, i4
i4 : s1, s2, s3
Applying the Top Trading Cycle Algorithm (TTCA) to this school choice problem leads to
a) i1 matched to s3, i2 to s1 and i3 to s4.
b) i1 matched to s3, i2 to s1 and i4 to s1.
c) i2 matched to s3, i3 to s2 and i4 to s1.
d) i1 matched to s3, i2 to s1 and i4 to s2.
e) None of the above.

Related Discussions:- coalitional game and matching markets

Full equilibrium strategy example, (a) A player wins if she takes the tota...

(a) A player wins if she takes the total to 100 and additions of any value from 1 through 10 are allowed. Thus, if you take the sum to 89, you are guaran- teed to win; your oppone

Games with strategic moves, Games with Strat e gic M ov es   ...

Games with Strat e gic M ov es   The ideas in this chapters can be brought to life and the students can better appreciate the subtleties of various strategic moves an

Kakutani, Twentieth century mathematician who expanded on earlier fastened ...

Twentieth century mathematician who expanded on earlier fastened purpose theorems. a hard and fast purpose theorem defines the conditions on a perform, f(x), beneath that there exi

Quiz to generate a grid, 1.a.out 2 1 Here is the grid that has been gene...

1.a.out 2 1 Here is the grid that has been generated: 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 0

Rock paper scissors, Scenario To determine who is needed to try to to th...

Scenario To determine who is needed to try to to the nightly chores, 2 youngsters simultaneously build one among 3 symbols with their fists - a rock, paper, or scissors. straigh

Tower defense, Tower defense - is a subgenre of real-time strategy games. T...

Tower defense - is a subgenre of real-time strategy games. The goal of tower defense games is to try to stop enemies from crossing a map by building towers which shoot at them as t

equilibrium refinement, An equilibrium refinement provides how of choosing...

An equilibrium refinement provides how of choosing one or many equilibria from among several in a very game. several games might contain many Nash equilibria, and therefore supply

Prisoners’ dilemma game, The Prisoners’ Dilemma Game The idea th...

The Prisoners’ Dilemma Game The idea that tacit cooperation can be sustained in an ongoing relationship is very simple and students easily accept it. The formal analysis

Simultaneous move games with mixed strategies, This chapter introduces mixe...

This chapter introduces mixed strategies and the methods used to solve for mixed strategy equilibria. Students are likely to accept the idea of randomization more readily if they t

Compute the nash equilibrium, Consider two quantity-setting firms that prod...

Consider two quantity-setting firms that produce a homogeneous good. The inverse demand function for the good is p = A - (q 1 +q 2 ). Both firms have a cost function C = q 2 (a

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd