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

Player , Any participant in a very game who (i)  contains a nontrivial s...

Any participant in a very game who (i)  contains a nontrivial set of methods (more than one) and (ii) Selects among the methods primarily based on payoffs. If a player is non

Hicks, Winner of the Nobel Prize in 1972, Hicks is acknowledged mutually of...

Winner of the Nobel Prize in 1972, Hicks is acknowledged mutually of the leading economists normally equilibrium theory. he's credited with the introduction of the notion of elasti

Green –beard strategy, 1  A, Explain how a person can be free to choose but...

1  A, Explain how a person can be free to choose but his or her choices are casually determined by past event 2  B , Draw the casual tree for newcomb's problem when Eve can't pe

Rules of snake eyes game, Rules of Snake Eyes (small variation on game call...

Rules of Snake Eyes (small variation on game called Craps in USA) Player rolls two dice. On the first roll if the total of the dice is 2 (snake eyes): player wins and rece

What do you study about saving and investment spending, What do you study a...

What do you study about the saving, investment spending and financial system? Savings, Investment Spending, and the Financial System: 1. The correlation between savings and

Three words, if the first three words are "the boy''s down" what are the la...

if the first three words are "the boy''s down" what are the last three words?

Difference monopolistic competition and perfect competition, What is the di...

What is the different monopolistic competition and perfect competition? Monopolistic Competition versus Perfect Competition Into the long-run equilibrium of a monopolistical

Cournot, Nineteenth century French economist attributed with the introducti...

Nineteenth century French economist attributed with the introduction of the theory of profit maximizing producers. In his masterpiece, The Recherches, published in 1838, Cournot pr

Game playing in class-equilibrium payoffs example, (a) Equilibrium payoffs ...

(a) Equilibrium payoffs are (1, 0). Player A’s equilibrium strategy is S; B’s equilibrium strategy is “t if N.”   For (a): Player A has two strategies: (1) N or (2) S. P

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