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

Determine the bayesian nash equilibrium of a game, Stanley is auctioning an...

Stanley is auctioning an item that he values at zero. Betty and Billy, the two potential buyers, each have independent private values which are drawn from a uniform distribution, P

Best reply dynamic, The best reply dynamic is usally termed the Cournot adj...

The best reply dynamic is usally termed the Cournot adjustment model or Cournot learning after Augustin Cournot who first proposed it in the context of a duopoly model. Each of two

Fictitious play , A method by that players assume that the methods of their...

A method by that players assume that the methods of their opponents are randomly chosen from some unknown stationary distribution. In every amount, a player selects her best respon

Dynamic game, Normal 0 false false false EN-US X-NONE...

Normal 0 false false false EN-US X-NONE X-NONE

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

Find the nash equilibria - strategic game, Two people are engaged in a join...

Two people are engaged in a joint project. If each person i puts in the e ort xi, a nonnegative number equal to at most 1, which costs her c(x i ), the outcome of the project is wo

Game playing in class-2 players take turns choosing a number, Problem:-Two ...

Problem:-Two players take turns choosing a number between 1 and 10 (inclusive), and a cumulative total of their choices is kept. The player to take the total exactly to 100 is the

Ring, A collection of colluding bidders. Ring members comply with rig bids ...

A collection of colluding bidders. Ring members comply with rig bids by agreeing to not bid against one another, either by avoiding the auction or by putting phony (phantom) bids

Multiple item auction, Normal 0 false false false EN-US...

Normal 0 false false false EN-US X-NONE X-NONE

What are the important forms of product differentiation, What are the impor...

What are the important forms of product differentiation? There are three significant forms of product differentiation, which are: 1. Differentiation through style or type –

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