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

Identifying restrictions, In many cases we are interested in only one (or a...

In many cases we are interested in only one (or a few) of the equations of the model and attempts to measure its parameters statistically without a complete knowledge of the entire

What terms are included in the monopolistic competition, What terms are inc...

What terms are included in the monopolistic competition? Product Differentiation: 1. The meaning of monopolistic competition and product differentiation 2. Why monopolist

Dominant strategy , Normal 0 false false false EN-US ...

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

Vickrey auction, A sealed-bid second worth auction during which participant...

A sealed-bid second worth auction during which participants every simultaneously submit bids. The auctioneer discloses the identity of the very best bidder who is said the winner.

Procurement auction, A market mechanism during which an object, service, or...

A market mechanism during which an object, service, or set of objects is being purchased, instead of sold, to the auctioneer. The auction provides a selected set of rules which wil

Asynchrony, In a repeated game it is often unspecified that players move co...

In a repeated game it is often unspecified that players move concurrently at predefined time intervals. However, if few players update their policies at different time intervals, t

Totally mixed strategy, A mixed strategy during which the player assigns st...

A mixed strategy during which the player assigns strictly positive chance to each pure strategy.Morgenstern, Oskar,Coauthor of Theory of Games and Economic Behavior with John von N

Identify the pure strategy equilibria, Consider the following three games (...

Consider the following three games (Chicken, Matching Pennies, Stag Hunt): Chicken Player 2 Player 1 D V D -100;-100 10;-10 V -10; 10 -1;-1 Matching Pennies Pla

Pure strategy, A pure strategy defines a selected move or action that a pla...

A pure strategy defines a selected move or action that a player can follow in each potential attainable state of affairs in a very game. Such moves might not be random, or drawn fr

Assurance game, Assurance game Scenario "Assurance game" may be a generi...

Assurance game Scenario "Assurance game" may be a generic name for the sport a lot of commonly called "Stag Hunt." The French thinker, Jean Jacques Rousseau, presented the subse

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