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

Bidder, An auction associates who submits offers (or bids) to sale or buy  ...

An auction associates who submits offers (or bids) to sale or buy  the goods being auctioned.

Pareto coordination game, Scenario Two corporations should simultaneousl...

Scenario Two corporations should simultaneously elect a technology to use for his or her compatible merchandise. If the corporations adopt totally different standards, few sales

Uniform worth, A uniform worth auction may be a multiunit auction during wh...

A uniform worth auction may be a multiunit auction during which each winning bidder pays identical worth, which can or might not be equal to the participants' bids. Alternatively,

Bayes, Eighteenth century British mathematician who recognized a method for...

Eighteenth century British mathematician who recognized a method for probabilistic mathematical inference. His Bayes Theorem, published posthumously, treats probability as a logic.

Bid, . A bid is an sign by a potential buyer of the price the buyer is read...

. A bid is an sign by a potential buyer of the price the buyer is ready to pay for the object being auctioned. In a Procurement Auction, the bid is an sign of the price a seller is

Games with sequential moves-president liv problem , The most basic version ...

The most basic version of a LIV allows the executive office holder (Governor or President) to accept part of a bill passed by the legislature (so that part becomes law) and to veto

Simultaneous game, A simultaneous game is one during which all players buil...

A simultaneous game is one during which all players build choices (or choose a strategy) while not information of the methods that are being chosen by different players. Although t

Absolute auction, A general term for an English auction in which there is n...

A general term for an English auction in which there is no reserve price, guaranteeing that the object will be sold to the highest bidder regardless of the quantity of the bid.

Solve for the bayesian nash equilibrium, Consider the Cournot duopoly model...

Consider the Cournot duopoly model in which two rms, 1 and 2, simultaneously choose the quantities they will sell in the market, q 1 and q 2 . The price each receives for each uni

Bidding ring, A set of colluding bidders. Ring participants agree to rig bi...

A set of colluding bidders. Ring participants agree to rig bids by agreeing not to bid against each other, either by avoiding the auction or by placing phony (phantom) bids.

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