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

Find a bayesian nash equilibrium, In Bontemps, Louisiana there are only two...

In Bontemps, Louisiana there are only two places to spend time: Merlotte's bar and Fangtasia. Sookie and Eric have made plans to spend Friday night together, but they never decided

Payoff, In any game, payoffs are numbers that represent the motivations of ...

In any game, payoffs are numbers that represent the motivations of players. Payoffs might represent profit, quantity, "utility," or different continuous measures (cardinal payoffs)

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

Minimum bid, A minimum bid is that the smallest acceptable bid in an auctio...

A minimum bid is that the smallest acceptable bid in an auction. a gap bid, the primary bid placed within the auction, should be a minimum of as high because the minimum bid or the

Game 4 auctioning a penny jar (winner’s curse), GAME 4 Auctioning a Penny J...

GAME 4 Auctioning a Penny Jar (Winner’s Curse) Show a jar of pennies; pass it around so each student can have a closer look and form an estimate of the contents. Show the stud

Payoffs, mixed strategy game with ordinal and cardinal payoffs example plea...

mixed strategy game with ordinal and cardinal payoffs example please

Bidder''s choice, A multiunit auction mechanism for assigning heterogeneous...

A multiunit auction mechanism for assigning heterogeneous (different) objects. The highest bidder in the first round selects one item among those offered for sale. Then, a second r

Hawk-dove game , Scenario The hawk-dove game is additionally commonly ca...

Scenario The hawk-dove game is additionally commonly called the sport of chicken. 2 hooligans with one thing to prove drive at one another on a slender road. The primary to swer

Utility, In any game, utility represents the motivations of players. A util...

In any game, utility represents the motivations of players. A utility perform for a given player assigns variety for each potential outcome of the sport with the property that a be

Explain oligopoly''s structure and use game theory, Explain oligopoly's str...

Explain oligopoly's structure and use game theory to explain why oligopoly firms tend not to use price to compete. Answer- Oligopoly is an imperfect market where there are

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