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

Reverse auction, While ancient auctions involve one seller and plenty of co...

While ancient auctions involve one seller and plenty of consumers, a reverse auction typically involves several sellers and one buyer. for instance, procurement auctions are used t

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 –

Formulate the situation as strategic game - nash equilibrium, Two individua...

Two individuals use a common resource (a river or a forest, for example) to produce output. The more the resource is used, the less output any given individual can produce. Denote

Repeated game, When players interact by enjoying an identical stage game (s...

When players interact by enjoying an identical stage game (such because the prisoner's dilemma) varied times, the sport is termed a repeated game. not like a game played once, a re

Multiple nash equilibria, The following is a payoff matrix for a non-cooper...

The following is a payoff matrix for a non-cooperative simultaneous move game between 2 players. The payoffs are in the order (Player 1; Player 2): What is/are the Nash Equil

Rollback equilibrium, Rollback equilibrium       (b) In t...

Rollback equilibrium       (b) In the rollback equilibrium, A and B vote For while C and D vote Against; this leads to payoffs of (3, 4, 3, 4). The complete equil

DYnamic, saaaaaaasfffffffffffffffffffaaaczzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz...

saaaaaaasfffffffffffffffffffaaaczzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Deadlock , Description The simplest of William Poundstone's social dilem...

Description The simplest of William Poundstone's social dilemmas during which the every player contains a dominant strategy and also the equilibrium is Pareto optimal. the sole

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

non-credible threat , A non-credible threat may be a threat created by a p...

A non-credible threat may be a threat created by a player in a very Sequential Game which might not be within the best interest for the player to hold out. The hope is that the thr

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