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

Principal agent, A class of games of imperfect data during which one player...

A class of games of imperfect data during which one player (the principal) tries to supply incentives to the opposite (the agent) to encourage the agent to act within the principal

Rationality , One of the foremost common assumptions created in game theory...

One of the foremost common assumptions created in game theory (along with common information of rationality). In its mildest kind, rationality implies that each player is motivated

All-pay auction, A type of auction in which the highest bidder is rewarded ...

A type of auction in which the highest bidder is rewarded the object, but all bidders pay the auctioneer their bids. This differs from traditional first price auctions in which onl

Combining simultaneous and sequential moves, Combining Simultaneous and...

Combining Simultaneous and  Sequential Moves The material in this chapter covers a variety of issues that require some knowledge of the analysis of both sequential- move

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

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

Heuristic, A heuristic is an aid to learning, casually brought up as a rule...

A heuristic is an aid to learning, casually brought up as a rule of thumb. Formally, a heuristic may be a mechanism capable of altering its internal model of the surroundings in re

Nash Equilibria, Two people are engaged in a joint project. If each person ...

Two people are engaged in a joint project. If each person i puts in the effort xi, the outcome of the project is worth f(x1, x2). Each person’s effort level xi is a number between

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

Ship, Ship, Captain and Crew (sometimes called Ship, Captain and Mate) was ...

Ship, Captain and Crew (sometimes called Ship, Captain and Mate) was a popular bar game played for drinks with five dice and throwing cup. Each player gets three throws. He has to

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