Who has power? Module 3

Question 1

What is a negotiation core?

Answer 1

A set of feasible allocations that cannot be improved upon by a subset of the negotiation’s parties

Question 2

What does it mean for a negotiation to have an empty core?

Answer 2

There is no coalition with all parties that cannot be improved upon for a subset of those parties

Question 3

In a two-player cooperative bargaining game, what is the feasible set?

Answer 3

Set of possible utilities that result from any possible agreements

Question 4

In a two-player cooperative bargaining game, what is the disagreement point?

Answer 4

The set of utilities that result if parties fail to reach an agreement

Question 5

What is a “bargaining solution” in a two-player cooperative bargaining game?

Answer 5

A rule that leads to “good” agreements

Question 6

What determines the disagreement point in a two-player cooperative bargaining game?

Answer 6

The BATNAs and reservation values

Question 7

What is the ZOPA of a two-player cooperative bargaining game?

Answer 7

All (u1, u2) in U such that u1>d1 and u2>d2

Question 8

Express the Nash bargaining solution of a two-player cooperative bargaining game

Answer 8

The point (z1, z2) in U that satisfies 
(z1-d1)(z2-d2)>or=(u1-d1)(u2-d2) for all (u1, u2) in U with u1>d1 and u2>d2

Question 9

What four properties does the Nash bargaining solution satisfy?

Answer 9

Pareto efficiency
Symmetry
Independence of irrelevant alternatives
Linear invariance

Question 10

Name all solutions that satisfy the properties of Pareto efficiency, symmetry, independence of irrelevant alternatives and linear invariance

Answer 10

Nash bargaining solution

Question 11

When is a bargaining game symmetric?

Answer 11

If d1=d2 and U is symmetric around the 45 degree line

Question 12

Describe in simple terms what it means if a bargaining game is symmetric

Answer 12

Players are identical

Question 13

When is a bargaining solution symmetric?

Answer 13

If for every symmetric game the solution lies on the 45 degree line, i.e. u1=u2

Question 14

What can we say about parties utilities in a symmetric bargaining solution?

Answer 14

They are equal

Question 15

When does a bargaining solution satisfy the independence of irrelevant alternatives assumption?

Answer 15

When the bargaining solution of game W equals the bargaining solution of game S, when W is a subset of U and s(U, d) is in W

Question 16

When does a bargaining solution satisfy linear invariance?

Answer 16

When the original utilities undergo a linear transformation, the new solution is the same having gone through the same linear transformation

Question 17

What happens to preferences when utilities of a bargaining solution undergo a linear transformation?

Answer 17

They remain the same, predict the same choices

Question 18

How to calculate/establish the Raiffa-Kalai-Smorodinsky bargaining solution?

Answer 18

Determine the maximum u1 possible, and the maximum u2 possible, and mark this point. Then draw a line connecting the disagreement point and this new point. The solution is where this line intersects the outer boundary of U

Question 19

What makes up a cooperative game?

Answer 19

The set of players, N.

V, the function that gives the utility generated by each coalition S

Question 20

What is another name for the set of players (N) in a cooperative game?

Answer 20

The grand coalition

Question 21

When does a game have transferable utility?

Answer 21

When total utility from an agreement can be freely distributed between coalition members

Question 22

When is a transferable utility game super additive?

Answer 22

When the union of all coalitions gives a value at least as large as the total value generated by all coalitions separately

Question 23

What is the Pareto efficient outcomes of a superadditive transferable-utility game?

Answer 23

To form the grand coalition

Question 24

In a superadditive transferable-utility game, when is a payoff distribution efficient?

Answer 24

When the sum of payoffs equals the value of the grand coalition

Question 25

In a superadditive transferable-utility game, when is a payoff distribution individually rational?

Answer 25

When the payoff to individual i of the grand coalition is greater than their payoff on their own

Question 26

In a superadditive transferable-utility game, when is a payoff distribution coalitionally rational?

Answer 26

If all players in the grand coalition are better off than in any other coalition

Question 27

If a payoff distribution is coalitionally rational, what else can we say about it?

Answer 27

It is individually rational

Question 28

What is the core of a superadditive transferable-utility game?

Answer 28

The set of payoff distributions that are efficient and coalitionally rational

Question 29

Another way to describe the core? In simple terms

Answer 29

An agreement that cannot be challenged by any subcoalition

Question 30

What does the Shapley value tell us?

Answer 30

The average of each player’s marginal contribution to all possible coalitions

Question 31

How many different orders are there for a game with N players when joining the grand coalition?

Answer 31

N!

Question 32

What four properties does the Shapley value satisfy?

Answer 32

Efficiency
Dummy
Additivity
Equal treatment of equals

Question 33

What is a dummy player?

Answer 33

A player that does not add any value to any coalition

Question 34

When is the dummy property satisfied?

Answer 34

When they payoff given to any dummy player is 0

Question 35

What does additivity mean?

Answer 35

That the combined payoff of two separate games with the same set of players is equal to the payoffs of a larger game containing both individual games with the same set of players

Question 36

What is the equal treatment of equals property?

Answer 36

That the payoffs of any two players that have the same contribution to all coalitions are equal

Question 37

What is another name of the equal treatment of equals property?

Answer 37

Symmetry

Question 38

What does the Shapley value propose?

Answer 38

How to distribute the payoffs in a cooperative game