Who has power? Module 3 Flashcards
What is a negotiation core?
A set of feasible allocations that cannot be improved upon by a subset of the negotiation’s parties
What does it mean for a negotiation to have an empty core?
There is no coalition with all parties that cannot be improved upon for a subset of those parties
In a two-player cooperative bargaining game, what is the feasible set?
Set of possible utilities that result from any possible agreements
In a two-player cooperative bargaining game, what is the disagreement point?
The set of utilities that result if parties fail to reach an agreement
What is a “bargaining solution” in a two-player cooperative bargaining game?
A rule that leads to “good” agreements
What determines the disagreement point in a two-player cooperative bargaining game?
The BATNAs and reservation values
What is the ZOPA of a two-player cooperative bargaining game?
All (u1, u2) in U such that u1>d1 and u2>d2
Express the Nash bargaining solution of a two-player cooperative bargaining game
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
What four properties does the Nash bargaining solution satisfy?
Pareto efficiency
Symmetry
Independence of irrelevant alternatives
Linear invariance
Name all solutions that satisfy the properties of Pareto efficiency, symmetry, independence of irrelevant alternatives and linear invariance
Nash bargaining solution
When is a bargaining game symmetric?
If d1=d2 and U is symmetric around the 45 degree line
Describe in simple terms what it means if a bargaining game is symmetric
Players are identical
When is a bargaining solution symmetric?
If for every symmetric game the solution lies on the 45 degree line, i.e. u1=u2
What can we say about parties utilities in a symmetric bargaining solution?
They are equal
When does a bargaining solution satisfy the independence of irrelevant alternatives assumption?
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
When does a bargaining solution satisfy linear invariance?
When the original utilities undergo a linear transformation, the new solution is the same having gone through the same linear transformation
What happens to preferences when utilities of a bargaining solution undergo a linear transformation?
They remain the same, predict the same choices
How to calculate/establish the Raiffa-Kalai-Smorodinsky bargaining solution?
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
What makes up a cooperative game?
The set of players, N.
V, the function that gives the utility generated by each coalition S
What is another name for the set of players (N) in a cooperative game?
The grand coalition
When does a game have transferable utility?
When total utility from an agreement can be freely distributed between coalition members
When is a transferable utility game super additive?
When the union of all coalitions gives a value at least as large as the total value generated by all coalitions separately
What is the Pareto efficient outcomes of a superadditive transferable-utility game?
To form the grand coalition
In a superadditive transferable-utility game, when is a payoff distribution efficient?
When the sum of payoffs equals the value of the grand coalition
In a superadditive transferable-utility game, when is a payoff distribution individually rational?
When the payoff to individual i of the grand coalition is greater than their payoff on their own
In a superadditive transferable-utility game, when is a payoff distribution coalitionally rational?
If all players in the grand coalition are better off than in any other coalition
If a payoff distribution is coalitionally rational, what else can we say about it?
It is individually rational
What is the core of a superadditive transferable-utility game?
The set of payoff distributions that are efficient and coalitionally rational
Another way to describe the core? In simple terms
An agreement that cannot be challenged by any subcoalition
What does the Shapley value tell us?
The average of each player’s marginal contribution to all possible coalitions
How many different orders are there for a game with N players when joining the grand coalition?
N!
What four properties does the Shapley value satisfy?
Efficiency
Dummy
Additivity
Equal treatment of equals
What is a dummy player?
A player that does not add any value to any coalition
When is the dummy property satisfied?
When they payoff given to any dummy player is 0
What does additivity mean?
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
What is the equal treatment of equals property?
That the payoffs of any two players that have the same contribution to all coalitions are equal
What is another name of the equal treatment of equals property?
Symmetry
What does the Shapley value propose?
How to distribute the payoffs in a cooperative game
