nash bargaining theory: axiommatic and strategic approaches

Question 1

what is the formalisation of the bargaining theory?

Answer 1

Question 2

what is the goal of axiomatic bargaining theory?

Answer 2

Question 3

what is Nashs definition of bargaining solution?

Answer 3

a function such that for each problem in the class it chooses an alternative in that problem. the solution outcome is a binding agreement between agents

Question 4

what is the class of Nash two person bargaining problems described as?

Answer 4

Question 5

what is the nash solution geographically with a disagreement point of 0,0?

Answer 5

Question 6

what occurs in a nash demand game (NDG)

Answer 6

Question 7

what approach does the Nash program take?

Answer 7

it uses the strategic (noncooperative) approach to provide noncooperative foundations for axiomatic (cooperative) bargaining solutions
it intends to bridge the gap between the noncooperative and cooperative counterparts of game theory

Question 8

what does the cooperative bargaining theory do

Answer 8

Question 9

what does the strategic (noncooperative) approach do?

Answer 9

Question 10

what is the advantage of the axiomatic approach?

Answer 10

Question 11

how does the strategic and cooperative approach complement each other?

Answer 11

Question 12

what is an axiom?

Answer 12

An axiom is the mathematical expression of our intuition of how
a solution should behave in certain situations

Question 13

what are the two categories of axioms?

Answer 13

Question 14

what is an axiomatic characterisation?

Answer 14

Question 15

what is a comprehensive problem?

Answer 15

comprehensive
problems: for a comprehensive problem, if a point x is in S, then so is any point y with d ≤ y ≤ x. (The Pareto frontier is never upward
sloping anywhere.)
comprehensiveness comes from free disposal of utility

Question 16

what is a strictly comprehensive problem?

Answer 16

Question 17

what is the formal definition of a bargaining solution?

Answer 17

Question 18

what are the four axioms laid out by nash for a bargaining solution?

Answer 18

pareto optimality, symmetry (SYM), Scale Invariance (SI) and
Independence of Irrelevant Alternatives (IIA)

Question 19

what is the symmetry axiom?

Answer 19

Symmetry (SYM): if a problem (S, d) is symmetric with respect to the
45◦ line, its solution outcome should be on that line.

Question 20

what type of axiom is symetry?

Answer 20

it is a punctual axiom

Question 21

what is the pareto optimality axiom?

Answer 21

Pareto-optimality (PO): there should be no alternative in S that
even weakly dominated the solution outcome (i.e., there should
be no alternative in S at which one agent’s payoff is at least as
large as its solution outcome payoff, and at least one agent’s payoff
is larger than that).
* In other words, the solution outcome should be on ∂S.
* From a normative viewpoint, it is difficult to see why Pareto-
optimality should not be required.

Question 22

what type of axioms is the pareto optimality axiom?

Answer 22

it is a punctual axiom

Question 23

what is the minimal amount of axioms to find an outcome of a symmetric?

Answer 23

two punctual axioms, symmetrty and pareto optimality can determine the outcome of any symmetric

Question 24

what type of axiom is scale invarianace?

Answer 24

scale invariance is an relational axiom

Question 25

what type of axiom is independence of irrelevant alternatives?

Answer 25

indepence of irrelevant alternaltives are relational

Question 26

what is scale invariance?

Answer 26

Question 27

how does the scale invariance hold out in reality?

Answer 27

the axiom routinely gets violated in lab experiments

Question 28

how can scale invariance be shown graphically?

Answer 28

Question 29

what is the independence of irrelevant alternatives (IIA)?

Answer 29

if keeping the disagreement point constant, the feasible set contracts but the alternative chosen as solution outcome in the initial feasible set still remains feasible, then it should remain the solution outcome of the new smaller feasible set

Question 30

how can independence of irrelevant alternatives be shown graphically?

Answer 30

Question 31

what does the IIA cover?

Answer 31

Question 32

what are the weighted nash solutions characterised by?

Answer 32

Question 33

what does individidual monotonicity state

Answer 33

Individual monotonicity states that an expansion of the feasible set that is favourable to an agent should not hurt him

Question 34

what is the kalai smorodinsky solution?

Answer 34

Question 35

does the kalai smorodinsky generalise to the three agent cases?

Answer 35

it does not generalise to the three agents case preserving strong pareto optimality

Question 36

what is the mid point denonomination?

Answer 36

Question 37

what is the discrete raiffa solution?

Answer 37

The Discrete Raiffa solution (proposed by Raiffa, 1953, characterized by Anbarci and Sun, 2013, Games and Economic Behavior) selects the limit of the following sequence {mt}: m1 is the average of the ideal payoffs; then mt+1 = m(S, mt), is the average of the ideal payoffs of that round obtained when it is used as disagreement point, etc.

Question 38

what axioms does the egaliatrian solution satisfy?

Answer 38

Question 39

how can the egalitarian solution be shown graphically?

Answer 39

Question 40

what does strong monotonicity without an ideal point change require?

Answer 40

Question 41

what is the equal sacrafice solution axioms?

Answer 41

Question 42

how can the equal sacrafice solution be represented graphically?

Answer 42

Question 43

what is an area monotonicity?

Answer 43

Question 44

what axioms does equal area solution satisfy?

Answer 44

Question 45

how can the equal area solution be represented graphically?

Answer 45

Question 46

what is reference point monotonicity?

Answer 46

Reference point monotonicity requires that Agent 2 not be made worse off when the initial conflict-free bargaining problem S is augmented as described above.

Question 47

what is a conflict free bargaining solution?

Answer 47

a solution where both agents can receive their ideal pay offs

Question 48

what is the average payoff solution axioms?

Answer 48

Question 49

how can the average payoff solution be shown graphically?

Answer 49

Question 50

how can the different solutions be shown on a linear pareto frontier?

Answer 50