nash bargaining theory: axiommatic and strategic approaches Flashcards
what is the formalisation of the bargaining theory?
what is the goal of axiomatic bargaining theory?
what is Nashs definition of bargaining solution?
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
what is the class of Nash two person bargaining problems described as?
what is the nash solution geographically with a disagreement point of 0,0?
what occurs in a nash demand game (NDG)
what approach does the Nash program take?
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
what does the cooperative bargaining theory do
what does the strategic (noncooperative) approach do?
what is the advantage of the axiomatic approach?
how does the strategic and cooperative approach complement each other?
what is an axiom?
An axiom is the mathematical expression of our intuition of how
a solution should behave in certain situations
what are the two categories of axioms?
what is an axiomatic characterisation?
what is a comprehensive problem?
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
what is a strictly comprehensive problem?
what is the formal definition of a bargaining solution?
what are the four axioms laid out by nash for a bargaining solution?
pareto optimality, symmetry (SYM), Scale Invariance (SI) and
Independence of Irrelevant Alternatives (IIA)
what is the symmetry axiom?
Symmetry (SYM): if a problem (S, d) is symmetric with respect to the
45◦ line, its solution outcome should be on that line.
what type of axiom is symetry?
it is a punctual axiom
what is the pareto optimality axiom?
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.
what is scale invariance?
how can scale invariance be shown graphically?
how can independence of irrelevant alternatives be shown graphically?
what does the IIA cover?
what are the weighted nash solutions characterised by?
what does individidual monotonicity state
Individual monotonicity states that an expansion of the feasible
set that is favourable to an agent should not hurt him
what is the kalai smorodinsky solution?
does the kalai smorodinsky generalise to the three agent cases?
it does not generalise to the three agents case preserving strong pareto optimality
what is the mid point denonomination?
what is the discrete raiffa solution?
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.
what axioms does the egaliatrian solution satisfy?
how can the egalitarian solution be shown graphically?
what does strong monotonicity without an ideal point change require?
what is the equal sacrafice solution axioms?
how can the equal sacrafice solution be represented graphically?
what is an area monotonicity?
what axioms does equal area solution satisfy?
how can the equal area solution be represented graphically?
what is the average payoff solution axioms?
how can the average payoff solution be shown graphically?
how can the different solutions be shown on a linear pareto frontier?
