Editing Bargaining (section)

===Game theory===
[[Nash bargaining game|Bargaining games]] refer to situations where two or more players must reach an agreement regarding how to distribute an object or monetary amount. Each player prefers to reach an agreement in these games, rather than abstain from doing so. However, each prefers that the agreement favor their interests. Examples of such situations include the bargaining involved in a labor union and the directors of a company negotiating wage increases, the dispute between two communities about the distribution of a common territory, or the conditions under which two countries agree on nuclear disarmament. Analyzing these kinds of problems looks for a solution that specifies which component in dispute corresponds to each party involved.
 
Players in a [[bargaining problem]] can bargain for the objective as a whole at a precise moment in time. The problem can also be divided so that parts of the whole objective become subject to bargaining during different stages.

In a classical bargaining problem, the result is an agreement reached between all interested parties or the status quo of the problem. It is clear that studying how individual parties make their decisions is insufficient for predicting what agreement will be reached. However, classical bargaining theory assumes that each participant in a bargaining process will choose between possible agreements, following the conduct predicted by the rational choice model. It is particularly assumed that each player's preferences regarding the possible agreements can be represented by a [[von Neumann–Morgenstern utility theorem]] function.

[[John Forbes Nash Jr.|Nash]] [1950] defines a classical bargaining problem as being a set of joint allocations of utility, some of which correspond to what the players would obtain if they reach an agreement, and another that represents what they would get if they failed to do so.

A bargaining game for two players is defined as a pair (F,d) where F is the set of possible joint utility allocations (possible agreements), and ''d'' is the [[Cooperative_bargaining#Disagreement_point|disagreement point]].

For the definition of a specific bargaining solution, it is usual to follow Nash's proposal, setting out the [[Axiom|axioms]] this solution should satisfy. Some of the most frequent axioms used in the building of bargaining solutions are [[efficiency]], symmetry, independence of irrelevant alternatives, scalar invariance, monotonicity, etc.

The [[Nash bargaining solution]] is the bargaining solution that maximizes the product of an agent's utilities on the bargaining set.

The Nash bargaining solution, however, only deals with the simplest structure of bargaining. It is not dynamic (failing to deal with how [[Pareto efficiency|Pareto]] outcomes are achieved). Instead, for situations where the structure of the bargaining game is important, a more mainstream game-theoretic approach is useful. This can allow players' preferences over time and risk to be incorporated into the solution of bargaining games. It can also show how the details can matter. For example, the Nash bargaining solution for the [[prisoners' dilemma]] is different from the Nash equilibrium.