Bilateral bargaining:

The  bargaining problem  is  the  simplest, most abstract ingredient,  of  any situation  in  which  two  (or more)  agents are  able  to  produce  some  benefit through cooperation provided they  agree  in  advance on  a  division between them.  If they fail to agree, the potential benefit never materialises and both of them loose.

For  example, there is  a  gain  to  both  a  trade union and  an  employer from reaching an agreement on more flexible working hours so that production can respond  more readily  to  fluctuations  in  demand.  The  question  is,  how  the surplus, which will  be  generated  from  greater flexibility, is to be distributed between  labour and capital  in  the form of  higher  wages and  profits.  If we notice carefully, bargaining problems are everywhere  in  the society.

Therefore, problems  cannot  merely  be  regarded  as a  technical affair  as  it involves social issues of power and justice. There are two very different approaches which game theorists have adopted  in their analysis  of  bargaining problem. The first is the so-called  axiomatic approach. In this approach game, theorists present a  series of axioms, which are considered  to  be  rules for  solving  the  problem  should satisfy. Then through formal analysis, they typically show that one criterion for dividing the gains satisfies these axioms. The second approach treats the bargaining game to  be  non-cooperative.  The bargaining process  is modeled step  by  step as a dynamic non-cooperative game, with one person making an offer and then the other and  so on. Here, we will  discuss  the axiomatic approach  in  detail. The outcome of this approach  is often referred as Nash bargaining solution  (Nash bargaining solution is quite different from Nash equilibfium).