Question

This question will concern Nash Bargaining. (a) Show that when two agents are splitting a surplus X and agent i agent has bargaining parameter ?, the share ?i of the surplus that agent i gets will be equal to ?. (b) Consider a problem of Nash Bargaining in which an employer bargains with a worker. The worker has outside wage offer w^o from another firm, is paid wage w by the firm bargaining, and produces profit ? for the firm that’s bargaining. The firm has bargaining power ? and the worker has bargaining power 1 ? ?. What is the solution of the Nash Bargaining problem?

Answer 1

(a) If the player splits such that i <y then the players will have incentive to deviate and increase the share by I+< y and still be better off for all >0 and Being very small. Thus this deviation will take place until =y.

(b) the solution to this game is that w=w0. That is the firm offers a wage rate equal to the wage from outside w0. Consider a deviation from W<w0. In this case the output of the firm would be zero and the firm would want to deviate to choosing w=w0. Consider w>w0. In this case the firm would decrease w by a very small amount Such that the wage is w-> w0. Thus iteratively, the firm would end up offering w=w0 and the workers will accept the wage.