Unions and Collective Bargaining

1
Topic 4 Part II
Unions and Collective Bargaining
2
The Generalized Nash Cooperative Solution

• Model Setup
• A and B players
• v total value obtained if an agreement is
  reached
• a, b BATNA (Best Alternative to a Negotiated
  Agreement) for Players A and B,
  respectively
• v (a b) gt 0 bargaining surplus is positive
• h, k bargaining strengths (power) for Players A
  and B, respectively (exogenous variables)
• x, y bargaining outcomes if an agreement is
  reached
• Agreement should be enforceable no possibility
  of deviation of a party from the agreement

3
The Generalized Nash Cooperative Solution

• Nash analyzed the properties that an acceptable
  bargaining outcome (x, y) should have (axiomatic
  approach) and proved that a bargaining outcome
  that hold these properties is unique and can be
  derived analytically
• Efficiency is one of the properties of this
  bargaining outcome no available mutual gain
  should go unexploited, i.e., the bargaining
  outcome should lie in the efficiency frontier
• v x y

4
The Generalized Nash Cooperative Solution

• The bargaining outcome can be characterized by
  the following maximization problem
• max (x a)h (y b)k
• x, y
• s.t.
• y v - x

5
The Generalized Nash Cooperative Solution

• The solution of the optimization problem provides
  the values for x and y
• x h(v b) ka/(kh)
• y v x

6
The Generalized Nash Cooperative Solution

• Nash bargaining formula for splitting the surplus
  (implied by the bargaining solution)
• (y b)/(x a) k/h
• This formula shows that the bargaining solution
  implies that the ratio of surpluses shared by A
  and B depends on the relative bargaining power of
  the players the higher the relative bargaining
  power of the player, the higher his/her relative
  share of surplus