Cooperative Bargaining

Question 1

What is Coase theorum?

Answer 1

• The idea that from two endowments players should always agree a pareto efficient deal.
• They will always end up on a point on the contract curve

Question 2

How do you create a payoff space?

Answer 2

• Firstly show all payoffs from pure strategies

1. Mixed strategies are just weighted average of pure strategies so any payoff inbetween them is possible (red)
2. Free disposal - any player can reduce their own payoff (blue)
3. Side payments - can compensate each other, line through max joint surplus, slope -1 - The Bargaining Set

Question 3

What is the Bargaining set?

Answer 3

• The line that goes through the maximum joint surplus, the slope is -1 showing the potnetial to trade payoffs
• Coase says that the agreement will be on the bargaining set and will therefore be pareto efficent
  
  • This requires zero transaction costs
  • Doesnt say where on the set it will be though

Question 4

How does Nash Bargaining work?

Answer 4

• Payoffs represented by (X, b, d)
  
  • feasible payoff, breakdown, deadlock
• Use Nash product = (x₁ - d₁)^à (x₂ - d₂)^ß = c
• use x₂ = surplus - x₁
• find F.O.C: ^dc/_dx1 = 0
• Then find the values of x₁ and x₂
• Check that they satisfy x₁ > b₁ and x₂ > b₂

Question 5

What do you do if the solution for x_i is below b_i?

Answer 5

Question 6

How does risk aversion work in the divide the dollar game?

Answer 6