Question

1. Players A and B are bargaining over the price of a service contract. The highest price thatplayer B is willingto pay is OMR300. The lowest price that player A is willing to accept isOMR150. Suppose that each player’s discount factor is dA = dB = 0.05.

1. For a subgame perfect equilibrium to exist, what price should player B offer for thecontract in the first round? What portion of the surplus will player A receive? Whatportion of the surplus will player B keep?
2. Suppose that player B’s discount factor remains dB = 0.05, but player A’s discountfactor increases to dA = 0.07. What price should player B offer for the contract inthe first round? What portion of the surplus will player A receive? What portion of thesurplus will player Bkeep?

Answer 1

According to the question ,

A is willing to accept lowest price = 150

B is willing to pay maximum price=300

so the gains from trade , M=300-150=150

1] both have discountinh factor =0.05

therefore both will balance with 75

so now B will offer 150+75=225

through which A will get profit of 75 and also , B will retain surplus of 75 with himself.

2] no the discounting factors are, A= 0.07

and B=0.05

then buyer will offer M*[1-0.7*0.5]=150*.65=97.5

therefore, B will offer 150+97.5=247.5

according to this A will get benefit of 97.5 and B will get surplus of 52.5