Question

Q.3 Player 1 and player 2 bargain over sharing 300 dollars. The bargaining procedure follows the Rubinstein bargaining model. Player 1's share is Ху 300 where Δ is the time interval between subsequent periods. Calculate player l's and player 2's share if Δ approaches zerO

Answer 1

Given

X1*+X2*=$300

X1*=300*(1-e^-(t/5)/(1-e^-(3t/5)

Where t= time interval

as t approaches to zero

X1* = lim (t -0){300*(1-e^-(t/5)/(1-e^-(3t/5)}

Since by simply putting t=0 we are getting X1*=0/0 which is not defined so we differentiated numerator and denominator seperately and putting t=0

X1*=300*{(1/5)*(e^-(t/5)}/{3/5)*(e^-(3t/5)}

X1*=300*(1/3)=100

X2*=200