Economic Of Negotiations

Economic of Negotiations
Assignment
Question 1
Ua(Xa)= Xa^α Xa+Xb=1
Ub(Xb)=Xb (da,db) = (0,0)

Ub(Xb)= 1-Xa
Ub(Xb)=1-Ua(Xa)^(1/α)



-g´(Ua)=(Ub-db)/(Ua-da)


(1/α)*Ua^(1/α-1)=(1-Ua^█(1/α@ ))/Ua

(1/α)Ua^(1/α )=1-Ua^(1/α)

(1/α) Ua^(1/α)+Ua^(1/α )=1

(1+α) Ua^(1/α)=α

Ua=(α/(1+α))^α

NBS is:

Xa=(α/(1+α)) ; Xb=1-(α/(1+α)) ; Ua=(α/(1+α))^α; Ub=1- (α/(1+α))


α can be interpreted as how much person A values the saloon in terms of utility. If he doesnt value the bar (if he doesnt like the cake) then α is 0, and he gets 0 from the cake. If he really likes the cake, so α = 1, and he gets ½ of the cake.







Question 2

The direction of implementing the discount factors in NBS is by giving or fetching bargaining power depending if a player is more or less patient. Its necessary to use the asymmetric NBS to turn this question.





Ua(Xa)= Xa Xa+Xb=1
Ub(Xb)=Xb ( da,db)= (0,0)


Ub(Xb)=1-Ua(Xa)




-g´(Ua)=γ/(1-γ) (Ub-db)/(Ua-da)

1= γ/(1-γ) (1-Ua)/Ua

Ua= γ
NBS is
Ua= γ ; Ub=1- γ ; Xa= γ ; Xb=1- γ



b)

If they apply Rubenstein model then:


1-Xa= δbXb ; 1-Xb= δaXa
By solving the system:
X^* a=(1-δb)/(1-δaδb) ; X^* b=(1-δa)/(1-δaδb)

equipoise Strategies
Player A invariably plead X^* a=(1-δb)/(1-δaδb) and accepts any offer Xb≤(1-δa)/(1-δaδb)
Player B always offer X^* b=(1-δa)/(1-δaδb) and accepts any offer Xa≤(1-δb)/(1-δaδb)

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