Econ387: Introduction to Game Theory
QUIZ 7
The Lamborghini (L) solution to bargaining problems is known to satisfy the following
properties:
• Independence of Utility Scale (IUS)
• Independence of Irrelevant Alternatives (IIA)
The (L) solution to the following problem is given below and shown by “ “
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
Problem (I)
3
3.5
4
4.5
5
(Problem 2)
(Problem 3)
5
5
5
4.5
4.5
4.5
4
4
4
3.5
3.5
3.5
3
3
3
2.5
2.5
2.5
2
2
2
1.5
1.5
1.5
1
1
1
0.5
0.5
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Problem 1 is a subset of the original problem given above where some irrelevant alternatives are
deleted.(ui>4.5 and u2>3.5). Thus the solution in problem 1 would be (2.5, 3.5) since L solution satisfies
IIA.
Problem 2 is a scaled version of the original problem where the scaling factors are a1=1 and a2=0.5
Since L solution satisfies IUS, the solution in problem 2 is (2.5, 1.75)
If we scale the original problem with a1=0.5 and a2=1 we will get a set in which the solution will be (1.25,,
3.5) since L solution satisfies IUS. Note that this set we would get would contain Problem 3. Now we can
delete u1>2.25 and get the set given in problem 3 whose solution would be (1.25, 3.5) since L solution
satisfies IIA.