Question

We have the assignment (Buyer 1, Seller 1), (Buyer 2, Seller 2). The payoffs are:

Buyer 1 = 11

Seller 1 = 15

Buyer 2 = 10

Seller 2 = 6

Buyer 1 and Seller 2 can generate together 16. Buyer 2 and Seller 1 can generate together 26. Is the assignment stable?

Answer 1

In the suggested information of an assignment where we have

Buyer	Payoffs	Seller	Paoffs
1	11	1	15
2	10	2	6

So, here the probable solutions and combinations can be made of like;

	Buyer 1	Seller 1	Buyer 1	Seller 2	Buyer 2	Seller 1	Buyer 2	Seller 2
Payoffs	11	15	11	6	10	15	10	6
Total Payoffs	26	17	25	16

So here, if we check then the probable solutions by making the combination is as per the above table where B1 & S1 together is making 26 as total payoffs, B1&S2 is making 17 as total payoffs, B2 & S1 is having 25 as total payoffs, and in last B2 & S2 is making the lowest payoff as 16.

So out of the given probable payoffs of all the buyers and seller the highest is amonst Buyer 1 and Seller 1, however the lowest is between Buyer 2 and Seller 2.

However if we check the stability and consistency in the provided assignments then there is overall inconsistency in nature also the whole combination is not stable in payoffs.

Also in the problem provided the probable solution provided for Buyer 1 and Seller 2 then it is presented as 16 whereas the solution is provided as 17 and in other combination the Buyer 2 and Seller 1 is giving 26 instead of 25.

So the overall suggested solution is confirms the instability of the solutions in the payoffs group.