Nash Equilibrium and a Player

Nash Equilibrium and a Player's Best Response

Felix and Oscar share an apartment. Felix likes things clean and neat, whereas Oscar is somewhat less fastidious. Their utilities form a neat apartment, net of the hours worked in order to get it that way, are shown in the following game matrix.

		Oscar
		3 hours	6 hours	9 hours
Felix	3 hours	-13, -8	4, -1	7, -4
	6 hours	-4, -1	4, -1	4, -4
	9 hours	1, 2	1, -1	1, -4

For this example let's adopt the notation: Felix's best response when Oscar plays 3 is to work 9, represented as

b^F(3^O)=9

Oscar's best response when Felix plays 6 is to work either 3 or 6 hours, represented as

b^O(6^F)=3,6

We can go through the table and find all of the best responses and summarize them in a table:

Felix	Oscar
b^F(3^O)=9	b^O(9^F)=3
b^F(9^O)=3	b^O(3^F)=6
b^F(6^O)=3, 6	b^O(6^F)=3,6

From the summary table you can see that we have used best response play to find three Nash Equilibria. Only one of these is the IEDS solution to the game. Which one?