Find all pure Nash Equilibria B T B 83 28 T 94 54SolutionHer

Find all pure Nash Equilibria.

B T

B (8,3) (2,8)

T (9,4) (5,4)

Solution

Here we start with first cell and see if row player wants to switch choices . Since 8 < 9 row player wants to switch so best respond 9 is circled red. Similarly in second cell of row player as 2 <5, row player wants to switch so bese respond 5 is circles red.

Now next step is to decide the column player`s best respond. Since 8 > 3 and 4=4, so color 8 blue in cell BT at right top and color blue 4 IN cell TT .

Now Nash equilibrium exists where player B`s best respond is same as the player A`s best respond and that is cell (5,4).

Thus required Nash equilibrium is (5,4).