Find the Nash equilibria of the following game column row a

Find the Nash equilibria of the following game

Solution

suppose column represents stretegy for player 1 and its pay off is x axis point.

and row represents stretegy for player 2 and its pay off is y axis point.

nash equilibrium is a point at which no player can get incermental benifit from changig its action when he player knows others stretegy

For player 1

if player 1 choses its b strategy then he will benificied if player 2 chooses its a stertegy (because max(10,2) =10)

if player 1 choses its a strategy then he will benificied if player 2 chooses its a stertegy (because max(13, 5) =13)

For player 2

if player 2 choses its a strategy then he will benificied if player 1 chooses its a stertegy (because max(10,3) =10)

  if player 2 choses its b strategy then he will benificied if player 1 chooses its a stertegy (because max(8,-5) =8)

thus there will no increamnet in both player benifit if both choses a startegy, therfore nash equalibrium exist at (a,a)