Question

c1c2c3 20,20 0,0 -24,2 16,16 -2,-2 30,2 16,-2 0,0

Find the Nash Equilibria. Can it be found by iterated dominance? Why or why not?

Answer 1

Answer Nash Equilibrium IG I C2 163 92 / 20,20 0,0 -2,30 r -24,2 16, 16 -2,-2 73 30,2 16, -2 10,0 Using the concept of dominant strategies, we see: for the row player , r is dominated by rz Therefore he would never play ra Reduced matrin : (Deleting r2) -la 1 C 103 er | 20,20 0,0 -2,30 93 | 30,2 16,-2 | 0,0 Here again we see that for the row player r, is strictly dominated by ra This he would never play a r, over rz Reduced matrin & (Deleting ry) | وعلى | r3/30, 2/16, -20,0 Here we see that for the column player Ca is strictly dominated by C. Thus he would never play Ca over c,

Reduced matrina (Deleting (₂) Тc, TC2 93 30,2 0,0 Again it can be seen that for the column player Cg is strictly dominated by clothes the column will never play C₂ over C, Reduced matrix : ( Deleting (3) Reduced matrina 2 ) is the Nash M3 30,2 ' equilibrium Thus after deletion of all dominated Strategies we are just left with the strategy ra, ci) which is this the nash equilibrium strategy. Also, yes the nash equilibrium was found using iterated dominance since there to were rows and columns that were strictly dominated by corresponding rows or columns.