Solving matching pennies Player 2 Head Tail Player 1's best response B1(g): Player Head -1,1 1-1 For q<0.5,Head (r=1)1 Tail 1,-1 -1, 1 1- For q>0.5,Tail (r=0) For q=0.5,indifferent (0srs1) q 1-9 Player 2's best response Mixed strategy B2（r): Nash equilibrium For r<0.5,Tail (q=0) 1 >For r>0.5,Head (q=1) >For r=0.5,indifferent (0sqs1) √Check 12 x=0.5∈B1(0.5) q=0.5∈B2(0.5) 1/2 1 9Solving matching pennies Player 2 Head Tail Player 1 Head -1 , 1 1 , -1 Tail 1 , -1 -1 , 1 9 ◼ Player 1’s best response B1(q): ➢ For q<0.5, Head (r=1) ➢ For q>0.5, Tail (r=0) ➢ For q=0.5, indifferent (0r1) ◼ Player 2’s best response B2(r): ➢ For r<0.5, Tail (q=0) ➢ For r>0.5, Head (q=1) ➢ For r=0.5, indifferent (0q1) ✓ Check r = 0.5  B1(0.5) q = 0.5  B2(0.5) 1 q r 1 1/2 1/2 r 1-r q 1-q Mixed strategy Nash equilibrium