Solving matching pennies Player 2 Head Player 1's best response B1(q): Playe Head 1 1 1 For g<0.5, Head(r1)1 1 1 1 1-x For q0.5, Tail(r0) Forq=0.5, indifferent(0≤r≤1) 1-q Player 2's best response Mixed strategy B2(x) Nash equilibrium For r<0.5, Tail(go) For r0.5, Head (q=1) Forr=0.5, indifferent(0≤q≤1) v Check 1/2 0.5∈B1(0.5) q=0.5∈B2(0.5) 1/2Solving 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