Mixed strategy equilibrium: 2-player each with two pure strategies Player 2 S21(q) S2(1-q) Player 11(r) l1(S1,S21),a2(S1,21) l1(S1,S2,2(1,S2 2(1-r)a(s12s2l,a2(s12s2)|a1(s1s2),u2(2,S2 Mixed strategy Nash equilibrium A pair of mixed strategies (r,1-r),(q,1-q2) is a Nash equilibrium if(r, I-r%)is a best response to(g*, 1-g*), and(q*, 1-g*)is a best response to(r*, I-r%). That is v1(P,1-r),(qx,1-q3)2v1(r,1-r),(q,1-q2), for al0≤r≤1 v2(P,1-r),(qx,1-q3)≥v2(P,1-P3),(q,1-q), for all0≤q≤1Mixed strategy equilibrium: 2-player each with two pure strategies Player 2 s21 ( q ) s22 ( 1- q ) Player 1 s11 ( r ) u1 (s11, s21), u2 (s11, s21) u1 (s11, s22), u2 (s11, s22) s12 (1- r ) u1 (s12, s21), u2 (s12, s21) u1 (s12, s22), u2 (s12, s22) 18 ◼ Mixed strategy Nash equilibrium: ◼ A pair of mixed strategies ((r*, 1-r*), (q*, 1-q*)) is a Nash equilibrium if (r*,1-r*) is a best response to (q*, 1-q*), and (q*, 1-q*) is a best response to (r*,1-r*). That is, v1 ((r*, 1-r*),(q*, 1-q*))  v1 ((r, 1-r),(q*, 1-q*)), for all 0 r 1 v2 ((r*, 1-r*),(q*, 1-q*))  v2 ((r*, 1-r*),(q, 1-q)), for all 0 q 1