## Battle of the Sexes

### Define Generalised Expectation for general 2*2 minimax)

E1(x,y):=(a11*x*y + a12*x*(1-y)) + (a21*(1-x)*y + a22*(1-x)*(1-y));
E2(x,y):=(b11*x*y + b12*x*(1-y)) + (b21*(1-x)*y + b22*(1-x)*(1-y));

### Define Expectation Co-efficients (for Battle of Sexes)

a11:1;
b11:4;
a12:0;
b12:0;
a21:0;
b21:0;
a22:4;
b22:1;

Expand(E1(x,y));

Expand(E2(x,y));

### Plot Graph (Parametric in two variables x,y)

plot3d([E1(x,y),E2(x,y),1],[x,0,1],[y,0,1],[legend,"Battle of the Sexes"],[xlabel, "hello"],[ylabel, "bye"],[zlabel, "Z"]);