be = 0.9
    de  = 1
    al1 = 1
    al2 = 1
    al3 = 0.1
    c[x_] := 0.5 x^2
    f[x1_, x2_] :=  al1 x1 + al2 x2 + al3 (x1 x2)^(0.5)
    a2N[a1_] := ArgMax[-c[a2] + be de (1 + de) f[a1, a2], a2]
    a1N = ArgMax[-c[a1] - be de c[a2N[a1]] +  be de^2 (1 + de) f[a1,a2N[a1]], a1]