Hi, guys How to use FindInstance or others to make y2[[1]] maximum.

Clear["`*"];
H = 6; L = 1; B = 2; \[Alpha] = 3/10;
\[Eta]1a = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - \((p1 - L)\)\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)); \[Eta]2a = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(p2\), \(H\)], 1], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(p2\), \(L\)], 1], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)); \[Eta]3a = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[Max[
\*FractionBox[\(H*\[Eta]2a - p1*\[Eta]2a + p2\), \(H\)], 1], B]\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[Max[
\*FractionBox[\(L*\[Eta]2a - p1*\[Eta]2a + p2\), \(L\)], 1], B]\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\));
y1 = Maximize[{2*p1*(1 - \[Eta]1a)^2 + 
     2*(p1 + p2)*\[Eta]1a*(1 - \[Eta]1a) + 2*p2*(\[Eta]1a)^2, 
    H > L > 0 && g >= B > 1 && 0 < p1 <= L && g*p1 >= p2 >= p1}, {p1, 
    p2, g}];
y2 = Maximize[{2*p2*(\[Eta]2a)^2, 
    H > L > 0 && g >= B > 1 && 0 < p2 <= B*H && p2 <= g*L}, {p2, g}];
y3 = Maximize[{(p1 + p2)*\[Eta]3a*\[Eta]2a + 
     2*p2*(1 - \[Eta]3a)*\[Eta]1a + (p2 + 
        p1)*(1 - \[Eta]3a)*(1 - \[Eta]1a), 
    H > L > 0 && g >= B > 1 && 0 < p1 <= L && g*p1 >= p2 >= p1}, {p1, 
    p2, g}];
N[y1[[1]]]
N[y2[[1]]]
N[y3[[1]]]
N[Max[y1[[1]], y2[[1]], y3[[1]]]]

We can obtain the results after assigning values to H,L,B and alpha to find which Maximize value is the global maximimum. But no matter what values I assigned to H,L,B and alpha, it is impossible to derive that y2[[1]] is the global maximimum. Thus, I wonder if we can use FindInstance or FindRoot or other commands to realize it. Thank you!