begin{tikzpicture}
    begin{groupplot}[group style={group size= 2 by 1},height=6cm,width=6cm,xmin=0.5,ymin=0.5,ymax=1,xmax=1,samples=500,ytick={0.5,1},xtick={0.5,1}, xlabel={$v_1$},
    axis lines=left]
        nextgroupplot[title={}, ylabel={$x_1$}]
              addplot[blue,]{min(1,(x/(2*(1-min(1,x)))))};label{plots:plot1};
              addplot[black] {((3*x-1)/(2*x))};label{plots:plot2};
                addplot[black, dashed] {(x)};label{plots:plot3};
         nextgroupplot[title={}, ylabel={$x_2$}]
              addplot[blue]{(max((2-3*x)/(2-2*x),0))};label{plots:plot1};                addplot[black] {(1-x)/(2*x)};label{plots:plot2};
                addplot[black, dashed] {(1-x)};label{plots:plot3};
                coordinate (top) at (rel axis cs:0,1);% coordinate at top of the first plot
                coordinate (bot) at (rel axis cs:1,0);% coordinate at bottom of the last plot
    end{groupplot}
    path (top-|current bounding box.west)--
          node[anchor=south,rotate=90] { }
          (bot-|current bounding box.west);
% legend
path (top|-current bounding box.south)--
      coordinate(legendpos)
      (bot|-current bounding box.south);
matrix[
    matrix of nodes,
    anchor=north,
    draw,
    inner sep=0.2em,
    draw
  ]at([yshift=-1ex, xshift=-17ex]legendpos)
  {
    ref{plots:plot1}& F(x)&[5pt]
    ref{plots:plot2}& G(x)&[5pt]
    ref{plots:plot3}& H(x)& \};
end{tikzpicture}