\begin{tikzpicture}
    \begin{groupplot}[
      group style={group size=2 by 1, horizontal sep=2cm}, no markers,
      height=5cm, width=7cm,
      axis x line=bottom, axis y line=left      
]
% PLOT 1
  \nextgroupplot[
    xlabel = Payoff,
    ylabel = $v(x)$,
    xmin=-2, xmax=2,
    ymin=-4, ymax=3,
    extra x tick style={major tick length=0mm, grid=none},
    xtick={-2, 0, 2},
    xticklabels={-2, 0, 2}, 
    ytick={-4, 0, 3}    
  ]
    \addplot[red, thick,  domain=-2:2, samples=200, variable=\t](
      {t },
      { ((t+abs(t))/2)^(0.5) - 2.5 * ((abs(t)-t)/2)^0.5 }
    );
    \draw[dotted, color=black] (axis cs:-2,0) -- (axis cs:2,0);
    \draw[dotted, color=black] (axis cs:0,-4) -- (axis cs:0,3);
  % PLOT 2
  \nextgroupplot[
    xlabel = P,
    ylabel = $w(P)$,
    xmin=0, xmax=1,
    ymin=0, ymax=1,    
    xtick={0, 0.5, 1},
    ytick={0, 0.5, 1}
  ]
    \addplot[color=black, dotted, domain=0:1, samples=100, variable=\t ](
    {t },
    {t^1 / (t^1 + (1-t)^1)^(1/1) }
    );
    \addplot[color=black, dashed, domain=0:1, samples=100, variable=\t](
    {t },
    {t^0.65 / (t^0.65 + (1-t)^0.65)^(1/0.65) }
    );
   \addplot[color=black, solid, domain=0:1, samples=100, variable=\t](
    {t },
    {t^0.4 / (t^0.4 + (1-t)^0.4)^(1/0.4) }
    );
  \end{groupplot}
\end{tikzpicture}