Follow-up: Drawing Game Tree with Curved Informational Sets and Several Nodes, using Tikz and Forest

The main motivation for posting this is to eliminate the spaces you added in the rconnect style, and which cause errors in the above code. Apart from that, you can use labels to add the players. The other request I do not understand because I am not working on game theory, so I do not know what these terms mean.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage[edges]{forest}
\usepackage[outline]{contour}
\usetikzlibrary{fit,shapes.misc,arrows.meta,positioning}
\tikzset{rconnect/.style args={#1 and #2}{insert path={
($(#1)+(270+\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})$)
arc(270+\pgfkeysvalueof{/tikz/rconnect/angle}:90+\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})
to[out=\pgfkeysvalueof{/tikz/rconnect/angle},in=180-\pgfkeysvalueof{/tikz/rconnect/angle}]
($(#2)+(90-\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})$)
arc(90-\pgfkeysvalueof{/tikz/rconnect/angle}:-90-\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})
to[in=\pgfkeysvalueof{/tikz/rconnect/angle},out=180-\pgfkeysvalueof{/tikz/rconnect/angle}]
cycle}},rconnect/.cd,radius/.initial=6.5pt,angle/.initial=-12}

\begin{document}

\begin{forest}
for tree={s sep=0.1cm,l sep=1.2cm,font=\scriptsize,
where n children=0{align=center,draw,edge={thick,-{Circle}}}                {circle,fill,inner sep=0pt,minimum size=2mm},
where n=1{edge label={node[midway,above left=0pt,font=\scriptsize]{S}}}        {edge
label={node[midway,above right=0pt,font=\scriptsize]{E}}},
edge={thick}
}
  [,label=above:Nature,alias=T
   [,label=above left:Player 1,alias=L
   [,label=above left:Player 2,alias=LL
     [
      [{$B-C$ \\ $0$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
    [,label=above right:Player 2,alias=LR
     [
      [{$B-C$ \\ $0$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
   ]
   [,label=above right:Player 1,alias=R
    [,label=above left:Player 2,alias=RL
     [
      [{$B-C$ \\ $\bar{R}$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
    [,label=above right:Player 2,alias=RR
     [
      [{$B-C$ \\ $\bar{R}$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
   ]
  ]
\node[draw,dashed,rounded rectangle,fit=(L) (R)] (F1){};  
\draw[dashed,blue] let \p1=($(F1.north)-(F1.center)$) in
 [/tikz/rconnect/radius=\y1]  [rconnect=LL and RL];
\draw[dashed,red] let \p1=($(F1.north)-(F1.center)$) in
 [/tikz/rconnect/radius=\y1]  [rconnect=LR and RR];
\end{forest}
\end{document}

enter image description here

As for your comment: uisng this great answer one could do the following: store the items on the left or right in lists, and then attach the items according to the levels. (If you really need to, you can replace "Hibernate" by something else.;-)

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage[edges]{forest}
\usepackage[outline]{contour}
\usetikzlibrary{fit,shapes.misc,arrows.meta,positioning}
\tikzset{rconnect/.style args={#1 and #2}{insert path={
($(#1)+(270+\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})$)
arc(270+\pgfkeysvalueof{/tikz/rconnect/angle}:90+\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})
to[out=\pgfkeysvalueof{/tikz/rconnect/angle},in=180-\pgfkeysvalueof{/tikz/rconnect/angle}]
($(#2)+(90-\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})$)
arc(90-\pgfkeysvalueof{/tikz/rconnect/angle}:-90-\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})
to[in=\pgfkeysvalueof{/tikz/rconnect/angle},out=180-\pgfkeysvalueof{/tikz/rconnect/angle}]
cycle}},rconnect/.cd,radius/.initial=6.5pt,angle/.initial=-12}

\begin{document}
\edef\LstLeft{0,"$p$","Go","Wait","A"}
\edef\LstRight{0,"$1-p$","Stay","Hibernate","B"}
\begin{forest}
for tree={s sep=0.1cm,l sep=1.2cm,font=\scriptsize,
where n children=0{align=center,draw,edge={thick,-{Circle}}}{circle,fill,inner sep=0pt,minimum size=2mm},
before drawing tree={
        if level=0{}{
          if n'=1{
            edge label/.wrap pgfmath arg={node [midway, right=.5em]
            {\pgfmathparse{{\LstLeft}[#1]}\pgfmathresult}}{level()},
          }{
            edge label/.wrap pgfmath arg={node [midway, left=.5em] 
            {\pgfmathparse{{\LstRight}[#1]}\pgfmathresult}}{level()},
          },
        }{}
      },
%where n=1{edge label={node[midway,above left=0pt,font=\scriptsize]{S}}}{edge label={node[midway,above right=0pt,font=\scriptsize]{E}}},
edge={thick}
}
  [,label=above:Nature,alias=T
   [,label=above left:Player 1,alias=L
   [,label=above left:Player 2,alias=LL
     [
      [{$B-C$ \\ $0$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
    [,label=above right:Player 2,alias=LR
     [
      [{$B-C$ \\ $0$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
   ]
   [,label=above right:Player 1,alias=R
    [,label=above left:Player 2,alias=RL
     [
      [{$B-C$ \\ $\bar{R}$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
    [,label=above right:Player 2,alias=RR
     [
      [{$B-C$ \\ $\bar{R}$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
   ]
  ]
\node[draw,dashed,rounded rectangle,fit=(L) (R)] (F1){};  
\draw[dashed,blue] let \p1=($(F1.north)-(F1.center)$) in
 [/tikz/rconnect/radius=\y1]  [rconnect=LL and RL];
\draw[dashed,red] let \p1=($(F1.north)-(F1.center)$) in
 [/tikz/rconnect/radius=\y1]  [rconnect=LR and RR];
\end{forest}
\end{document}

enter image description here


Another solution to use the istgame package:

enter image description here

\documentclass{standalone}

\usepackage{amsmath}
\usepackage{makecell}

\usepackage{istgame}

\NewDocumentCommand\mact{m}
{\makecell[c]{#1}}
\NewDocumentCommand\mpay{m}
{\begin{pmatrix}#1\end{pmatrix}}

\begin{document}

\begin{istgame}[font=\footnotesize]
\setistmathTF*001
\xtShowEndPoints
% top part
\xtdistance{25mm}{120mm}
\istroot(0)[chance node]{Nature}
  \istb{\mact{$R=O$\\(Cooperative\\Player)}}[above left,xshift=-10pt]
  \istb{\mact{$R=\bar R$\\(Competitive\\Player)}}[above right,xshift=10pt]  \endist
\xtdistance{25mm}{50mm}
\istroot(A)(0-1)%<180>{Player 1}
  \istb{\mact{Introduce\\Proposal}}[l]  \endist
\istroot(B)(0-2)%<0>{Player 1}
  \istb{\mact{Introduce\\Proposal}}[r]  \endist
% left part
\xtdistance{25mm}{60mm}
\istroot(A0)(A-1)<180>{Player 2}
  \istb{Go}[al]  \istb{Stay}[ar]  \endist
\xtdistance{25mm}{30mm}
\istroot(A1)(A0-1)<0>{$(B-C,O)$}
  \istb{\mact{Introduce\\Proposal\\(I)}}[al]  \istb{\mact{Delay\\(D)}}[ar]  \endist
\istroot(A2)(A0-2)<180>{$(B,X)$}
  \istb{I}[al]  \istb{D}[ar]  \endist
\xtdistance{25mm}{15mm}
\istroot(A3)(A1-1)<180>{Player 2}
  \istb{Go (G)}[l]{\mpay{B-C\\O}}  \istb{Stay (S)}[r]{\mpay{B\\X}}  \endist
\istroot(A4)(A1-2)<180>{Player 2}
  \istb{G}[l]{\mpay{B-L\\X-L}}     \istb{S}[r]{\mpay{B-C\\O}}       \endist
\istroot(A5)(A2-1)<180>{Player 2}
  \istb{G}[l]{\mpay{B\\X}}         \istb{S}[r]{\mpay{B-L\\X-L}}     \endist
\istroot(A6)(A2-2)<180>{Player 2}
  \istb{G}[l]{\mpay{B\\O}}         \istb{S}[r]{\mpay{L\\O}}         \endist
% right part
\xtdistance{25mm}{60mm}
\istroot(B0)(B-1)<180>{Player 2}
  \istb{Go}[al]  \istb{Stay}[ar]  \endist
\xtdistance{25mm}{30mm}
\istroot(B1)(B0-1)<0>{$(B-C,\bar R)$}
  \istb{I}[al]  \istb{D}[ar]  \endist
\istroot(B2)(B0-2)<180>{$(B,X)$}
  \istb{I}[al]  \istb{D}[ar]  \endist
\xtdistance{25mm}{15mm}
\istroot(B3)(B1-1)<180>{Player 2}
  \istb{G}[l]{\mpay{B\\-L}}        \istb{S}[r]{\mpay{B-L\\R-L}}  \endist
\istroot(B4)(B1-2)<180>{Player 2}
  \istb{G}[l]{\mpay{B\\\bar R}}    \istb{S}[r]{\mpay{B\\O}}      \endist
\istroot(B5)(B2-1)<180>{Player 2}
  \istb{G}[l]{\mpay{B\\\bar R}}    \istb{S}[r]{\mpay{B-L\\L}}    \endist
\istroot(B6)(B2-2)<180>{Player 2}
  \istb{G}[l]{\mpay{B-R\\\bar R}}  \istb{S}[r]{\mpay{B-L\\X-L}}  \endist
% information sets
\setxtinfosetstyle{dashed}
\xtInfosetO(A)(B){Player 1}(1.5em)
\xtCInfosetO[blue](A1)!.35!(B1)<1.15>{Player 1}(1.5em)
\xtCInfosetO[red](A2)!.5!(B2)<.75>{Player 1}(1.5em)
\end{istgame}

\end{document}

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