TikZ - game tree representation with continuum of moves

Question

I have been using TikZ to draw game-trees for my game-theory lectures (mostly using the automata package) but I could not figure out how to draw an arc across the edges the leave a given node. When we want to denote that a player has a continuum of actions available at a node, we usually draw an arc across the edge leaving such node. For example see the arc crossing the edges that leave the first node in this picture:

Any suggestions on how I could try to implement this in TikZ? Thanks!

Answer 1

Here you have a possible solution:

1.- place two coordinates over the edges (from TiKZ's manual section Edges From the parent node) and

2.- draw the arc between them. How? look at: Draw an arc between 2 nodes and label it in TikZ

\documentclass[border=3mm]{standalone}

\usepackage{tikz}
\usetikzlibrary{trees}

\begin{document}
\begin{tikzpicture}[every node/.style={fill,circle,inner sep=2pt}]
\node (root) {}     
   child {node (a1) {} edge from parent coordinate[pos=.45] (a11)}
    child {node (a2) {}}
    child {node (a3) {} edge from parent coordinate[pos=.45] (a31)}
    ;
%\node at (a11) {};
%\node at (a31) {};
\draw[bend right] (a11) to (a31);
\end{tikzpicture}
\end{document}