Using GraphViz to Diagram an Extensive-Form Game

Question

I'm attempting to diagram an extensive form game in GraphViz. Compiling the code results in a graph that is correct in all ways except one. I want the "War" label to be placed to the left of the edge it labels, such that the edge is closest to "r" and not "W".

This is my "game" or graph so far:

    digraph hierarchy_of_D  { 

            graph [rankdir ="UD"] 
            node [color=black,shape=circle]
            //splines="polyline"

     I [label="R"] 

     subgraph infoset1 
      { 
       label="whatever" 
       rank="same" 
       1 [label="C"]
       2 [label="C"]
      } 


     I -> 1 [label="War"] //fix how this floats right of the line
     I -> 2 [label="Peace"]
     1 -> 2 [style=dashed, dir=none] 

     subgraph info21 
      { 
        rank="same" 
        3 [label="(2,2)", rank=sink, shape="plaintext"]
        4 [label="(5,1)", rank=sink, shape="plaintext"]
        5 [label="(1,5)", rank=sink, shape="plaintext"]
        6 [label="(4,4)", rank=sink, shape="plaintext"]
       } 

       1 -> 3 [label="War"]
       1 -> 4 [label="Peace"]
       2 -> 5 [label="War"]
       2 -> 6 [label="Peace"]

    } 

Any ideas? I've already tried the following, which does not do what I want:

1 -> 3 [label="War/l"]

See also this question and that question, neither of which have an answer. C'mon now, this is worth triple points!