Thanks for the sign test suggestion. I'll take a look at what we can learn from that.
Michael Kearns has a number of papers in this area:
The first two papers are on graph coloring and consensus. The third paper is also on graph consensus but introduces a slight variant in which some subjects are paid more if a particular consensus outcome is reached. The fourth paper is on a different network game. Also, in case you're interested in reading more about what I talked about today, here's an extended abstract on what we did: