As it turns out, two eyes looking at you seems to have the effect of making you more honest. 
The paper "Cues of being watched enhance cooperation in a real-world setting," found here at the NIH, conducted a study where either a set of eyes or a picture of flowers was placed above an "honesty box" in a university kitchen. 
While the study is from way back in 2006, we were turned onto it by a submission to the /r/DataIsBeautiful subreddit by Redditor celacanto. 
 Here's a chart showing the average amount of money contributed for a liter of milk (the x-axis) and what picture was up in each week (y-axis).


eyes chart
NIH
What do we see:
  • Seductive eyes do not appear to be substantially more likely to compel someone to pony up.
  • A neutral or angry expression does move the dial
  • A creepy guy staring at you makes it increase substantially
Does this mean that you should bring an unblinking old man into every negotiation? Probably not. But it certainly does underscore the power of eye contact.