Thomas Schelling's book The Strategy of Conflict has a focus on the ways that people can benefit in a conflict from being, or being perceived as, irrational or constrained in their choices or access to information. Clearly you can't be better off in all areas of life by making irrational or random decisions, but there are some specific situations of conflict where you might be, if others are aware of it.

One familiar example

https://en.wikipedia.org/wiki/Chicken_(game)

where if people think you are very irrational, you're likely to win!

http://lesswrong.com/lw/dc7/nash_equilibria_and_schelling_po...

No, but you'll have a job on Wall Street or maybe be a hedge fund manager.

I think more of the scorpion and the frog: https://en.wikipedia.org/wiki/The_Scorpion_and_the_Frog