It's a tricky one. This is how I'd translate it. Unfortunately, I have no proof that this is the best translation, except my "gut feeling". ;-)

We show that the optimal mechanism discriminates against the informationally advantaged bidder to ensure truthful
or
Be a professional and Qualify your client or Qualify yourself

Na GOOGLI nájdete rad väzieb o "vymedzovaní seba samého voči niekomu/niečomu" so slovesom "qualify". Má to logiku: ak chcem seba vymedziť, musím sa "kvalifikovať", ak sa chcem vymedziť voči niekomu, musím jeho ohodnotiť.

http://www.thefreedictionary.com/contrast
http://wiki.answers.com/Q/Is_it_in_Contrast_with_or_in_contr...

... in relation to which they defined themselves.

They took it (this current in thought) as a reference point, or, to be more precise, they defined themselves (their positions) in relation to it.

The aligned themselves with it or against it or in some way in relation to it.

"smer 20-ho str. voci ktoremu sa XY a jeho generacia vymedzovali"
cize postavili a (u)stanovili nieco, daco...
delimit - establish limits of, to set out or establish the limits or boundaries of something
delimit - stanovit hranice, ohranicit a vymezdit nieco ale aj daco, urcit rozsah (platnosti)

... smer... 20. storočia, voči ktorému sa napríklad A. Melicherčík a jeho generácia vymedzovali.
...the direction... 20th century, which A. Melichercik and his generation, for example, were defining themselves against.

Native examples of usage:
...and although one must define oneself against the homogeneity of the cultural milieu...
http://www.barcelonareview.com/rev/22.htm

The struggle to define oneself against stereotypes is something I feel very passionately about...
http://www.storiesfromtheweb.org/sfwolderarea/authorzoneinte...

or possibly
... smer... 20. storočia, voči ktorému sa napríklad A. Melicherčík a jeho generácia vymedzovali.
...the direction... 20th century, which A. Melichercik and his generation, for example, were self defining themselves against.

...there is a need for some to self define oneself against the majority Jewish view or status which...
http://www.hurryupharry.org/2008/07/01/how-to-appear-mad/

And I would use the past progressive tense (minulý čas priebehový) (were defining...) because their effort, which lasted a longer period of time, may or may not have been finished. In other words, this is what they were trying to do. They were trying to define themselves against something but it is not clear if eventually they succeeded in it or not.
vymedzili (the simple past tense) - defined themselves against something
vymedzovali - were defining themselves against something