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1.
big players usually refers to ones who use to rule some other person or entity or everyone.
Sense 1:

"I want to become a big player instead of a player after graduation" It means I want to hire people who will work under me rather than I work under any after my graduation.

Sense 2:

"These big players are ruining the country." It means our leaders are not doing good jobs for our country.
by you.mere January 07, 2011