What is this game with 9 sticks with black and white beads?
BoardGameGeek has a similar game called Rex which only has 3 beads per peg. But it is basically a 3 in a row game (horizontally, vertically and diagonally) with the twist that the center 3 pegs allow one to form a triangle too. No doubt one could also play a scoring version to see who gets the most points when the pegs are full. 

Exactly what you version of the game might be called, or who made it is a mystery. But for such simple games many "folkart" versions have been made.