Bandu

From BoardGameGeek.com:

Players take turns choosing blocks and giving them to each other to place on their structure. A player may pay a certain number of ‘beans’ to refuse a block and it gets passed to the next player. When a player’s structure falls, they are out of the game. Last player standing wins.

Description of Bandu (1992, Milton Bradley, 2-6 players):
Bandu is based upon the game of Bausack. Each player is given a base block and a number of beans. During a turn, a player chooses a wood block from a common supply and either holds a Refuse or Use auction. All player bid with their beans and the winner/loser must place the piece on their tower. If your tower falls you are out of the game. The last tower standing wins.