Karn

From BoardGameGeek:

How to play: This is a turn-based game starting with white, then black. You start by placing a support piece on the board, and then your opponent does the same; from there, you need to build up and block your opponent from doing the same. Rule 1 - Blocks and Columns may only be placed on the Board or on a Platform; you cannot place on a platform in the area above your opponent's column or your own block unless it is an owned platform where you may place a column (See Rule 3 for platform information). Rule 2 - A Platform may only be placed across a Block and a Column of the same colour or across two different colour blocks or two different coloured columns that are orthogonally adjacent and on the same level. Rule 3 - A Platform is owned by you if both supporting pieces are yours, shared if one supporting piece is yours, and off-limits if neither supporting piece is yours. You cannot build on a Platform that is off-limits to you. Rule 4 - A 2×1 tower may only continue directly upward for two Platforms. To build higher, the next Platform must connect from a different stack or direction. Rule 5 - Running out of legal moves: If your move leaves you with no legal moves, your opponent gets one final turn, and then the game ends. If your move leaves your opponent with no legal moves, that move counts as the final turn and the game ends immediately. Rule 6 - Scoring: When the game ends, start by counting the highest level with support pieces; blocks are worth 1 point, and columns are worth 2. If the scores tie, move down a level and repeat until you find a difference; the person with the higher score wins. If all levels are a complete draw, white receives +0.5 and wins.