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We introduce the following class of partizan games, called pomax games. Givena partially ordered set whose elements are colored black or white, the playersBlack and White take turns removing any maximal element of their own color. Ifthere is no such element, the player loses.  We prove that pomax games are always integer-valued and for colored treeposets and chess-colored Young diagram posets we give a simple formula for thevalue of the game. However, for pomax games on general posets of height 3 weshow that the problem of deciding the winner is PSPACE-complete and for posetsof height 2 we prove NP-hardness.  Pomax games are just a special case of a larger class of integer-valued gamesthat we call element-removal games, and we pose some open questions regardingelement-removal games that are not pomax games.

Pomax games - a family of partizan games played on posets