Let f be a choice function on a set of feasible alternatives A, with state space \(\Theta\) and a finite number of players. f is implementable in subgame perfect equilibria if there exists an extensive form game whose unique subgame perfect equilibrium is f(\(\theta)\) for every \(\theta\in \Theta\). This paper studies nonmonotonic f (hence, not implementable by Nash equilibria) which are implementable in subgame perfect equilibria. These include the choice function for transferable utility economies with a single public good. In this case, the implementing mechanism is actually balanced. The key idea of the proof is to put the agents in a ``shrinking cake'' environment if they misreveal \(\theta\).