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Is there some nice game-theoretic solution that deals with the 'free rider problem', in the sense of making everyone pay in proportion to their honest valuation? Like how Vickery Auctions reveal honest prices, or Sperner's lemma can help with envy-free rent division?
Can you give an operational definition (or concrete example) of the free rider 'problem'? There are a couple of different things that you might not like about the phenomenon, and I'm not sure exactly which is the problem you're concerned about.
Exclusion is the most common "solution" (auctions and "fair" divisions being specific allocation mechanisms within that). Don't let "free riders" actually ride, and there's no problem.