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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?
I suspect the answer is "not in general, unless you're willing to pump extra money into the payment-extracting mechanism". Depending on how generally you define "free rider problem", at least some examples of the problem are likely to be captured by Holmström's theorem: a system which pays each member of a team to to provide inputs to produce output can't balance its budget (exactly split the output's value among the team members), be self-enforcing, and Pareto efficient.
I think your fresh paint example is susceptible to Holmströmean lo... (read more)