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.
Exclusion isn’t always socially appropriate. If I take a cab home everyday (which I pay for), and a friend can literally take a free ride because her place is on the way, should I “exclude” her if she doesn’t want to share the cost? She claims it doesn’t cost me extra, I’d be paying for the cab anyway if she lived somewhere else.
But of course I can come up with un-excludable externalities:
I share a house that’s in pretty bad shape, and I decide to get some fresh painting done. This is a net benefit to all the housemates, but we would value them differently. I want this slightly more than all the others. So I have to pay the entire amount.
Sure, that’s why I asked you to describe what the “problem” you want to address is. Free stuff isn’t a problem for recipients. Some providers consider it a problem, but IMO it’s usually a different problem than they think.
The cab driver may be sad that they didn’t get revenue from the second rider, and consider that to be a big problem. Your housemates may not consider old paint a problem, and almost certainly don’t consider free paint to be a problem. You or your housemates may or may not consider jealousy or bad feelings about “fairness” to be problems.
See also: kickstarter—everyone pledges what they want, nobody pays unless the funding minimum is met.
For your side of the painting problem (you want new paint, and suspect your housemates do too, but you’re not willing to pay for the whole thing), auction design can likely work. If you demand equality, it’s easy—everyone agrees to pay their share or the painting doesn’t happen. If you don’t, then everyone secretly writes down the amount they’re willing to pay, and if the pot covers the painting, do it. Any extra gets refunded proportionally (or spent on better paint).
I guess it’s worth mentioning one common “solution”: extortion/taxation. Threaten to punish people who don’t pay what you think they owe. Usually combined with opacity and not telling anyone exactly how their payments are spent.
This is not really a solution though, because it’s not incentive compatible. There’s nothing to ensure that the extortionist will spend the money on providing the desired goods, and attempts at creating such incentives must ultimately fail for the same underlying reasons as the original problem. (This is of course assuming no excludability—if a club owner can ban some members from her club and invite others to join for a fee, she is incented to manage the club to the members’ benefit, for standard Coasian reasons!)
It’s a solution for the extortionist, and that’s who is experiencing free riding as a problem.
Threatening your housemates that you’ll replace them if they don’t pony up for painting or threatening jail if a resident doesn’t pay taxes could be done by bad actors (and IMO often is), but that’s only a difference in purpose, not in activity. Extortion is, by it’s very nature, incentive-compatible with collecting revenue: its only aim is to provide incentive for the freeloaders to pay.
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 logic. Suppose you’ve found a painter who’s willing to do an amount of painting proportional to the money they’re given; you’re willing to pay for $40 worth of painting but your two housemates would only pay for $20 worth of painting. If you propose to either housemate that you pay $20 to the painter while the housemates pay $10 each, the housemate will (assuming they act as homo economicus spherical cows) notice that if they don’t pay anything, $30 of painting will still get done, more than the $20 they wanted in the first place. So they won’t pay anything, as you expected.
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.
Exclusion isn’t always socially appropriate. If I take a cab home everyday (which I pay for), and a friend can literally take a free ride because her place is on the way, should I “exclude” her if she doesn’t want to share the cost? She claims it doesn’t cost me extra, I’d be paying for the cab anyway if she lived somewhere else.
But of course I can come up with un-excludable externalities:
I share a house that’s in pretty bad shape, and I decide to get some fresh painting done. This is a net benefit to all the housemates, but we would value them differently. I want this slightly more than all the others. So I have to pay the entire amount.
Sure, that’s why I asked you to describe what the “problem” you want to address is. Free stuff isn’t a problem for recipients. Some providers consider it a problem, but IMO it’s usually a different problem than they think.
The cab driver may be sad that they didn’t get revenue from the second rider, and consider that to be a big problem. Your housemates may not consider old paint a problem, and almost certainly don’t consider free paint to be a problem. You or your housemates may or may not consider jealousy or bad feelings about “fairness” to be problems.
See also: kickstarter—everyone pledges what they want, nobody pays unless the funding minimum is met.
For your side of the painting problem (you want new paint, and suspect your housemates do too, but you’re not willing to pay for the whole thing), auction design can likely work. If you demand equality, it’s easy—everyone agrees to pay their share or the painting doesn’t happen. If you don’t, then everyone secretly writes down the amount they’re willing to pay, and if the pot covers the painting, do it. Any extra gets refunded proportionally (or spent on better paint).
I guess it’s worth mentioning one common “solution”: extortion/taxation. Threaten to punish people who don’t pay what you think they owe. Usually combined with opacity and not telling anyone exactly how their payments are spent.
This is not really a solution though, because it’s not incentive compatible. There’s nothing to ensure that the extortionist will spend the money on providing the desired goods, and attempts at creating such incentives must ultimately fail for the same underlying reasons as the original problem. (This is of course assuming no excludability—if a club owner can ban some members from her club and invite others to join for a fee, she is incented to manage the club to the members’ benefit, for standard Coasian reasons!)
It’s a solution for the extortionist, and that’s who is experiencing free riding as a problem.
Threatening your housemates that you’ll replace them if they don’t pony up for painting or threatening jail if a resident doesn’t pay taxes could be done by bad actors (and IMO often is), but that’s only a difference in purpose, not in activity. Extortion is, by it’s very nature, incentive-compatible with collecting revenue: its only aim is to provide incentive for the freeloaders to pay.
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 logic. Suppose you’ve found a painter who’s willing to do an amount of painting proportional to the money they’re given; you’re willing to pay for $40 worth of painting but your two housemates would only pay for $20 worth of painting. If you propose to either housemate that you pay $20 to the painter while the housemates pay $10 each, the housemate will (assuming they act as homo economicus spherical cows) notice that if they don’t pay anything, $30 of painting will still get done, more than the $20 they wanted in the first place. So they won’t pay anything, as you expected.
The Sveriges Riksbank Prize winner Elinor Ostrom won the price for research on the tragedy on the commons. She came up with a few principles: http://www.onthecommons.org/magazine/elinor-ostroms-8-principles-managing-commmons
It’s empiric data based research as opposed to a nice theoretic solution but depending on your use-case that might be even better ;)