The refund
bonus.

Why valuable goods go unbuilt

Consider a town on a floodplain. A dike six feet high would keep every house dry. Its cost exceeds what any one family can bear, so it must be financed jointly. Each family reasons as follows.

If no one else contributes, my contribution is wasted, since a half-built dike holds back nothing. I keep my money. If everyone else contributes, the dike is built regardless of what I do, and I enjoy the protection for free. I keep my money again. Whatever I expect of my neighbors, withholding looks rational. Every family reasons the same way, and the dike goes unbuilt.

The dike is a public good. Once it stands, it protects everyone nearby, and a neighbor who contributed nothing cannot easily be excluded. That property is what makes it hard to finance.

Paul Samuelson gave this category its modern formulation in 1954, and he drew a pessimistic conclusion from it. Each person does better by understating what the good is worth to him, so it is, in Samuelson's words, “in the selfish interest of each person to give false signals, to pretend to have less interest in a given collective consumption activity than he really has.” From this he concluded that “no decentralized pricing system can serve to determine optimally these levels of collective consumption.” Public goods, on this view, are what governments are for. Refund bonuses are a challenge to that conclusion.

The difficulty has a standard formal statement. Say the dike is worth 50 to me and my share of the cost is 20.

Two distinct forces produce this outcome, and Amartya Sen drew attention to the difference. Each occupies one column of the table above, which the buttons will isolate in turn. The assurance problem is the second column, where too few neighbors are contributing and anything I put in would be thrown away on a dike that never rises. In the first column the dike goes up whatever I do, nothing I contribute is at risk, and I hold back only because keeping my twenty beats spending it. That is the free-rider problem.

The assurance contract and its weakness

One remedy has a long history. The town announces that the dike will be built only if enough residents pledge toward it, and that pledges will be returned in full if too few come forward. A pledge is now safe. Either enough neighbors join and the dike is built, or too few join and the money comes back. The fear of a wasted contribution is gone, and so the assurance problem is solved.

This is the mechanism behind all-or-nothing crowdfunding. Kickstarter collects a pledge only if a project reaches its goal by the deadline, so every such campaign is an assurance contract. The device is older than the platforms. Joseph Pulitzer's campaign for the pedestal of the Statue of Liberty ran on the same principle.

The free-rider problem is untouched. A resident who believes enough of his neighbors will pledge still does best by keeping his money, since the dike will protect him whether or not he pays for it. That column of the table has not moved.

The game has many equilibria. Everyone pledging is one of them, and so is nobody pledging, because one person's pessimism justifies another's. If I expect you to hold back, holding back is rational for me, and my holding back is what makes your expectation correct. Neither of us is making a mistake, which is what makes the outcome so stable. With twenty-five potential contributors the equilibria run into the millions, and the good goes unprovided in nearly all of them.

So the assurance contract clears the assurance problem, leaves free riding standing, and is vulnerable to self-fulfilling pessimism. Field data are consistent with this fragility.

Most campaigns fail, and the modal failure raises almost nothing. The assurance contract removes the risk of losing one's money while leaving intact the equilibrium in which everyone waits.

The refund bonus

In 1998 Alexander Tabarrok proposed a modification. Pay contributors precisely when the campaign fails.

The payment is a refund bonus. A contributor pledges as before. If the campaign reaches its goal, she pays her share and receives the good. If it falls short, she gets her money back together with a bonus, a payment for having been willing when willingness turned out to be insufficient.

Consider a contributor who expects the campaign to fail. Under the assurance contract she had no reason to pledge, and her expectation confirmed itself. Now pledging pays her the bonus while abstaining pays her nothing, so she pledges. Every contributor who shares her pessimism reasons the same way. Any outcome in which too few agents pledge gives each of the abstainers a strict reason to come in, so no such outcome is an equilibrium at all.

This is the central result. Every equilibrium of the refund bonus game provides the public good. The failure states have been removed from the game rather than made less likely within it.

Set against Samuelson's conclusion, this is a strong claim. A profit-seeking entrepreneur offering an ordinary contract, with no taxing power and no coercion available to him, can bring a public good into existence. Part of Samuelson's ground is conceded, since the argument assumes the efficient size of the good can be estimated and takes up only the problem of getting people to pay for it. On that problem the pessimism does not hold.

Because no equilibrium ends in failure, the bonus is never actually paid. The promise does its work entirely off the equilibrium path, which is the same reason deposit insurance stops bank runs in the Diamond and Dybvig analysis. Once depositors know their funds are guaranteed, no run occurs, and the guarantee is never invoked.

The payoff tables below take the argument in three steps.

A special case: unanimity

Tabarrok gives particular attention to the contract that requires every agent to accept. It has a property the general case lacks. When acceptance from everyone is needed, an agent who abstains guarantees failure and collects nothing, so the option of being carried disappears from the table. Accepting then pays more whatever anyone else does, which makes it a dominant strategy, and the all-accept outcome is the unique subgame-perfect equilibrium. This is the case that gives the dominant assurance contract its name.

From binary choices to continuous contributions

Tabarrok's model asks each agent for a binary decision, a fixed share accepted or declined. Real fundraising involves contributions of varying size from people with varying valuations. In 2014 Robertas Zubrickas extended the mechanism to this richer setting and strengthened its efficiency properties.

In his version the refund bonus is proportional to one's own contribution. Take a thousand-dollar drinking fountain for a neighborhood. One member commits a hundred dollars and pledges that if the total falls short, the hundred will be divided among the other contributors in proportion to what each gave. The incentive this creates is sharp. When contributions lag, an additional dollar buys a larger share of the bonus fund, so contributors compete for it. Competition drives total contributions up to the provision point, at which point the good is provided and the bonus, once again, goes unpaid.

Zubrickas established a stronger result as well. When the bonus fund is set equal to the net value of the project, the mechanism has a unique equilibrium, and in it each person contributes the same fraction of his own valuation. That is Lindahl pricing, a longstanding benchmark of public economics, obtained here from a decentralized contribution game of exactly the kind Samuelson judged unequal to the task.

The experimental evidence

Timothy Cason, Tabarrok, and Zubrickas have tested the mechanism in a series of incentivized laboratory experiments. The results support the theory on each of its main claims.

Refund bonuses raise crowdfunding success by half

The first test appeared in 2021. Groups of ten subjects had two minutes to fund a project requiring 300 experimental dollars, with the running total visible to all. Some groups faced the standard assurance contract. Others were offered a refund bonus, paid either on any contribution or only on contributions made in the first minute.

Without a bonus, fewer than half the campaigns reached the threshold. With a bonus restricted to early contributions, two thirds did. Targeting the first minute matters because early contributions signal to later givers that the campaign is likely to succeed, and the induced cooperation persisted after the bonus window closed. Benjamin Franklin raised money on the same principle. He advised solicitors to show prospective donors the list of those who had already given.

A natural objection concerns cost. If the sponsor must promise bonuses, the payouts on failed campaigns might erode the returns. In the 2021 data they did not. The additional successful campaigns generated enough surplus to cover the bonuses paid on failures, so with a modest markup the scheme was self-financing.

The bonus as a signal of quality

Crowdfunding suffers from a second failure. Entrepreneurs know the quality of their projects and backers do not, so weak projects attract funding while strong ones go unfunded. In a 2024 paper in Management Science, the same authors show that refund bonuses address this information asymmetry as well.

The logic runs through expected cost. A strong project is likely to reach its goal, so its entrepreneur rarely pays the bonus, and the promise is cheap to make. A weak project is likely to fail, so the same promise is expensive. Offering a bonus therefore serves as a credible signal of quality, in the manner of Spence's warranty argument. In the laboratory, when entrepreneurs chose whether to offer bonuses, the market sorted.

Good projects were funded more than two and a half times as often when entrepreneurs chose the bonuses themselves. Assigning the same bonuses at random eliminated the effect, which identifies the choice, and the information it carries, as the active ingredient.

The holdout problem

The most recent work applies the mechanism to asset assembly. When a developer must acquire many adjacent parcels for a rail line or a hospital, each remaining owner gains bargaining power as the project nears completion, and the incentive to hold out for a larger payment grows. Assembly can stall even when it is socially valuable. The strategic structure resembles the public goods problem, with over-extraction in place of under-contribution.

The refund bonus applies for the same reason as before. If owners who agree to sell receive a bonus whenever the assembly fails, agreement pays in both states of the world, and expectations of failure can no longer sustain themselves. A 2026 experiment measures the effect.

Theory predicts a large effect. A bonus worth less than a tenth of the offered price raises the predicted assembly rate by more than 160 percent, from 9.6 to 25.2 percent. The experiment delivers almost exactly this. By the final rounds the observed success rates were 10 percent without the bonus and 25 percent with it, and realized efficiency over the second half of the sessions roughly doubled. Behavior converged to the theoretical prediction as subjects gained experience.

Potential applications

The mechanism applies wherever a valuable outcome requires many parties to commit together. Several domains stand out.

Why adoption has been slow

The theory is nearly thirty years old and the experimental support is consistent. Deployments remain rare.

Part of the explanation is that an entrepreneur must commit funds before any revenue arrives, and financially constrained or risk-averse entrepreneurs may hesitate even where the expected cost is near zero. Part of it is unfamiliarity. Robert Shiller has documented useful financial innovations that lay unused for decades before adoption, and the 2024 paper places refund bonuses in that category. The wheeled suitcase existed as a possibility long before anyone manufactured one.

The open questions are now practical rather than theoretical: optimal bonus size, contract drafting, and performance in the field at scale. Those questions will be answered by deployment.