Many Zeros

Assorted thoughts on economics.

All-or-Nothing Crowdfunding as a Coordinating Device

Suppose you have an idea for a creative project, but you don’t have enough money to get it off the ground. If you can’t persuade your family and friends or a bank to lend you the money, you might turn to your potential customers for funding. If you can convince enough of them to pay you in advance, you’ll have enough money to get your project underway.

Consider an entrepreneur trying to fund a new product by taking pre-orders through her own website. Suppose that she offers a discount on the retail price as an incentive for people to pre-order. If her business goes bankrupt before production finishes, anyone who took a leap of faith by pre-ordering will lose their money. This means that potential customers have to worry about what other potential customers will do. If they think the project will succeed, they are better off pre-ordering and getting the discount than waiting and paying the full retail price. However, if they think that very few others will pre-order and the project will fail, it makes sense for them to wait and see what happens.

For example, suppose the retail price is $20 and the pre-order price is $10. A potential customer who values the product at $30 and thinks the probability of the project succeeding is p faces the following options:

  • Pre-order, and get ($30−$10) of consumer surplus with probability p and lose $10 with probability 1−p.
  • Wait, and get ($30−$20) of consumer surplus with probability p and nothing with probability 1−p.

Assuming for simplicity that our potential customer is risk-neutral, he will only pre-order if he thinks the project has a 50% or better chance of success. Since the success of the project depends on enough people like him pre-ordering, there is the potential here for multiple equilibria and self-fulfilling prophecies.

Potential Customer’s Payoffs
(Non-Refundable Pre-orders)
All Other Customers
Pre-order Wait & See
Customer Pre-order $20 −$10
Wait & See $10 $0

In the good equilibrium, everybody is happy to pre-order because they expect everyone else to do the same, the project succeeds and everyone gets $20 of consumer surplus. In the bad equilibrium, nobody pre-orders because they (correctly) anticipate that the project will fail.

An important benefit of crowdfunding sites like Kickstarter is that they can eliminate this kind of coordination failure. There are now many sites using a similar formula: entrepreneurs create a project page to pitch their idea and offer rewards, and set a funding goal and a deadline. The crucial innovation, however, is in the processing of payments. Instead of charging people’s credit cards as soon as they make a pledge, Kickstarter has an “all-or-nothing” rule: if a project falls short of its funding goal, none of the backers are charged.

All-or-nothing funding removes the risk of losing your money because too few other people invested in the project. As long as you trust the entrepreneur to deliver on her promises, backing the project becomes what game theorists call a weakly dominant strategy: no matter what anyone else does, you won’t be made worse off by backing, and you may end up better off.

Potential Customer’s Payoffs
(All-or-Nothing Funding)
All Other Customers
Back Wait & See
Customer Back $20 $0
Wait & See $10 $0

If there are enough people interested in a project to meet its funding goal, and they think it has some chance of succeeding (p > 0), then with all-or-nothing funding the only equilibrium should be the good one in which the project gets funded.

Having seen how all-or-nothing crowdfunding might solve one kind of coordination problem between backers, let’s consider one kind of coordination problem it can’t solve. Suppose we have two entrepreneurs named Alice and Bob, each of whom is a potential backer of the other’s project. Let’s assume that backing a project costs $10, and they value each other’s products at $20. Both of them are on the cusp of reaching their funding goals: if Alice backs Bob, his project will be funded and vice versa.

Let’s also assume that the profit from a successfully funded project is $10, so each of them can only afford to back the other’s project if their own project is funded. If Bob backs Alice’s successful project but his own project fails, he has to go without another product he values even more highly (at $30, say) than the one he receives from Alice.

Entrepreneurs’ Payoffs
Back Don’t Back
Alice Back $20, $20 −$10, $10
Don’t Back $10, −$10 $0, $0

From the payoff table we can see that there are two equilibria here: a good one in which Alice and Bob back each others’ projects, and a bad one in which neither offer backing because they both (justifiably) fear not being funded themselves. Whereas all-or-nothing crowdfunding can ease concerns about how many others will back a given project, it can’t alleviate a reluctance to back projects based on pessimism about one’s own income.