Imagine bidding for a housing property. You’ve studied its location, condition, and potential resale value, and so have your competitors, but none of you know what information the others have. Meanwhile, the auctioneer faces a parallel information problem. It wants the property to go to whoever values it most, but it also lacks the information to identify that person.
The winner gets the property at what they consider a fair price. But that could also just mean they were the most optimistic bidder. In game theory, that’s what’s known as the “winner’s curse”—when no one has all the information, the winner may simply be the one who overestimates the value the most.
In a situation where no one has all the information, how can rules help us make smarter decisions?
In a recent study published in the journal Econometrica, NYU Shanghai Associate Professor of Economics Emiliano Catonini and his coauthor Pierpaolo Battigalli from Bocconi University examine how a sequential mechanism—a dynamic, step-by-step rule—can achieve its intended outcome even when the designer doesn’t know what participants believe about one another.
People often withhold private knowledge because their own bidding strategy depends on factors they have yet to discover, Catonini explains. “To be willing to reveal your information, it’s crucial that you have already learned something from somebody else,” he says.
A sequential mechanism asks for one small piece of information at a time, so no one has to commit blindly, while a static or simultaneous mechanism - rules that ask everyone to make their decisions at once - will not achieve the same result, Catonini says.
The study finds that a sequential mechanism works even if the designer’s assumptions about participants’ beliefs were wrong or too narrow.
In the study, Catonini and his coauthor formalize a classical mechanism design setting. In their example, three participants are bidding on the same thing. If the rules simply asked each participant—A, B, and C, in turn, to reveal everything they know, the second participant, B, would hold back the information. The sequential mechanism therefore gives the second participant another option: share only part of what he knows.
That small freedom therefore changes his incentives and gives the other participants a reason to reveal what they know. The existence of the other option is what makes the sequence work, despite it being unused. In the end, the participant who places the most value on what they are bidding on wins it, regardless of the order in which they reveal information. That interpretation of others’ unexpected choices as deliberate and rational is a form of intuitive reasoning known as “forward induction.”
“Our mathematical proof shows that through forward induction, it doesn’t matter what people know or believe about each other’s information at the outset,” says Catonini. “This type of mechanism will still work. Economists call this robust implementation.”
Their finding resolves a persistent challenge in institutional design: crafting market rules and policies that remain reliable regardless of participants’ private beliefs about one another. Traditional theoretical models suggest that real-world uncertainty severely restricts what policy mechanisms can accomplish. The study overcomes this limitation by analyzing dynamic, step-by-step interactions where individuals reason through “forward induction.”
Catonini says that real-world applications for their findings are still a long way off, but could inform future work on the design of mechanisms for market settings such as auctions and resource allocation.
“Our work helps to solve problems that are related to the winner’s curse, and the approach remains at the research frontier, ” Catonini says. “For participants, the payoff is simplicity, because the hard reasoning happens in the design.”