Mechanism Design: An Interview with Axel Niemeyer
Assistant Professor of Economics Axel Niemeyer, who joined Caltech last summer after completing doctoral work at the University of Bonn, specializes in mechanism design, a subfield of economic theory. Mechanism design helps economists create rules and procedures for achieving desirable social or economic goals in different types of economic situations. Central to the theory is the observation that information and the resources needed to achieve economic goals—which might be the maximization of social welfare, efficiency, or fairness—are often spread across individuals who pursue their own independent interests. The rules must then be designed to coordinate these different interests in a way that is beneficial to the broader goal. We recently sat down with Niemeyer to discuss his research in the field.
What is mechanism design?
Often, when we do research in economics, we look at particular economic institutions, by which we mean all the rules and procedures that influence how individuals interact and decide in economic situations. We might explore, for example, how regulations affect trade and production in a market or how an income tax system affects people's labor decisions. Then we gather data and write theories about how these institutions work or when they might fail.
Mechanism design is a theory that asks the opposite question. Instead of asking how existing institutions work, mechanism design invites us to imagine all possible institutions—all the possible ways people can trade or sell at auction, for example, or all the ways we could run an election. Then we model how individuals would interact within these hypothetical systems based on the rules and procedures we devise. Out of all these possibilities, we aim to identify an institution—a mechanism—where individuals interact in ways that align best with a broader social or economic goal.
Can you give an example?
Yes, we can look at the example of an auction. We're trying to understand what, given the rules of the auction, people will bid if they are strategic about what they are doing. Imagine that we are running what's called a first-price auction: Everyone submits their bid in a sealed envelope, the highest bidder wins, and they pay the amount of their winning bid. In this scenario, let's say that I'm willing to spend $10. But if I can get the item for less than $10, that's better. I don't know how other people value this item; they're not sharing that information with me. So, thinking strategically, I have to weigh my options: If I bid more, I'm more likely to win the auction, but I may be paying more than I actually have to.
Now imagine instead that we change the format to a second-price auction. If I win, instead of paying my own bid, I pay the amount of the second highest bid. Here the strategic thing for me to do is no longer to hide the amount that I'm truly willing to spend, but to bid that amount, my true valuation, outright.
Something similar happens in elections if you vary the rules of how people can vote. If I'm only allowed one vote that goes to one candidate, I may think, "I really like candidate A, but I don't believe they can win the election. So maybe I should vote for candidate C instead." But we can imagine changing the rules for voting, perhaps allowing votes for multiple candidates. Then we can predict how this will change people's choices, and ultimately, the election's outcome.
Are you empirically testing these different formats, say for auctions or for voting?
It makes me really happy to see these theories getting tested empirically! That's not what I do though. I'm more of a theory person. We're trying to figure out, for a given economic situation and a given social or economic goal, what might be the best format to use.
Maybe you're an auctioneer who wants to maximize your revenue. What would be the optimal rules for an auction in this case? Or maybe you're an auctioneer who values efficiency: You want the goods to go to the people who can make the best use of them. If the government is running an auction to sell public assets, this may be the goal. Or if you're looking at rules for voting, maybe you want the winner to truly represent the population's preference.
Is it correct to say that you are working with a mathematical system that is sufficiently abstract that you can plug in either profit values, or efficiency values, or normative values like fairness?
Exactly. Part of the beauty of the theory is in its flexibility; we remain agnostic about what these goals or values should be. No matter the objective, we can try to design an institution that gets at the goal most closely.
A key concept in this approach is what we call an equilibrium, where if everyone follows a particular strategy, no one will have an incentive to try a different strategy. It's our forecast of what's likely to happen based on the rules we've set, considering what everyone knows and wants. Take the second-price auction as an example: Our equilibrium prediction is that people will bid their true valuation for the item. This way, if our goal is to ensure that the item goes to the person who values it most, the second-price auction does that for us, without us needing to have any idea about people's valuations upfront. Should we aim for a different goal, the ideal auction design might look quite different.
Is equilibrium a situation in which everybody feels they have been treated fairly?
No, an equilibrium doesn't necessarily need to be fair. It only means that given what everyone else is doing, you can't choose a different strategy that will improve your situation.
Is there a specific problem you are working with now?
Yes, a key idea in mechanism design is that we can achieve better outcomes by arranging side payments between the involved parties. For example, in elections with two options, the majority wins, but the majority might care very little about the candidate or the issue while the minority might care a huge amount. This can be an inefficient outcome, which we could overcome, at least in principle, using monetary transfers.
But in many settings, we can't make these kinds of transfers, either for ethical reasons, legal reasons, or just practical reasons. This is certainly true with elections, but also in many other scenarios. I'm interested in how we can attain efficiency in a variety of settings. For example, how can we ensure that essential goods and services reach those who genuinely need them most, or allocate limited funds within organizations effectively?
If you can't make or ask for payments, you have to find other ways to get people to reveal their true preferences and valuations—to not exaggerate or falsify what they really need. This might mean closely examining the claims people make, which can be a costly and time-consuming task. Then it's all about figuring out which claims to scrutinize and how thoroughly. Alternatively, we may utilize community knowledge. This is done in peer review for academic conferences or when targeting financial aid or credit to people in rural communities. Again, we must be careful of any strategic gaming this might invite. Another angle is to consider the repeated nature of many interactions. For example, if someone passes up on claiming resources today, signaling they're not in urgent need, we can promise to prioritize their needs in the future. This way, we can better identify those in need today.
But people do not know their own truth much of the time. You may know better than I do where the trade-offs are, and what the best choice is for me.
That's a great point. We all make mistakes sometimes or believe in erroneous facts. Or we might not pay enough attention to all the information out there. This raises interesting normative questions: Should the designer, if they think they know better, override people's preferences? Or should we stick to trying to figure out what people want, even if it seems like they're a bit off track?
It is the philosopher's job to answer that. As economists, we just say, give me the inputs: What is the economic situation? What is your goal? You can tell me what you want, and in principle, I can model the situation and try to solve the equations that will optimize the system for that.
