Policymakers concerned about inequalities in access to economics resources often introduce rules constraining transactions in individual markets—such as rent control—or even choose to distribute goods and services by circumventing markets completely, as is frequently the case for health care or transit. Traditional economic intuition opposes such policies because they introduce allocative inefficiencies. This intuition is often rooted in the second welfare theorem; however, the second welfare theorem does not apply when information about agents’ needs is imperfect—in such cases, there is a trade-off between efficiency and redistribution.

In Redistribution through Markets (with Scott Kominers and Mohammad Akbarpour), we investigate how the equity-efficiency trade-off is resolved in the simplest possible two-sided market for an indivisible homogenous good. If inequalities in the market are sufficiently pronounced and market behavior can be used to identify agents with highest need, welfare maximization may require the use of price controls and rationing. This paper is a conceptual introduction to the IMD research agenda, focusing on economic intuitions; the follow-up paper, Redistributive Allocation Mechanisms is more operational: We study a one-sided allocation problem with heterogeneous object qualities, accommodating observable characteristics of agents, and allowing the market designer to have more flexible preferences over revenue. The paper provides tools for solving mechanism-design problems with a redistributive objective and formulates high-level policy implications.

For a short summary of these two papers, you can take a look at the letter I wrote for Sigecom Exchanges: Inequality and Market Design.

From there, the agenda continues in a few different directions. The first direction focuses on applications. In An Economic Framework for Vaccine Prioritization (with Mohammad Akbarpour, Eric Budish, and Scott Kominers), we add externalities to the framework to study the problem of optimal allocation of vaccines in the presence of redistributive preferences. We show that the welfare-maximizing mechanism calls for a combination of priorities (based on observable information) with prices (that allow to additionally screen for unobserved characteristics). We also study allocative externalities in Optimal Membership Design (with Marco Reuter, Scott Kominers, and Changhwa Lee), focusing on how access to a community or platform should be regulated when different potential members contribute differently to others’ values for joining. In a short policy paper, A market-design response to the European energy crisis (with Mohammad Akbarpour, Scott Kominers, and Filip Tokarski), we apply our prior results to derive simple predictions about optimal regulation of energy prices. 

The second direction studies another type of market distortion frequently used to allocate scarce resources: ordeals. Ordeals are any type of activity that is costly to perform and does not directly benefit anyone (e.g., standing in line or filling out complicated forms). In Equity-efficiency trade-off in quasi-linear environments, I ask a simple question: When allocating financial aid to agents with unobserved heterogenous values for money, is it better to offer a lump-sum payment or screen through an ordeal? Because the equity-efficiency trade-off takes a particularly sharp form, the solution provides intuitions for other papers in the agenda (so the paper might be a good start if you are new to the topic). In practice, policymakers also face the dilemma of which ordeal to use. We provide some guidance in Comparison of Screening Devices (with Frank Yang and Mohammad Akbarpour) by decomposing the welfare effects of using an ordeal into a rent-provision and targeting-effectiveness channels. The paper attempts to make a connection to the rich empirical literature on this topic.

All papers discussed above adopt a market-design perspective: As a matter of fact, policymakers attempt to redistribute through markets; we might as well help them do it more effectively. However, it’s important to understand whether such policies can still be optimal when conventional tools for redistribution—such as income taxation—are also available. This is the question that the third research direction tries to answer. The starting point is the celebrated Atkinson-Stiglitz theorem which provides a negative answer under strong conditions. Studying this result led to Incentive separability (with Pawel Doligalski, Joanna Krysta, and Filip Tokarski). In this paper, we employ a mechanism-design approach to provide a unified treatment (with simple proofs) that delivers the Atkinson-Stiglitz and the Diamond-Mirrlees theorems (along a new application) as special cases. (I particularly recommend the paper to microeconomic theorists who want to better understand these classical public-finance results.) In ongoing work (with Pawel Doligalski, Mohammad Akbarpour, and Scott Kominers), we investigate the optimal interaction between income taxation and goods market distortions by studying a model in which agents differ both in their ability to produce income and in their taste for goods (stay tuned for a draft).   

Although this is an ex-post connection, my only matching paper, Deferred Acceptance with Compensation Chains, is related to the IMD agenda by asking whether a more equitable stable matching can be achieved by letting both sides of the market make offers in a standard one-to-one matching problem. The paper introduces a class of DACC algorithms that—unlike the classical DA algorithms—generate the entire set of stable matchings.

My interest in mechanism design is driven primarily by a combination of the elegance of the mechanism-design framework with its potential to be relevant for practical policy questions. The Inequality-aware Market Design agenda (outlined above) is primarily an application of mechanism design. Below, I describe three other topics I have studied using a mechanism-design framework: property rights, simplicity versus complexity, and optimal transparency of trading mechanisms.

While property rights have been extensively studied, most analyses of property rights take their form as given and consider the effects of their reallocation among different economic actors. In contrast, in A mechanism-design approach to property rights (with Ellen Muir), we fix who holds a property right but allow for its flexible design. Fundamentally, we view property rights as determining the holder’s outside options in economic interactions. This perspective allows us to use mechanism-design techniques to characterize the optimal property right and show that its form often differs from the classical one. The tools we develop connect to the literature on mechanism design with type-dependent outside options.

Practical applications of mechanism design often call for mechanisms that are simple enough for real-life agents to understand. A compelling argument in favor of simple mechanisms seems to be that the outcome of a complex mechanism may be unpredictable when agents cannot figure out their optimal strategies. We demonstrate that this logic may be incomplete in Are Simple Mechanisms Optimal when Agents are Unsophisticated? (with Jiangtao Li). There may exist complex mechanism that strictly outperform the best simple mechanism even if agents always resolve their strategic confusion in the worst possible way for the designer. We also show that in some environments the best simple mechanism cannot be dominated this way by a complex one.

I have always been fascinated by the issue of optimal transparency of trading mechanisms. Most theoretical models study trading mechanisms (e.g., auctions) in a “vacuum,” abstracting away from subsequent interactions taking place in a wider market context. In my job market paper, Mechanism Design with Aftermarkets: Cutoff Mechanisms, I studied a framework in which the agent who acquires a good in an allocation mechanism subsequently interacts with third parties (e.g., in a resale game). In such a setting, the mechanism designer has an additional tool: She can disclose information about the agent’s behavior in the mechanism—the transparency of the mechanism matters because it changes the information structure of the aftermarket. I focused on the properties of cutoff mechanisms which are implementable for all aftermarkets and optimal (under additional conditions) in submodular aftermarkets. Analyzing cutoff mechanisms leads to a clean interaction between the mechanism and information design parts of the problem. In two spinoff papers, I relaxed the restriction to cutoff mechanism by looking at simpler settings. In Mechanism Design with Aftermarkets: Optimal Mechanisms under Binary Actions, I studied optimal mechanisms for a simple class of aftermarkets, and in Mechanism Design with Aftermarkets: On the Impossibility of Pure Information Intermediation, I considered a version of the model in which the designer acts as a pure information intermediary (there is no allocation of a good). If you’re curious how the agenda started, you can check out the paper that I wrote in my first year of grad school, The Effects of Post-Auction Bargaining between Bidders, which studied the problem from a purely game-theoretic perspective (the one thing I like about that paper is that it is one of very few attempts to calculate mixed-strategy equilibria of auctions when they are followed by an aftermarket).

Two of my other research agendas emerged from the interest in optimal transparency. On a more technical side, studying transparency requires tools at the intersection of mechanism and information design. Implementability, Walrasian Equilibria, and Efficient Matchings (with Anthony Zhang) was an attempt to understand mechanism design with a multi-dimensional allocation space—a case frequently arising when information disclosure is part of the mechanism’s outcome. I have also worked on new solution techniques to pure information design problems (see the Information Design section). On a more applied side, I investigated optimal transparency in the context of financial markets (see the Financial Over-the-Counter Markets section).

Bayesian persuasion problems admit a conceptually simple solution through concavification of the Sender’s value function. However, computing the concavification is intractable in all but the simplest cases. In the most technical of my research agendas, I explore duality as a potential solution technique to information design problems. In The Simple Economics of Optimal Persuasion (with Giorgio Martini), we show that optimality of a persuasion scheme can be demonstrated via a price function for posterior beliefs: The Sender acts as a consumer who purchases posterior beliefs at their prices subject to a budget constraint. This approach yields a tractable solution technique in case the Sender’s value function only depends on the induced posterior mean. The Persuasion Duality (with Anton Kolotilin) provides a unified treatment of duality in persuasion problems. The paper offers a geometric interpretation of the dual variable, proves strong duality in a general case, and develops an application to multidimensional moment persuasion, thereby extending and clarifying the connections between previous approaches.

When using the information-design framework in more applied work, I was always concerned about the assumption that the Sender can perfectly predict the distribution of information that the Receiver acquires from alternative sources (most typically, the Sender is the sole provider of information). In Preparing for the Worst but Hoping for the Best: Robust (Bayesian) Persuasion (with Alessandro Pavan), we propose a robust approach to persuasion that relaxes that assumption. We assume that the Sender has a conjecture about the learning environment of the Receiver but does not trust it: As a result, she first eliminates all information policies that do not provide the optimal payoff guarantee against the most adversarial scenario; then, she uses her conjecture to select the best policy among worst-case optimal ones. We show that robust solutions are tractable and can be found by applying tools developed for the standard persuasion model (including duality techniques).

One of the defining features of financial over-the-counter markets—relative to traditional centralized exchanges—is their opacity. Traders in OTC markets often lack information about quotes available in the market and must search to find a trade counterparty; they may also be unable to access information about past transaction prices. Regulators have been concerned about OTC market opacity, and they frequently intervene to increase their transparency. Given my theoretical interest in transparency from a mechanism- and information-design perspectives, financial OTC markets have become an important part of my agenda.

In Benchmarks in Search Markets (with Darrell Duffie and Haoxiang Zhu), we investigate the transparency role of benchmarks—which reveal information about average prices in the market. We derive conditions under which introducing a benchmark to an otherwise opaque market increases efficiency; we analyze the optimal disclosure mechanism using information-design tools; and we ask whether benchmarks are likely to be supported by market participants or require a regulatory intervention. Benchmarks fulfil their informational role only if they reflect true information about market fundamentals. The so-called Libor scandal revealed that some of the most important financial benchmarks were routinely being manipulated for private benefit by large traders. We provide a response to this problem in Robust Benchmark Design (with Darrell Duffie), where we characterize the optimal benchmark design based on transaction data generated by strategic traders whose preferences depend on the benchmark fixing. Effectively, we solve a problem of an econometrician trying to find an efficient estimator but with the twist that the estimator’s choice directly effects the data-generating process.

Benchmarks are just one source of transparency in OTC markets. Transparency can also be increased by lowering search costs, disclosing past transaction data (post-trade transparency), or moving trading to platforms where traders can see all available quotes (pre-trade transparency). In Optimal Transparency in Over-the-Counter Markets (with Maren Vairo), we build a dynamic trading model with adverse selection that allows us to compare different transparency regimes. We show that post-trade transparency improves upon an opaque market but is dominated by pre-trade transparency. Lowering search costs or adding post-trade transparency to a pre-trade transparent market may have detrimental effects on welfare. We also use mechanism design to characterize the optimal trading mechanism.

I had the privilege to co-author a survey article about the research of Paul Milgrom (my co-advisor) and Bob Wilson, following their 2020 Nobel prize in Economics: Discovering Auctions: Contributions of Paul Milgrom and Robert Wilson (with Alexander Teytelboym, Shengwu Li, Scott Kominers, and Mohammad Akbarpour).

At some point I got involved in the design of the Polish kidney exchange program. Even though I am no longer active in this area, you can read about the program in a survey article to which I contributed a chapter: Modelling and optimisation in European Kidney Exchange Programmes.

Older papers:
Optimal Constants in a LlogL Inequality for Continuous Martingales (in Polish), Undergraduate Thesis in Mathematics, 2012
Fiscal Policy Under Rational Inattention, Undergraduate Thesis in Economics, 2011