An Invitation to Market Design

Market design seeks to translate economic theory and analysis into practical solutions to real-world problems. By redesigning both the rules that guide market transactions and the infrastructure that enables those transactions to take place, market designers can address a broad range of market failures. In this paper, we illustrate the process and power of market design through three examples: the design of medical residency matching programs; a scrip system to allocate food donations to food banks; and the recent “Incentive Auction” that reallocated wireless spectrum from television broadcasters to telecoms. Our lead examples show how effective market design can encourage participation, reduce gaming, and aggregate information, in order to improve liquidity, efficiency, and equity in markets. We also discuss a number of fruitful applications of market design in other areas of economic and public policy.


Introduction
Market design seeks to turn economic theory and analysis into practical solutions to realworld problems.Market designers iterate back and forth between theory and practice in order to improve the function of markets-settings in which economic incentives matter.
The goal of the market design approach is to mitigate some of the frictions and externalities that prevent markets from reaching the first best,1 while at the same time aligning market outcomes with society's objectives beyond pure economic efficiency.
In practice, market design is largely concerned with the rules that guide market transactions and the infrastructure that enables those transactions to take place-two ingredients that jointly constitute marketplaces (Eisenmann et al., 2006;Eisenmann and Kominers, 2017).Rules may take many forms, ranging from simple guidelines (e.g., "swipe right" to accept a date on Tinder) 2 to dozens of pages of minutiae (as are common, for example, in government procurement and spectrum auctions).Infrastructure may be physical (e.g., a room in which market participants can meet and negotiate), but need not be-infrastructure might, for example, be technological, legal, or social.
Marketplaces need not be centralised, but they must coordinate and facilitate transactions.For example, over-the-counter financial marketplaces facilitate transactions without centralising them, whereas limit-order books centralise all transactions for particular financial instruments.Likewise, a company may be sold through a multilateral negotiation or a single auction (Bulow andKlemperer, 1996, 2009).Marketplaces can be run freely by firms, regulated, or organised by governments; they may or may not involve monetary transfers; and they may or may not require/enforce participation.In other words: marketplaces, like markets, can take almost any form.
In recent years, market(place) design has evolved into a field in its own right, involving not just economists, but also computer scientists, operations researchers, engineers, and practitioners (Klemperer, 2004;Milgrom, 2004;Roth, 2015;Fisman and Sullivan, 2016).
This issue of the Oxford Review of Economic Policy presents a number of policy and business domains in which market design has played-and continues to play-a crucial role.Schmalensee and Stavins (2017) consider the success of permit trading in reducing emissions of lead, sulphur dioxide, nitrogen oxides, and carbon dioxide.Cramton (2017) examines the organisation of electricity markets, with a particular focus on the Electric Reliability Council of Texas (ERCOT), which manages a large-scale, liberalised electicity market.Cantillon (2017) discusses how matching theory has improved the efficiency and fairness of primary and secondary school admissions throughout Europe and the United States.Edelman (2017) analyses a number of strategies that online marketplaces adopt in order to retain and engage their customers.Kyle and Lee (2017) propose a strategy for reducing the rents accruing to high-frequency traders who seek to arbitrage across financial marketplaces.Sönmez and Ünver (2017) describe recent progress in the design of lifesaving paired kidney exchanges, and discuss the possibilities of liver, lung, and multi-organ exchange.Finally, Li (2017) offers a new perspective on the ethical foundations of market design. 3He proposes that the market designer's job is to optimise the market outcome with respect to society's preferred objective function, while "maintain [ing] an informed neutrality between reasonable ethical positions" regarding the objective function itself (as well as the associated constraints). 4 In this paper, we illustrate the process and power of market design through three examples: the design of medical residency matching programs; a scrip system to allocate food donations to food banks; and the recent "Incentive Auction" that reallocated wireless spectrum from television broadcasters to telecoms.In each case, we explain the underlying problem and design objectives, describe the solution in terms of rules and infrastructure, and draw lessons for other markets.Our examples illustrate how effective market design can encourage participation, reduce gaming, and aggregate information, in order to improve liquidity, efficiency, and equity in markets.
The examples we consider also reveal that market design is an adaptive process with complex objectives and constraints.Market designers often work in contexts in which inequality and fairness are first-order concerns, and in which market participation cannot be enforced (and so must be treated as endogenous).Some settings also involve social and legal restrictions on transactions (e.g., a complete prohibition on monetary payments) and/or fiendish computational problems.
To tackle poor market performance in the real world, market designers draw upon on a number of fields of economic theory including mechanism design, auction theory, matching theory, social choice, and industrial organisation, as well as work in experimental economics, computer science, and operations research.The market designer's toolkit offers promise for tackling problems in a range of new domains: Alongside digital platforms, organ exchanges, and financial markets-all of which are explored in further detail in this issue-we discuss a number of prospective future applications, including refugee resettlement, biodiversity conservation, transportation, and intellectual property.Some of the applications we describe 3 Understanding ethics in market design requires us to go beyond the ethics of market redistribution of society's resources (Rawls, 1971;Nozick, 1974;Sen, 1985), the limits of commercial exchange (Smith, 1759;Sandel, 2012), and the economic borders of the state (Keynes, 1936;Hicks, 1939;Hayek, 1945;Helm, 1990)-none of which we tackle directly here.
4 Of course, as Li (2017) notes, market design experts should-and do-play a crucial role in the public discourse about what the objective function and constraints ought to be.
would require entirely new marketplaces; others would necessitate only minor adjustments to existing rules and transaction infrastructure.Without a doubt, the settings we discuss offer many exciting theoretical and practical directions for market design.

The problem
After completing medical school, doctors in the United States and United Kingdom (as well as many other countries) take up training residencies in their fields of specialisation.
In 2017, there were over 31,000 residency positions in the United States alone.
From the early 1900s to 1945, the American medical residency labor market faced a crisis of unraveling: Offers would be made earlier and earlier each year-and eventually, doctors found themselves accepting residency positions before they had completed much of their training or had opportunities to explore specialisation fields.Unraveling led to significant mismatch-doctors often turned out to be ill-suited for the residencies they had accepted.But unraveling was a product of the incentives created by the residency matching market-while all the hospitals agreed that offers should be made later, each individual hospital wanted to make offers earlier than all the others, so as to lock in high-quality candidates (A.E. Roth andXing, 1994, 1997;A. E. Roth, 2008a,b).
In 1945, the Association of American Medical Colleges (AAMC) imposed a new set of rules aimed at making sure that all residency offers were made on the same day; this at least partially succeeded in coordinating timing, but made market-clearing chaotic and congested.Hospitals and candidates would contract and re-contract by making and accepting offers in a frenzy of phone calls-and many positions were left unfilled at the end of the day.In the 1950s, the AAMC centralised the residency matching system further, organising a clearinghouse that solicited preference lists from doctors and hospitals and then assigned residencies based on a version of what is now called the deferred acceptance algorithm (Gale and Shapley, 1962;A. E. Roth, 1984;A. E. Roth and Sotomayor, 1990).In the deferred acceptance algorithm, one side sequentially "proposes" to the other side of the market.At each stage, the proposal recipients "hold" their favourite proposals and reject all others.Rejected agents then propose to their next most preferred partners, and the algorithm continues, eventually terminating when no agent has new proposals to make.5 The original medical residency match, now called the National Resident Matching Program (NRMP), used a hospital-proposing version of the deferred acceptance algorithm and ran successfully for several decades.However, by 1995 the NRMP faced a new difficulty: Medical students were marrying each other in growing numbers (driven in large part by an influx of women into medical professions), yet the NRMP provided no mechanism for couples to express preferences for co-located residencies (A.E. Roth and Peranson, 1999;A. E. Roth, 2002).Couples were thus often forced to negotiate jobs outside the match; this threatened to lead back to the chaos of the late 1940s.

The solution
The original NRMP appears to have been successful in part because the deferred acceptance algorithm produces an outcome that is stable in the sense that no doctor and hospital mutually prefer each other to their assigned matches. 6Stable mechanisms have been shown to reduce unraveling, and have been key drivers of successful residency matching programs throughout the US and UK (A.E. Roth, 1990Roth, , 1991;;Kagel and A. E. Roth, 2000;Niederle and A. E. Roth, 2003;B. N. Roth and Shorrer, 2017).
In the presence of couples, however, the existence of stable matchings cannot always be guaranteed (A.E. Roth, 1984;Klaus and Klijn, 2005;Biró and Klijn, 2013;Hatfield and Kominers, 2017).Consequently, A. E. Roth and Peranson (1999) developed a subtle extension of deferred acceptance that enabled couples to submit preferences jointly, while carefully mitigating as many market instabilities as possible.A. E. Roth and Peranson (1999) then demonstrated via simulation that their mechanism was likely to find stable matchings in the NRMP context in practice.
An additional adjustment, originally suggested by A. E. Roth (1984), was to switch to a doctor-proposing version of deferred acceptance, as that algorithm has substantial benefits for doctors.Indeed, doctor-proposing deferred acceptance finds the best stable outcome from the doctors' perspective, and is strategyproof in the sense that it removes any incentive for doctors to misrepresent their preferences over hospitals (A.E. Roth, 2002Roth, , 2008a,b),b).7 Ensuring strategic simplicity for doctors was of particular importance because doctors (unlike hospitals) are short-run players-they only go through the NRMP once, and thus do not have opportunities to learn the workings of the system over time. 8,9 The NRMP adopted the (doctor-proposing) A. E. Roth and Peranson (1999) mechanism in 1997, and has used it successfully since then.Every year so far, the NRMP has found stable doctor-hospital matches even in the presence of couples, and recent theoretical work has helped us start to understand why.10 Rules: Doctor-proposing deferred acceptance algorithm, with the A. E. Roth and Peranson (1999) modification to allow for couples.
Infrastructure: Annual centralised system that coordinates preference submission for doctors and hospitals and implements the matching algorithm.

Related applications
Centralised matching mechanisms are used successfully in a number of contexts beyond medical residency matching.School choice systems throughout the United States and European Union use variants of deferred acceptance mechanism to match students to schools; in school choice contexts, requiring stability corresponds to eliminating justified envy among participants.11Similar systems are used to assign lawyers (Dimakopoulos and Heller, 2017) and teachers (Hatfield and Kominers, 2015) to traineeships in Germany, to match psychology students to Masters programs in Israel (Hassidim et al., 2017), and to assign cadets to branches of military service (Sönmez, 2013;Sönmez and Switzer, 2013).
To adapt the deferred acceptance algorithm for broader applications, economists have explored ways of incorporating affirmative action and other priority constraints12 and specifying contract terms beyond who matches with whom. 13More recent work has shown that generalisations of the deferred acceptance algorithm can also be used to clear networked markets (Ostrovsky, 2008;Westkamp, 2010;Hatfield and Kominers, 2012;Hatfield et al., 2013;Fleiner et al., 2017;Morstyn et al., 2017).Not all labor markets can be centralised easily, however.One particularly stark case is the market for federal law clerks in the United States, in which unraveling has been a persistent problem for many years, despite multiple attempts to reorganise the marketplace (Avery et al., 2001(Avery et al., , 2007)).The key problem in the law clerk market appears to be one of market power: Because federal judges have many opportunities to affect clerks' future careers, they exert so much authority that clerks are unable to turn down (or renege upon) early job offers. 14,15It is still unclear exactly when, in general, stable matching can encourage full participation, as it appears to do in the NRMP,16 although recent work of B. N. Roth and Shorrer (2017) gets close to an answer to this question.

Allocating food donations to food banks
The problem Feeding America, a large nonprofit organisation, provides nutritional support for almost 30 million Americans through a network of food banks.
Prior to 2005, Feeding America allocated centrally received donations using a rough proxy based on the demographics and populations of its food banks' catchment areas.
Feeding America would offer each donation it received to food banks according to a ranking of perceived need.Any time a food bank accepted a donation, it would be responsible for pickup and storage; any time it refused, Feeding America would offer the donation elsewhere.Food banks that were offered donations would not be contacted again for a while, irrespective of whether they accepted or rejected their offers.That is, Feeding America was rationing offers of donations, rather than donations themselves-effectively, refusals were treated like indications of lower need.
Rationing offers was widely perceived as fair-but it was also quite inefficient.Food banks receive supplemental donations from outside Feeding America's system-so in principle a food bank might have to refuse offers due to unobservable, transitory supply shocks.(If an outside yogurt donation fills up a food bank's refrigerators, then that food bank does not have the capacity to accept a dairy donation immediately, even if it would be glad to accept such a donation a week later.)Importantly, some food banks also had to turn down large donations simply because they could not afford to pay the associated transport costs.And many food banks would accept offers they did not especially want, fearing that refusal would be interpreted as an indication of low need, and lead to fewer offers in the future.

The solution
In 2005, in consultation with a team of academics from the University of Chicago, Feeding America switched from rationing offers to a marketplace solution: Each day, Feeding America operates daily spot markets for food donations (cleared via first-price, sealed-bid auctions), using a scrip currency called "shares" (Prendergast, 2017). 17The presence of "clearing prices"-even if denominated in scrip-ensure an efficient allocation of food donations.Moreover, the differences in clearing prices reveal the aggregate marginal rates of substitution for different food items (boxed pasta and frozen chicken, for example, turn out to be far more valuable than soda).Shares themselves are distributed according to perceived need-and because the currency is internal to the Feeding America system, better-resourced food banks are not privileged over others, as they would be if cash were used instead of scrip.
Feeding America's marketplace features a number of design advantages beyond just the move to market-based allocation: Food banks can post their extra outside donations into the marketplace and "sell" them for scrip.Additionally, smaller food banks can access scrip-denominated credit, and can bid together and split transportation costs.Because donations are posted centrally and prices respond to demand, virtually any donation can be placed with some food bank; this has reduced food waste dramatically and enabled Feeding America to take in hundreds of millions of pounds of new donations.Prendergast (2017) has estimated that the increase in accepted donations over the first year of the marketplace enabled Feeding America's food bank network to feed roughly 55,000 additional people per day.Moreover, in order to maintain its commitment to fairness, every day Feeding America redistributes the scrip paid by food banks that "bought" donations, so that smaller food banks benefit from each auction-even those they lose to bigger food banks.
Using scrip enables Feeding America to gather dispersed and private information about food banks' preferences into a price signal, just as a competitive market would (Hayek, 1945).Yet at the same time, food allocation is not just "left to the free market"-Feeding America ensures fairness though it daily redistribution of scrip.Thus, Feeding America's food donation marketplace illustrates the power of market mechanisms as designs that can operate successfully outside the traditional market economy.
Rules: First-price, multi-item, sealed-bid auctions (that allow for joint bids), followed by a scrip reallocation procedure.
Infrastructure: Daily, scrip-based, electronic auction platform for posting food donations and submitting bids, along with a scrip account for each food bank.

Related applications
One of the reasons why the Feeding America marketplace has run so well is that shares are redistributed daily, and thus have essentially maintained their value.By contrast, when the exchange value of scrip varies substantially over time (or across market participants), scrip money supplies can suffer from bubbles and crashes.The (in)famous Capitol Hill babysitting co-op, in which couples exchanged scrip corresponding to baby-sitting time, provides a vivid illustration: After a negative shock to the supply of scrip (which arose for administrative reasons), many couples stopped going out and started hoarding scrip; the value of scrip then rose sharply, and all baby-sitting in the co-op stopped (Sweeney and Sweeney, 1977).
Scrip currency is used fairly commonly in marketplaces, despite the inherent macropolicy risks.One recent application of scrip has been course allocation at business schools (where most courses are optional, and many of the popular courses are oversubscribed; see Sönmez and Ünver (2010), Budish (2011), and Budish and Cantillon (2012)).In the business school context, using scrip currency imposes a budget constraint on students, forcing them to internalise tradeoffs among their most-preferred courses.Thus scrip allows students to express the relative intensities of their preferences over courses; in principle, this should allow registrars to allocate courses to the students who value them most highly, just as a competitive market would. 18But scrip value fluctuation is a substantial problem in many business school course allocation settings.Business schools often use mechanisms that behave as if scrip savings have value on their own, even though the scrip is worthless outside the course allocation system; this results in students missing out on courses they want while being left with large supplies of scrip (Sönmez and Ünver, 2010), 19 as well as in graduating students attempting to spend all their remaining scrip at once, artificially inflating course prices (Budish, 2011).Recently, Budish (2011) showed how to get around both aggregateand individual-level scrip value fluctuation by using a pseudo-market mechanism with induced budgets and (approximately) full market-clearing in every semester (see also Hylland and Zeckhauser (1979); Bogomolnaia and Moulin (2001); Budish et al. (2013); Liu and Pycia ( 2016)).The Budish (2011) "Course Match" mechanism has recently been adopted and used successfully at the University of Pennsylvania's Wharton School (Budish and Kessler, 2016;Budish et al., 2016).
18 Having some cardinal preference information allows the designer to Pareto-improve on outcomes achieved with only ordinal rankings of courses; for that same reason, Crawford (2008) suggested introducing flexible salaries into the NRMP, which currently collects only ordinal preferences over programs and residents.
19 A similar problem arose in the first phase of the EU Emissions Trading Scheme: The EU decided that member states could choose whether to allow first-phase (2005)(2006)(2007) permits to be used in the second phase (2008)(2009)(2010)(2011)(2012).But when the verified emission numbers for 2005 were revealed in April 2006, it became clear that there was a large oversupply of permits and the price of first-phase carbon permits collapsed to nearly 0 (Alberola et al., 2008).

The US wireless spectrum Incentive Auction
The problem Wireless spectrum is a valuable but limited resource.Allocating spectrum licenses is now a classic market design problem-economists have been designing and implementing successful spectrum auctions since the early 1990s (Milgrom, 1989(Milgrom, , 2000(Milgrom, , 2004;;McAfee and McMillan, 1996;Binmore and Klemperer, 2002;Klemperer, 2002Klemperer, , 2004;;Cramton et al., 2011). 20n the United States, some of the most useful spectrum-able to penetrate concrete in cities and travel long distances to cover rural areas-was allocated early on to television broadcasters.But today, fewer people watch broadcast television, and there is substantial demand for mobile broadband spectrum to support wireless applications.Thus, it makes sense to repurpose some of the broadcast spectrum for telecom use.
Since telecoms often place higher value on spectrum than television broadcasters do, one might expect to observe widespread sale of spectrum licences from broadcasters to telecom companies.However, spectrum exchange is complicated: broadcasters hold local licenses, while telecoms require national networks.Thus, individual spectrum licenses are only valuable for exchange if they can be assembled together into regional networks.21But if a telecom company were to contract sequentially with individual broadcasters, it could face an exposure problem: if the telecom could not buy the last spectrum license needed for its network, all the licences already purchased would be worth less.
The exposure problem amplifies broadcasters' incentive to "hold out" for high prices.
If the government cannot coerce stations to surrender their licenses, then each station might attempt to claim a large share of the telecoms' surplus; if many complementary licenses must be assembled, the probability of efficient trade then becomes vanishingly small (Cournot, 1838;Bergstrom, 1978;Mailath and Postlewaite, 1990).However, the theoretical inefficiency can be at least partially mitigated by the practical possibility of "repacking" spectrum across bandwidths: if instead of needing to purchase specific stations (e.g., all the stations occupying a particular frequency nationwide), telecom companies could make do with just a specific number of stations, then efficient trade is much more likely to succeed (Kominers and Weyl, 2012;Rosston, 2012).

The solution
Working with the US Federal Communications Commission (FCC), a team of economists and computer scientists developed a two-sided spectrum auction that became known as the "Incentive Auction" (Leyton-Brown et al., 2017;Milgrom, 2017;Milgrom and Segal, 2017).
The telecoms' exposure problem was addressed by running a "forward" ascending clock auction that allowed telecom companies to bid on licenses as packages.The holdout problem was mitigated in two ways: First, the government made a regulatory determination that while none of the almost 3000 television stations could be forced to give up their broadcasting rights, they could be reassigned to other frequencies as long as the reassignment did not subject them to significant interference from neighbouring stations.The idea was to reduce the complementarity of stations from the perspective of telecom companies-exactly the "repacking" scenario described in the preceding section.Second, instead of asking television broadcasters to declare prices for their spectrum licenses directly, the FCC ran a descending clock "reverse" auction for broadcasters' licenses.All stations were made initial buyback price offers, and then those offers were slowly reduced.Each time a station's price was reduced, that station chose whether to remain in the auction or exit irreversibly.As long as a station remained in, its license could be bought back at the current offer price.
Before any given station's price was lowered, an advanced feasibility-checking algorithm (Newman et al., forthcoming) would check whether that station could be reassigned in an (almost) interference-free way if it were to exit;22 the price offer would be lowered if an interference-free repacking could be found; and the price would be "frozen" (i.e., held fixed) otherwise.
The descending auction format made bidding particularly simple for the broadcasters: At each moment, every broadcaster effectively faced a "take-it-or-leave-it" price offer.
At each point in the auction, there was always some chance that all the broadcasters who remained in the auction would end up selling at their prevailing offer prices.Thus, whenever a broadcaster's offer price was above that broadcaster's private value of operating a television station, the optimal strategy was to remain in the auction, for a chance of making a profit.Likewise, it was optimal for broadcasters to exit the auction as soon as their offer prices fell below their private values (Milgrom and Segal, 2017;Li, forthcoming).
The simplicity of the reverse auction's design was particularly crucial for ensuring the participation of smaller stations.
Meanwhile, the full set of interference constraints turned out to be incredibly complex.Indeed, figuring out whether an interference-free reassignment exists at any clock price is a computationally intractable problem.Computer scientists worked closely with economists to develop cutting-edge feasibility checkers that could find solutions as quickly and accurately as possible between the ticks of the auction clock (Newman et al., forthcoming). 23he interference constraints also meant that the FCC could only reallocate spectrum once it knew exactly how much spectrum could be feasibly reallocated.For that reason, the Incentive Auction iterated in stages between rounds of the reverse auction that determined the supply of licenses and rounds of the forward auction that determined the demand for license packages.At each iteration, the FCC lowered the target amount of spectrum to be reallocated24 until it could ensure that the revenue from the forward auction fully covered the costs from the reverse auction. 25he bidding in the Incentive Auction ran from May 2016 to March 2017.In the end, 84 MHz of spectrum was transferred from television stations to telecom companies for mobile broadband and consumer devices (reassigning channels 38-51, corresponding to the 614-698 MHz range).The process also generated substantial revenue for the government: the telecom companies paid $19 billion in the forward auction, while television stations received over $10 billion in the reverse auction, netting the US Treasury over $7 billion after administrative and post-auction repacking costs.
Rules: Iterative (forward-reverse) double auction with package bidding.
Infrastructure: Regulations and technology supporting spectrum repacking; electronic auction platform; feasibility checking algorithms.

Related applications
Single-item auctions are ubiquitous, of course, but simple package auctions have also been used for a long time.There are now dozens of varieties of combinatorial auctions (Parkes and Ungar, 2000;Parkes et al., 2001;Cramton et al., 2006;Milgrom, 2007;Mishra and Parkes, 2007;Day and Milgrom, 2008;Erdil and Klemperer, 2010;Day and Cramton, 2012;Levin and Skrzypacz, 2016) that vary in their numbers of sellers (one or many), bidding languages (e.g., allowing bidders to express whether they are willing to win multiple packages or not), extensive form (sealed-bid or dynamic), price-adjustment procedures (monotonic or nonmonotonic), price structures (linear or nonlinear; anonymous or non-anonymous) and outcomes (e.g., core-selecting or Vickrey (1961)).26More combinatorial auctions are popular not just for spectrum allocation (Ausubel and Baranov, 2014;Cramton and Ockenfels, forthcoming), but also for diverse applications including truckload transportation (Sheffi, 2004), school meals (Olivares et al., 2012), and London bus routes (Cantillon and Pesendorfer, 2006).
Computationally complex constraints on market clearing also arise in a range of contexts (Milgrom, 2017).Competitive electricity markets such as ERCOT (Cramton, 2017), for example, need to clear at every point in time in order to avoid blackouts.However, to clear electricity markets, system operators need to continuously solve difficult integer optimisation problems because of infrastructure constraints involving start-up timing of individual generators and grid congestion.

Some key tenets
The market design solutions described in the preceding section draw upon rigorous economic theory, as well as ideas from computer science and operations research.Our examples illustrate how well-designed marketplace rules and infrastructure can: • encourage participation, making doctors and hospitals willing to join a single, centralised residency market, enabling small food banks to partner and bid jointly, and reducing telecom companies' exposure problems through package bidding; • reduce strategic gaming, incentivising doctors to report their true preferences over hospitals, removing food banks' incentives to accept unwanted food donations, and preventing television broadcasters from holding out for monopoly rents; and • aggregate information, collecting doctors' and hospitals' preferences into a single system, determining relative demand for different food donation types through scrip prices, and discovering market-clearing prices for many heterogeneous spectrum licenses.
Improving market function along the lines just described allows the designer to achieve a number of important objectives: • efficiency, improving the quality of job-candidate matches in medical residency programs, enabling demand differentiation in food allocation, and ensuring that spectrum licenses are held by the firms that value them the most; • liquidity, assigning as many doctors as possible, and filling as many residency positions as possible, placing almost every food donation, and thus reducing the number of donations that are wasted, and ensuring that telecoms can assemble swathes of spectrum licenses from a range of potential sellers; and • equity, making sure that no doctors miss out on residency positions at which they are preferred to accepted candidates, redistributing scrip paid in each food donation auction, so that small food banks can benefit even from the auctions they do not win, and ensuring that the public purse can benefit from the revenue raised in spectrum license reallocation.
The principles we have just described have already been identified in different marketplaces such as auctions, two-sided platforms, and matching clearinghouses (Klemperer, 2002;Eisenmann et al., 2006;A. E. Roth, 2008b). 27  However, while underlying principles are often consistent across market design applications, it is important to observe that achieving similar design objectives in the three examples we have described required substantially different choices of rules and infrastructure.The articles in this issue further highlight how different market contexts require different design solutions: In school choice and in kidney exchange, for example, there are social and legal constraints on the ability of the designer to use any form of currency-even scrip (Cantillon, 2017;Sönmez and Ünver, 2017).In electricity, financial, and permit markets, the designer is faced with a dynamic setting, and needs to ensure that market clearing can take place continuously (Cramton, 2017;Kyle and Lee, 2017;Schmalensee and Stavins, 2017).
27 Klemperer (2002) argued that "what really matters in auction design" is reducing entry deterrence (encouraging participation) and preventing collusion (reducing strategic gaming).Eisenmann et al. (2006) offered three challenges for two-sided platforms: getting pricing right, coping with winner-takes-all competition, and managing overlapping user bases (all of which relate to encouraging participation).
A. E. Roth (2008b) identified thickness (encouraging participation), managed congestion (aggregating information), and safety to reveal preferences (reducing strategic gaming) as key features of successful matching markets.
Additionally, it is essential to recognise that there are often fundamental tradeoffs among market design objectives.In auctions, for example, a designer typically trades off revenue against efficiency (Wilson, 1979;Myerson, 1981).In school choice, it is usually impossible to achieve Pareto-efficient outcomes for students while simultaneously guaranteeing that no student's priority is violated (Abdulkadiroğlu and Sönmez, 2003;Kesten, 2010;Cantillon, 2017).In kidney exchange, meanwhile, efficiency is constrained because the logistical costs of running simultaneous operations prevent doctors from conducting kidney exchanges across many pairs of patients at once (A.E. Roth, 2008b;Sönmez and Ünver, 2017).
And online or digital marketplace organisers often use simple mechanisms to encourage participation and reduce cognitive burden ("rate from 1 to 5 stars," "swipe left"), even though such mechanisms limit full preference elicitation (Milgrom, 2010;Budish et al., 2016;Edelman, 2017).
Successful market design solutions are bound to vary across markets because real-world settings have distinct (and sometimes unexpected) objectives, constraints, and tradeoffs.It would be odd, for example, to ask broadcasters to trade spectrum for scrip, or for us to sell residencies (or donated food) to the highest cash bidders, or ask users to submit full preference rankings on dating websites.There is no one-size-fits-all market design.

New marketplaces in areas of public policy
Next, we highlight several areas of public policy that could benefit from improved market design.Our list is far from exhaustive, but we hope it will nevertheless serve to stimulate new theoretical inquiries and practical solutions.

Digital markets
Online marketplaces have evolved from simple auction platforms (e.g., eBay) to large-scale sponsored search auctions (Edelman et al., 2007;Varian, 2007;Agarwal et al., 2009;Athey and Nekipelov, 2010;Athey and Ellison, 2011) to the sophisticated real-time pricing and matching infrastructure used in the sharing economy (e.g., ride-sharing apps such as Lyft and Uber (Cramer and Krueger, 2016;Azevedo and Weyl, 2016;Cohen et al., 2016; J. V. Hall and Krueger, 2016;Castillo et al., 2017), as well as short-term rental platforms such as Airbnb (Zervas et al., 2014;Fradkin et al., 2017)).Online platforms must fight many of the same battles faced in offline market design.28However, as Edelman (2017) points out, online settings introduce many new market design challenges.
One key problem is trust and anonymity: Why should I allow a complete stranger into my car, much less my home?How do I know that an online retailer will not misrepresent quality (and will ship my purchases)?Many online marketplaces overcome trust problems by creating review and reputation systems, but those systems can often be vulnerable to abuse and misrepresentation (Luca, 2016;Edelman, 2017;Fradkin et al., 2017).
Another issue involves data ownership and privacy.Online behaviour generates vast quantities of data, sometimes called "digital exhaust" (Luca, forthcoming); these data are increasingly valuable to advertisers and companies, who can mine them for use in developing and targeting new products.But currently, consumers have little control over how their data are used and distributed.Moreover, the value consumers place on privacy is unclear (Athey et al., 2017).We might imagine that in the future, individuals would receive a share of the value their data generates, perhaps by renting access in exchange for micro-payments; one market design approach draws upon "differential privacy," which allows data sharing while minimising private data leakage (Dwork, 2011;A. Roth and Schoenebeck, 2012;Dwork and A. Roth, 2014;Ghosh et al., 2014;Ghosh and A. Roth, 2015).
It is also worth noting that data privacy rules themselves have distributional consequences.Removing the ability of sellers to personalise prices (e.g., based on browser use, geography, and prior browsing history) forces merchants to price towards the middle of the distribution-and thus can often lead to price increases for consumers with the least ability to pay (Goldfarb and Tucker, 2011).Restrictions on data sharing can also prevent crucial information aggregation-for example, restrictions on sharing of electronic medical records have been shown to lead to increased neonatal mortality (Miller and Tucker, 2011).

Living-donor organ allocation
Thousands of people around the world are on dialysis and require kidney transplants in order to be able to lead healthy lives.However, commercial exchange of kidneys is prohibited in almost every country in the world.Many patients have friends or relatives who are willing to donate kidneys to them, but some of those prospective donors are unable to donate because of blood-or tissue-type mismatches.
If patient A has an incompatible donor A and patient B has an incompatible donor B , it is sometimes the case that B is compatible with A, and A is compatible with B-so in principle, A and B can "swap" donors.To enable patients to swap donors at scale, market designers have organised centralised kidney exchanges.Because it is not possible to contract over kidneys, early kidney exchanges required substantial logistical infrastructure-multiple simultaneous surgeries-so as to ensure that each exchange could be completed entirely at once (A.E. Roth et al., 2004Roth et al., , 2005aRoth et al., ,b, 2007)).Nowadays, many kidney exchanges are conducted in chains, whereby an altruistic, non-directed donor A donates to a patient B with an incompatible but willing donor B , and B then "pays it forward" by donating to another patient C in the future.If C has an incompatible but willing donor C , then C can donate in the future, and so forth, eventually leading to a long sequence of kidney exchanges over a period of years (Rees et al., 2009;Ashlagi et al., 2011Ashlagi et al., , 2012;;Anderson et al., 2015).
The success of kidney exchange in many countries has led market designers to explore further opportunities for saving lives through organ exchange.
One new possibility is international exchanges (Rees et al., 2017).Dialysis costs are so high that healthcare providers in affluent countries may be able to save money overall by enabling their patients with willing but incompatible kidney donors to exchange kidneys with patient-donor pairs from other countries.In an international kidney exchange, the affluent country's healthcare provider would cover all of the costs for the international donor and patient, including post-surgical and ongoing treatment; amazingly, this is still less expensive than long-term dialysis (Nikzad et al., 2017).The resulting welfare benefits can be substantial not only because of the lives saved, but also because of patients from poorer countries' getting access to world-class healthcare, and overall cost savings in richer countries.
A second frontier involves exchanges of organs beyond kidneys: lungs and livers (Sönmez and Ünver, 2017;Ergin et al., forthcoming).Lung exchange in particular may have enormous life-saving potential (Ergin et al., 2014).Taken to a logical extreme, we could even conceive of multi-organ exchanges in which a patient who needs a kidney can enter into an exchange with a donor who is willing to donate a kidney or a lung.29A crucial part of the success of many organ exchanges will be encouraging new donors to participate (Sunstein and Thaler, 2003;Kessler andA. E. Roth, 2012, 2014).

Financial markets
Trillions of dollars worth of financial instruments, including equity shares, bonds, and derivatives, are traded across the world every day.A rich finance literature has examined how market microstructure affects the performance of financial markets (O'Hara, 1995;Madhavan, 2000;Biais et al., 2005).
Many securities are traded via continuous limit order books that aggregate bids and asks into a central, publicly observed ledger.We often think of continuous limit order books as essentially equivalent to the competitive market ideal of running in perfectly continuous time.However, at microsecond intervals, limit order books can be surprisingly illiquid and uncompetitive; this creates incentives for high-frequency traders to invest in costly technology for arbitraging across different exchanges at the expense of slower traders, such as pension funds (Biais et al., 2015).
One attractive response to excessive high-frequency trading, proposed by Budish et al. (2015), is to change the market clearing rules so all exchanges run discrete auctions (see also Budish and Lee (2017)).Under frequent, discrete batch auctions, all orders received in each small time interval are treated equally, encouraging price rather than speed competition and reducing the incentive to place an order "first."An infrastructure solution, proposed by Kyle and Lee (2017), is to allow limit orders to be continuous not only in price and quantity, but also in time; that way, large trades could be spread over time and "flow" continuously into the exchange.Both the Budish et al. (2015) and Kyle and Lee (2017) approaches could remove the "first-to-act" advantages that high-frequency traders currently enjoy.
Meanwhile, a vast number of financial market transactions (e.g., for corporate bonds, mortgage-backed securities, and exotic derivatives) occur in over-the-counter markets, in which prices are not quoted publicly, and are instead settled through bilateral negotiations (Duffie et al., 2005;Zhu, 2011).Because bilateral offers can expire as soon as they are announced, participants often face high search costs-and can thus be exposed to unfavourable sets of transactions.Future work could investigate how to increase liquidity and improve coordination and efficiency in over-the-counter markets.

Refugee resettlement
The recent refugee crisis precipitated by conflict in Syria has pushed the number of forcibly displaced people around the world to 65 million, creating over 16 million refugees (United Nations High Commissioner for Refugees, 2017).Many EU countries were unprepared for the large number of refugees that have arrived since 2015, and the EU has struggled to find a system that would both fairly compensate those places that accept refugees and encourage other states to welcome more.
One macro-level proposal suggests combining country-level tradable refugee admission quotas with a matching system that allows refugees to express preferences over destination countries (Moraga and Rapoport, 2014).A more micro area in which market design can play a role is within-country resettlement: There is abundant evidence that the local areas to which refugees are resettled have strong impacts on refugees' economic outcomes (Åslund and Rooth, 2007;Åslund et al., 2011)-yet refugees are typically not consulted about where they would prefer to be resettled.Andersson and Ehlers (2016) have proposed a way to match refugees to housing in Sweden on the basis of family size and language compatibility.Meanwhile, Jones and Teytelboym (forthcoming) and Delacrétaz et al. (2016) have respectively proposed infrastructure and rules for a matching system that allows both local areas and refugees to express preferences over possible matches. 30Future research could combine refugee matching frameworks with financing mechanisms.

Natural ecosystems
Resource-intensive economic growth over the past three centuries has taken a toll on the stock of renewable natural capital.Rainforests are being decimated (Hansen et al., 2013), fish stocks are declining (Worm et al., 2009), biodiversity is disappearing (Cardinale et al., 2012;Dirzo et al., 2014), and the atmosphere is filling with anthropogenic carbon, causing dramatic changes in climate (Allen et al., 2009). 31  Many environmental externalities have been partially addressed via permit trading in the spirit of classic Pigouvian solutions (Montgomery, 1972).Environmental marketplace design often focuses on settings in which natural resources are to some extent substitutable: a ton of carbon emissions, for example, affects the atmosphere no matter where it comes from; one cod left in the sea will support the population as well as another cod.For example, following the success of sulphur dioxide permit trading to reduce acid rain in the US, the European Union led the world in setting up a carbon dioxide permit trading system (Schmalensee and Stavins, 2017).Meanwhile, many countries use individual tradable quotas (ITQs) to allocate fishing rights (Chu, 2009;Stavins, 2011;Bjørndal and Munro, 2012). 32Although many other innovative ecosystem market designs-payments for ecosystem services, wetland offset trading, and water quality permit trading-already exist in practice (Stoneham et al., 2003;Bishop and Pagiola, 2012;Shortle and Horan, 2013;Jayachandran et al., 2017), they have either failed to scale or have been controversial (Robertson and Hayden, 2008;Kinzig et al., 2011;Muradian et al., 2013).
Most natural ecosystems feature complementarities (Helm and Hepburn, 2012): trees need soil to grow, and soil requires tree roots to prevent it from being washed away; bees need flowers for nectar, and flowers need bees to pollinate them; cod often breed alongside haddock. 33However, associated property rights are often allocated in ways that ignore natural capital's underlying complementarities and interdependencies.Thus, (terrestrial) ecosystem protection faces similar problems of exposure and holdout to those that were 30 The proposed system is similar to existing systems for school choice (Cantillon, 2017), except it takes into account the fact that refugees typically arrive in families and require a number of different public services, such as housing, school places, and language or employment training-inducing combinatorial constraints similar to those encountered in course allocation or the Incentive Auction.
31 On the other hand, there is almost no evidence that non-renewable natural capital (mainly commodities and minerals that are traded on exchanges at market prices) is becoming more scarce (Hepburn et al., 2017).
33 This complementarity is compounded by the fact that much natural capital is critical: degrading it beyond a certain point causes irreversible collapse of ecosystems (Ekins et al., 2003).
tackled the Incentive Auction: investors want to conserve large swathes of adjacent land; this gives landowners substantial bargaining power (Nemes et al., 2008;Iftekhar et al., 2012).Marketplaces for ecosystem services are further complicated by issues of investment timing: landowners are typically paid after they have maintained/conserved their land.
If a landowner is paid to protect his meadow, but a nearby farmer pollutes an adjacent river-contaminating the whole ecosystem-then the efforts of the landowner go to waste.
If it is not possible to make payments contingent on the outcome of the whole ecosystem, then the designer might end up over-or under-compensating landowners.Moreover, if designers want to incentivise land improvements, then they also need to tackle ex ante moral hazard problems, as otherwise landowners would have incentives to degrade their land in order to be paid to improve it (Ferraro, 2008).
Nevertheless, advances in satellite technology and data processing are dramatically reducing costs of monitoring land use change, and could possibly allow ecosystem services marketplace infrastructure to be created at large scales (see, for example, NaturEtrade, a digital marketplace for ecosystem investment that uses satellite data to track ecosystem function).

Road and air transport
Traffic congestion is a classic externality problem that creates large welfare losses (Vickrey, 1969), and its management is becoming more effective because of technological advances (Cramton et al., 2017).Singapore, London, and many other cities around the world have developed sophisticated infrastructure for pricing access to city centres (Santos, 2005;Leape, 2006).The received wisdom has been that congestion pricing must create both winners and losers-there will always be those who cannot afford to pay and therefore are not be able to travel.However, the conventional view that congestion pricing is only redistributive is now being challenged: If congestion not only lengthens traffic queues but also reduces throughput, then congestion pricing can eliminate bottlenecks and thus be Pareto-improving without the need for compensation (J.Hall, 2017).
In parallel, ride-sharing companies like Lyft and Uber have used smartphone-based networks to supplant classical taxi technologies, by allowing customers to request rides from non-professional drivers at prices that reflect local supply and demand conditions (Cramer and Krueger, 2016).In the future, driverless cars will offer even greater possibilities for innovative ride-sharing marketplace designs that could combine individual and public transport.
Air transport also creates interesting market design possibilities.While academics have long promoted auctioning airport landing and take-off slots (Rassenti et al., 1982;Schummer and Vohra, 2013;Schummer and Abizada, 2017), there has been substantial resistance from industry (Sentance, 2003).Yet the difficulties of expanding airports in urban areas mean that efficient allocation of slots must soon become a priority. 34Moreover, the increases in drone, satellite, and rocket launches will create an important new problems in the coming decade: combined allocation of horizontal and vertical air traffic rights (Milgrom, 2017), as well as allocation of orbit rights.

Intellectual property
In recent years, there has been a sharp increase in patent lawsuits in the US, predominantly driven by non-practicing entities (NPEs), firms that amass patents just for the sake of enforcing intellectual property rights through licensing and litigation (rather than producing commercial products).A growing body of evidence (see, e.g., Cohen et al. (2017a)) suggests that NPEs on average act as patent trolls, pursuing opportunistic litigation (Cohen et al., 2016(Cohen et al., , 2017b)), shopping for favorable forums (Leychkis, 2007;Cohen et al., 2016), and often asserting low-quality patents (Love, 2013;Miller, 2013;Feng and Jaravel, 2015;Allison et al., forthcoming).Yet because litigation outcomes are uncertain and most of the upfront discovery costs in patent litigation fall on defendants, credible threat of the legal process is often sufficient to induce firms targeted by NPEs to settle, irrespective of lawsuit quality.
The 2011 America Invents Act placed some limitations on patent lawsuits and introduced a procedure by which third parties can challenge the validity of individual patents through a specialised government agency called the Patent Trial and Appeal Board.Further legislative patent reforms have been considered by the US Congress, but have stalled thus far.Moreover, most of the recent policy discussions have focused on rules imposing ex post cost shifting-plaintiffs that lose patent lawsuits would be required to pay defendants' legal fees, as they are in the UK and elsewhere (Helmers et al., 2013;Love et al., 2017).
Because many defendants (e.g., small startups) cannot afford to see cases through to completion, it is not clear how much fee shifting policies will affect outcomes (Klemperer, 2003).An alternative strategy for the redesign of the intellectual property litigation marketplace is to impose upfront screening rules: Cohen, Golden, Gurun, and Kominers (forthcoming) propose a system whereby all patent lawsuits would be preceded by a brief administrative review that provides a preliminary assessment of lawsuit quality.The review 34 On July 21 2017, 8,800 aircraft passed through UK airspace-the largest number ever.
process would assess the quality of each plaintiff's patents and infringement claims; these findings would be non-binding, but would be advisory in court proceedings and could be used to calibrate fee shifting and penalty rules.In extreme cases, the review process could even trigger re-examination of the asserted patents.If implemented correctly, preliminary review rules could substantially reduce incentives of NPEs to game the litigation system with frivolous lawsuits, while potentially bolstering the cases of plaintiffs with legitimate infringement claims.

Outlook
As market design becomes a more familiar part of practitioners' and policymakers' toolkits, its applications will extend far beyond the contexts we have described here.Today, market design is beginning to operate in the presence of
At the same time, market design is coming to interact more closely with the rest of economics and economic policy.We are, for example, beginning to understand how school choice systems interact with policies designed to improve school quality and composition (Calsamiglia and Miralles, 2016;Hatfield et al., 2016;Cantillon, 2017;Avery and Pathak, forthcoming), how the allocation of land rights can improve agricultural productivity and investment in human capital (Bryan et al., 2017;Glaeser and Kominers, forthcoming), and how auctions can reduce corruption in public procurement (Tran, 2009;Lewis-Faupel et al., 2016).Perhaps one of the greatest challenges for market design will come from problems in developing markets, where weak institutions necessitate new design approaches (Banerjee and Duflo, 2011;B. N. Roth, forthcoming).
It is essential that market design not be divorced from broader political and economic policy issues such as inequality (Atkinson, 2015), globalisation (Baldwin, 2016), and migration (Clements, 2018).And market designers should not work only within the boundaries of circumscribed marketplaces: The design of healthcare exchanges should reflect priorities in health policy; the design of financial exchanges should be linked to debates on financial regulation; and electricity market design should play a key role in the transition to a decarbonised economy.
The examples in this paper and the articles in this issue highlight many successes of market design and avenues for future work.Yet just as economics is a way of thinking about the world, market design is a way of thinking about economics.Thus, we hope and expect that market design approaches will prove valuable throughout economic policy-far beyond the applications we can imagine today.