Please see Professor Kominers’s personal website at www.scottkom.com.
Professor Kominers’s research focuses on market design, developing economic analysis that provides practical solutions to real-world problems. He works at all stages of the economic design process—building underlying theory and technology, identifying new design applications, and working with practitioners to implement solutions to market failures. He also advises startups engaged in marketplace development and design, serves on the National Leadership Council of the Society for Science & the Public, and co-leads one of the Human Capital and Economic Opportunity global working groups on inequality.
Professor Kominers has been supported by the National Science Foundation, the Star Family Fund, the William F. Milton Fund, and the Oxford Martin School, among others. He received the AMS-MAA-SIAM Frank and Brennie Morgan Prize in 2010, was named a Kavli Frontiers of Science Fellow in 2015, and won the Star Family Prize for Excellence in Advising in 2016.
We introduce an empirical framework for models of matching with imperfectly transferable utility and unobserved heterogeneity in tastes. Our framework allows us to characterize matching equilibrium in a flexible way that includes as special cases the classic fully- and non-transferable utility models, collective models, and settings with taxes on transfers, deadweight losses, and risk aversion. We allow for the introduction of a very general class of unobserved heterogeneity on agents' preferences. Under minimal assumptions, we show existence and uniqueness of equilibrium. We provide two algorithms to compute the equilibria in our model. The first algorithm operates under any structure of heterogeneity in preferences. The second algorithm is more efficient, but applies only in the case when random utilities are logit. We show that the log-likelihood of the model has a particularly simple expression and we compute its derivatives. As an application, we build a model of marriage with two-sided preferences over the partner type and private consumption. We estimate our model using the 2013 "Living Costs and Food Survey" database.
John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp
Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models’ definitions of substitutability to settings in which each agent can be both a buyer in some transactions and a seller in others and show that all these definitions are equivalent. We then introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We also prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability.
Hatfield, John William, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky, and Alexander Westkamp. "Full Substitutability." Theoretical Economics (forthcoming).
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We provide the first large-sample evidence on the behavior and impact of nonpracticing entities (NPEs) in the intellectual-property space. We find that, on average, NPEs appear to behave as opportunistic “patent trolls.” NPEs sue cash-rich firms and target cash in business segments unrelated to alleged infringement at essentially the same frequency as they target cash in segments related to alleged infringement. By contrast, cash is neither a key driver of intellectual-property lawsuits by practicing entities (e.g., IBM and Intel) nor of any other type of litigation against firms. We find further suggestive evidence of NPE opportunism: targeting of firms that have reduced ability to defend themselves, repeated assertions of lower-quality patents, increased assertion activity nearing patent expiration, and forum shopping. We find, moreover, that NPE litigation has a real negative impact on innovation at targeted firms: firms substantially reduce their innovative activity after settling with NPEs (or losing to them in court). Meanwhile, we neither find any markers of significant NPE pass-through to end innovators nor of a positive impact of NPEs on innovation in the industries in which they are most prevalent.
Cohen, Lauren, Umit Gurun, and Scott Duke Kominers. "Patent Trolls: Evidence from Targeted Firms."Management Science (forthcoming). (Cited in the United States Federal Trade Commission Report on Patent Assertion Entities, 2016.)
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Admissions policies often use reserves to grant certain applicants higher priority for some (but not all) available seats. Boston’s school choice system, for example, reserved half of each school’s seats for local neighborhood applicants while leaving the other half for open competition. This paper shows that in the presence of reserves, the effect of the precedence order (i.e., the order in which different types of seats are filled) on distributional objectives is comparable to the effect of adjusting reserve sizes. Either lowering the precedence order positions of reserve seats at a school or increasing the number of reserve seats weakly increases reserve-group assignment at that school. Using data from Boston, we show that reserve and precedence adjustments have similar quantitative effects. Our results illustrate that policies about precedence, heretofore underexplored, are inseparable from other aspects of admissions policy. Moreover, our findings explain the puzzling empirical fact that despite careful attention to the importance of neighborhood priority, Boston’s implementation of its 50-50 reserve–open seat split was nearly identical to the outcome of a counterfactual system without any reserves. Transparency about these issues—in particular, how precedence unintentionally undermined the intended admissions policy—led to the elimination of Boston’s walk zones.
We develop a model of intergenerational resource transmission that emphasizes the link between cross-sectional inequality and intergenerational mobility. By drawing on first principles of human capital theory, we derive several novel results. In particular, we show that, even in a world with perfect capital markets and without differences in innate ability, wealthy parents invest, on average, more in their offspring than poorer ones. As a result, persistence of economic status is higher at the top of the income distribution than in the middle. Successive generations of the same family may even cease to regress towards the mean. Moreover, we demonstrate that government interventions intended to ameliorate inequality may in fact lower intergenerational mobility—even when they do not directly favor the rich. Lastly, we consider how mobility is affected by changes in the marketplace.
This article gives a (very) brief exposition of what market design is, along with four examples of market design in action. Loosely themed after Robert Frost’s poem “Mending Wall,” the examples demonstrate ways in which market design can break barriers—physical, political, and/or metaphorical. Each example also illustrates one of four broader classes of ways that market design can create positive change: marketplace mechanism (re-)design, information provision, (re-)shaping the extensive margin, and market(place) creation.
We give a direct proof of one-sided strategy-proofness for worker-firm matching under continuously transferable utility. A new “Lone Wolf” theorem (Jagadeesan et al., 2017) for settings with transferable utility allows us to adapt the method of proving one-sided strategy-proofness that is typically used in settings with discrete transfers.
In this paper, we introduce a combinatorial optimization problem that models the investment decision a political candidate faces when treating his or her opponents’ campaign plans as given. Our formulation accounts for both the time cost of traveling between districts and the time expended while campaigning within districts. We describe a polynomial-time algorithm that computes a (2 + ∈)-approximation to the optimal solution of a discrete version of our problem by reducing the problem to another combinatorial optimization problem known as Orienteering.
New, "big" data sources allow measurement of city characteristics and outcome variables at higher frequencies and finer geographic scales than ever before. However, big data will not solve large urban social science questions on its own. Big data has the most value for the study of cities when it allows measurement of the previously opaque, or when it can be coupled with exogenous shocks to people or place. We describe a number of new urban data sources and illustrate how they can be used to improve the study and function of cities. We first show how Google Street View images can be used to predict income in New York City, suggesting that similar image data can be used to map wealth and poverty in previously unmeasured areas of the developing world. We then discuss how survey techniques can be improved to better measure willingness to pay for urban amenities. Finally, we explain how Internet data is being used to improve the quality of city services.
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.
Kominers, Scott Duke, Alexander Teytelboym, and Vincent P. Crawford. "An Invitation to Market Design."Oxford Review of Economic Policy 33, no. 4 (Winter 2017): 541–571.
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The patent system is commonly justified as a way to promote social welfare and, more specifically, technological progress. For years, however, there has been concern that patent litigation is undermining, rather than furthering, these goals. Particularly in the United States, the time, cost, and complications of patent suits provide openings for opportunistic assertions of infringement. This article proposes a way to address information problems that facilitate opportunistic assertion: an automatic process of administrative review at the threshold of infringement lawsuits in U.S. district courts. The results of this review would be nonbinding but admissible in later court proceedings. Whether conducted by an independent Patent Litigation Review Board or a division of the U.S. Patent and Trademark Office, such review would (1) help discourage—or bring to an earlier and less costly end—relatively weak patent-infringement lawsuits; (2) strengthen the litigation and bargaining positions of patentees with especially robust cases; (3) flag weaknesses in litigation positions to the benefit of private parties and the courts; and (4) provide policymakers with information that facilitates evaluation and adjustment of patent-system performance. This article uses multiple economic models to show the likely benefits of early stage administrative review. Nonetheless, because of the fluid and complex nature of the patent litigation landscape, this article proposes that the review process initially be adopted on a pilot basis.
Nikhil Naik, Scott Duke Kominers, Ramesh Raskar, Edward L. Glaeser and César A. Hidalgo
Which neighborhoods experience physical improvements? In this paper, we introduce a computer vision method to measure changes in the physical appearances of neighborhoods from time-series street-level imagery. We connect changes in the physical appearance of five U.S. cities with economic and demographic data and find three factors that predict neighborhood improvement. First, neighborhoods that are densely populated by college-educated adults are more likely to experience physical improvements—an observation that is compatible with the economic literature linking human capital and local success. Second, neighborhoods with better initial appearances experience, on average, larger positive improvements—an observation that is consistent with “tipping” theories of urban change. Third, neighborhood improvement correlates positively with physical proximity to the central business district and to other physically attractive neighborhoods—an observation that is consistent with the “invasion” theories of urban sociology. Together, our results provide support for three classical theories of urban change and illustrate the value of using computer vision methods and street-level imagery to understand the physical dynamics of cities.
Who will vote quadratically in large-N elections under quadratic voting (QV)? First, who will vote? Although the core QV literature assumes that everyone votes, turnout is endogenous. Drawing on other work, we consider the representativeness of endogenously determined turnout under QV. Second, who will vote quadratically? Conditional on turning out, we examine reasons that, in large-N elections, the number of votes that an individual casts may deviate substantially from that under pure, rational QV equilibrium play. Because turnout itself is driven by other factors, the same determinants may influence how voters who do turn out choose the quantity of votes to cast. Independently, the number of votes actually cast may deviate dramatically from pure QV predictions because of the complex and refined nature of equilibrium play. Most plausibly, voting behavior and outcomes would be determined predominately by social and psychological forces, would exhibit few of the features emphasized in the analysis of hyper-rational equilibrium play,and would have consequential properties that require a different research agenda to bring into focus. Some of our analysis also has implications for voting behavior under other procedures, including one person, one vote.
We introduce a framework of matching with flexible allotments that can be used to model firms with cross-division hiring restrictions. Our framework also allows us to nest some prior models of matching with distributional constraints. Building upon our recent work on observable substitutability, we show that multi-division choice functions with flexible allotments enable stable and strategy-proof matching; these results illustrate the value of clearly mapping when stable and strategy-proof matching is possible.
We develop a model of many-to-many matching with contracts that subsumes as special cases many-to-many matching markets and buyer/seller markets with heterogeneous and indivisible goods. In our setting, substitutable preferences are sufficient to guarantee the existence of stable outcomes; moreover, in contrast to results for the setting of many-to-one matching with contracts, if any agent’s preferences are not substitutable, then the existence of a stable outcome cannot be guaranteed. In many-to-many matching with contracts, a new market design issue arises: the design of the contract language can impact the set of stable outcomes. Bundling contractual primitives encourages substitutability of agents’ preferences over contracts and makes stable outcomes more likely to exist; however, bundling also makes the contractual language less expressive. Consequently, we see that, in choosing contract language, market designers face a tradeoff between expressiveness and stability.
We introduce a two-sided, many-to-one matching with contracts model in which agents with unit demand match to branches that may have multiple slots available to accept contracts. Each slot has its own linear priority order over contracts; a branch chooses contracts by filling its slots sequentially, according to an order of precedence. We demonstrate that in these matching markets with slot-specific priorities, branches’ choice functions may not satisfy the substitutability conditions typically crucial for matching with contracts. Despite this complication, we are able to show that stable outcomes exist in the slot-specific priorities framework and can be found by a cumulative offer mechanism that is strategy proof and respects unambiguous improvements in priority.
The proliferation of big data makes it possible to better target city services like hygiene inspections, but city governments rarely have the in-house talent needed for developing prediction algorithms. Cities could hire consultants, but a cheaper alternative is to crowdsource competence by making data public and offering a reward for the best algorithm. A simple model suggests that open tournaments dominate consulting contracts when cities can tolerate risk and when there is enough labor with low opportunity costs. We also report on an inexpensive Boston-based restaurant tournament, which yielded algorithms that proved reasonably accurate when tested "out-of-sample" on hygiene inspections.
We examine the profitability and implications of online discount vouchers, a relatively new marketing tool that offers consumers large discounts when they prepay for participating firms' goods and services. Within a model of repeat experience good purchase, we examine two mechanisms by which a discount voucher service can benefit affiliated firms: price discrimination and advertising. For vouchers to provide successful price discrimination, the valuations of consumers who have access to vouchers must generally be lower than those of consumers who do not have access to vouchers. Offering vouchers tends to be more profitable for firms which are patient or relatively unknown, and for firms with low marginal costs. Extensions to our model accommodate the possibilities of multiple voucher purchases and firm price re-optimization. Despite the potential benefits of online discount vouchers to certain firms in certain circumstances, our analysis reveals the narrow conditions in which vouchers are likely to increase firm profits.
The last decade has seen a sharp rise in patent litigation in the U.S., with 2015 having one of the highest patent lawsuit counts on record. In theory, this could be a consequence of growth in the commercialization of technology and innovation—patent lawsuits increase as more firms turn to intellectual property (IP) protection to safeguard their competitive advantages. However, the majority of recent patent litigation is driven by nonpracticing entities (NPEs), firms that generate no products but instead amass patent portfolios for the sake of enforcing IP rights afforded therein. We discuss new, large-sample evidence adding to a growing literature suggesting that NPEs—in particular, large patent aggregators—on average act as "patent trolls," suing cash-rich firms seemingly irrespective of actual patent infringement. This has a negative impact on future innovation activity at targeted firms. These results suggest a need to check the power of NPEs through changes in U.S. IP policy, in particular to screen out trolling early in the litigation process.
We model spatial clusters of similar firms. Our model highlights how agglomerative forces lead to localized, individual connections among firms, while interaction costs generate a defined distance over which attraction forces operate. Overlapping firm interactions yield agglomeration clusters that are much larger than the underlying agglomerative forces themselves. Empirically, we demonstrate that our model's assumptions are present in the structure of technology and labor flows within Silicon Valley. Our model further identifies how the lengths over which agglomerative forces operate influence the shapes and sizes of industrial clusters; we confirm these predictions using variations across patent technology clusters.
Abel Kho, John Cashy, Kathryn Jackson, Adam Pah, Satyender Goel, Jorn Boehnke, John Eric Humphries, Scott Duke Kominers and et al.
Objective
To design and implement a tool that creates a secure, privacy preserving linkage of electronic health record (EHR) data across multiple sites in a large metropolitan area in the United States (Chicago, IL), for use in clinical research.
Methods
The authors developed and distributed a software application that performs standardized data cleaning, preprocessing, and hashing of patient identifiers to remove all protected health information. The application creates seeded hash code combinations of patient identifiers using a Health Insurance Portability and Accountability Act compliant SHA-512 algorithm that minimizes re-identification risk. The authors subsequently linked individual records using a central honest broker with an algorithm that assigns weights to hash combinations in order to generate high specificity matches.
Results
The software application successfully linked and de-duplicated 7 million records across 6 institutions, resulting in a cohort of 5 million unique records. Using a manually reconciled set of 11 292 patients as a gold standard, the software achieved a sensitivity of 96% and a specificity of 100%, with a majority of the missed matches accounted for by patients with both a missing social security number and last name change. Using 3 disease examples, it is demonstrated that the software can reduce duplication of patient records across sites by as much as 28%.
Conclusions
Software that standardizes the assignment of a unique seeded hash identifier merged through an agreed upon third-party honest broker can enable large-scale secure linkage of EHR data for epidemiologic and public health research. The software algorithm can improve future epidemiologic research by providing more comprehensive data given that patients may make use of multiple healthcare systems.
We introduce a matching model in which agents engage in joint ventures via multilateral contracts. This approach allows us to consider production complementarities previously outside the scope of matching theory. We show analogues of the first and second welfare theorems and, when agents' utilities are concave in venture participation, show that competitive equilibria exist, correspond to stable outcomes, and yield core outcomes. Competitive equilibria exist in our setting even when externalities are present.
Matthew Cary, Aparna Das, Benjamin Edelman, Ioannis Giotis, Kurtis Heimerl, Anna Karlin, Scott Duke Kominers, Claire Mathieu and Michael Schwarz
We study the dynamics of multi-round position auctions, considering both the case of exogenous click-through rates and the case in which click-through rates are determined by an endogenous consumer search process. In both contexts, we demonstrate that the dynamic auctions converge to their associated static, envy-free equilibria. Furthermore, convergence is efficient, and the entry of low-quality advertisers does not slow convergence. Because our approach predominantly relies on assumptions common in the sponsored search literature, our results suggest that dynamic position auctions converge more generally.
Minh-Phuong Huynh-Le, Amanda J. Walker, Scott Duke Kominers, Ido Paz-Priel, Moody D. Wharam and Stephanie A. Terezakis
Involved field radiation therapy (IFRT) is integral in curative therapy for Hodgkin lymphoma (HL), although primarily used in patients with intermediate/high‐risk HL. We present failure patterns and clinical outcomes in a cohort of pediatric and young adult patients with HL treated with IFRT at the Johns Hopkins Hospital.
We provide an illustration of how the design of labor market clearing mechanisms can affect incentives for human capital acquisition. Specifically, we extend the labor market matching model (with discrete transfers) of Kelso and Crawford (1982) to incorporate the possibility that agents may invest in human capital before matching. We show that in this setting, the worker-optimal stable matching mechanism incentivizes workers to make (nearly) efficient human capital investments. En route to our main result, we show that so long as the space of salaries is sufficiently rich, every stable outcome in the Kelso and Crawford (1982) setting is approximately efficient.
We extend the folk theorem of repeated games to two settings in which players' information about others' play arrives with stochastic lags. In our first model, signals are almost-perfect if and when they do arrive, that is, each player either observes an almost-perfect signal of period-t play with some lag or else never sees a signal of period-t play. The second model has the same lag structure, but the information structure corresponds to a lagged form of imperfect public monitoring, and players are allowed to communicate via cheap-talk messages at the end of each period. In each case, we construct equilibria in “delayed-response strategies,” which ensure that players wait long enough to respond to signals that with high probability all relevant signals are received before players respond. To do so, we extend past work on private monitoring to obtain folk theorems despite the small residual amount of private information.
For relatively prime positive integers and r, we consider the least common multiple L_n:=\mathop{\textrm{lcm}}(u_0,u_1,\dots, u_n) of the finite arithmetic progression \{u_k:=u_0+kr\}_{k=0}^n. We derive new lower bounds on L_n that improve upon those obtained previously when either u_0 or n is large. When r is prime, our best bound is sharp up to a factor of n+1 for u_0 properly chosen, and is also nearly sharp as n\to\infty.
John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp
We introduce a model in which agents in a network can trade via bilateral contracts. We find that when continuous transfers are allowed and utilities are quasi-linear, the full substitutability of preferences is sufficient to guarantee the existence of stable outcomes for any underlying network structure. Furthermore, the set of stable outcomes is essentially equivalent to the set of competitive equilibria, and all stable outcomes are in the core and are efficient. By contrast, for any domain of preferences strictly larger than that of full substitutability, the existence of stable outcomes and competitive equilibria cannot be guaranteed.
In the past twenty-five years, derivatives markets have grown exponentially. Large, modern derivatives markets increasingly enable investors to hold economic interests in corporations without owning voting rights, and vice versa. This leads to both empty voters—investors whose voting rights in a corporation exceed their economic interests— and hidden owners—investors whose economic interests exceed their voting rights.
We present formal analysis that shows how, when financial markets are opaque, empty voting and hidden ownership can render financial markets unpredictable, unstable, and inefficient. By contrast, we show that when financial markets are transparent, empty voting and hidden ownership have dramatically different effects: they follow predictable patterns, encourage stable outcomes, and promote efficiency. Our analysis lends insight into the operation of securities markets in general and derivatives markets in particular. It also provides a new justification for a robust mandatory disclosure regime and facilitates analysis of proposed substantive securities regulations.
We use the supply chain matching framework to study the effects of firm exit. We show that the exit of an initial supplier or end consumer has monotonic effects on the welfare of initial suppliers and end consumers but may simultaneously have positive and negative effects on intermediaries. Furthermore, we demonstrate that there are no clear comparative statics for the effects of intermediary exit on the welfare of other firms; most surprisingly, intermediary exit may diminish the welfare of other firms at the same level of the supply chain.
In this note, we give simple examples of sets $\mathcal{S}$ of quadratic forms that have minimal $\mathcal{S}$-universality criteria of multiple cardinalities. This answers a question of Kim, Kim, and Oh [KKO05] in the negative.
Holdout problems prevent private (voluntary and self-financing) assembly of complementary goods—such as land or dispersed spectrum—from many self-interested sellers. While mechanisms that fully respect sellers' property rights cannot alleviate these holdout problems, traditional solutions, such as the use of coercive government powers of "eminent domain" to expropriate property, can encourage wasteful and unfair assemblies. We discuss the problems holdout creates for the efficient operation of markets and how previous approaches have used regulated coercion to address these challenges. We then investigate when encouraging competition can partially or fully substitute for coercion, focusing particularly on questions of spectrum allocation.
In this note, I extend the work of Echenique (2012) to show that a model of many-to-many matching with contracts may be embedded into a model of many-to-many matching with wage bargaining whenever (1) all agentsʼ preferences are substitutable and (2) the matching with contracts model is unitary, in the sense that every contractual relationship between a given firm–worker pair is specified in a single contract. Conversely, I show that unitarity is essentially necessary for the embedding result.
We provide an algorithm for testing the substitutability of a length-N preference relation over a set of contracts X in time O(|X|3⋅N3). Access to the preference relation is essential for this result: We show that a substitutability-testing algorithm with access only to an agentʼs choice function must make an expected number of queries exponential in |X|. An analogous result obtains when the agentʼs preferences are quasilinear in a numeraire and the algorithm only has access to the agentʼs underlying valuation function.
Hatfield, John William, Nicole Immorlica, and Scott Duke Kominers. "Testing Substitutability."Games and Economic Behavior 75, no. 2 (July 2012): 639–645.
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We show that in a unit demand discrete choice framework with at least three goods, demand cannot be additively separable in own price. This result sharpens the analogous result of Jaffe and Weyl (2010) in the case of linear demand and has implications for testing of the discrete choice assumption, out-of-sample prediction, and welfare analysis.
We introduce a model in which firms trade goods via bilateral contracts which specify a buyer, a seller, and the terms of the exchange. This setting subsumes (many-to-many) matching with contracts, as well as supply chain matching. When firms' relationships do not exhibit a supply chain structure, stable allocations need not exist. By contrast, in the presence of supply chain structure, a natural substitutability condition characterizes the maximal domain of firm preferences for which stable allocations are guaranteed to exist. Furthermore, the classical lattice structure, rural hospitals theorem, and one-sided strategy-proofness results all generalize to this setting. (JEL C78, D85, D86, L14)
Timothy G. Abbott, Zachary Abel, David Charlton, Erik D. Demaine, Martin L. Demaine and Scott Duke Kominers
We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously without self-intersection to form any polygon in the collection. This result settles the open problem about the existence of hinged dissections between pairs of polygons that goes back implicitly to 1864 and has been studied extensively in the past ten years. Our result generalizes and indeed builds upon the result from 1814 that polygons have common dissections (without hinges). Our proofs are constructive, giving explicit algorithms in all cases. For two planar polygons whose vertices lie on a rational grid, both the number of pieces and the running time required by our construction are pseudopolynomial. This bound is the best possible, even for unhinged dissections. Hinged dissections have possible applications to reconfigurable robotics, programmable matter, and nanomanufacturing.
Abbott, Timothy G., Zachary Abel, David Charlton, Erik D. Demaine, Martin L. Demaine, and Scott Duke Kominers. "Hinged Dissections Exist."Discrete & Computational Geometry 47, no. 1 (January 2012): 150–186.
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This note surveys recent work in generalized matching theory, focusing on trading networks with transferable utility. In trading networks with a finite set of contractual opportunities, the substitutability of agents’ preferences is essential for the guaranteed existence of stable outcomes and the correspondence of stable outcomes with competitive equilibria. Closely analogous results hold when venture participation is continuously adjustable, but under a concavity condition on agents’ preferences which allows for some types of complementarity.
Zachary Abel, Brad Ballinger, Prosenjit Bose, Sébastien Collette, Vida Dujmović, Ferran Hurtado, Scott Duke Kominers, Stefan Langerman, Attila Pór and David Wood
We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].
We prove that any parallel chip-firing game on a graph G with at least 4|E(G)| − |V(G)| chips stabilizes, i.e., such a game has eventual period of length 1. Furthermore, we obtain a polynomial bound on the number of rounds before stabilization. This result is a counterpoint to previous results which showed that the eventual periods of parallel chip-firing games with few chips need not be polynomially bounded.
In this note, we demonstrate that the problem of "many-to-one matching with (strict) preferences over colleagues" is actually more difficult than the classical many-to-one matching problem, "matching without preferences over colleagues." We give an explicit reduction of any problem of the latter type to a problem of the former type. This construction leads to the first algorithm which finds all stable matchings in the setting of "matching without preferences over colleagues," for any set of preferences. Our construction directly extends to generalized matching settings.
We give a new, purely coding-theoretic proof of Koch's criterion on the tetrad systems of Type II codes of length 24 using the theory of harmonic weight enumerators. This approach is inspired by Venkov's approach to the classification of the root systems of Type II lattices in R^{24}, and gives a new instance of the analogy between lattices and codes.
For relatively prime positive integers u_0 and r, we consider the arithmetic progression {u_k := u_0+k*r} (0 <= k <= n). Define L_n := lcm{u_0,u_1,...,u_n} and let a >= 2 be any integer. In this paper, we show that, for integers alpha,r >= a and n >= 2*alpha*r, we have L_n >= u_0*r^{alpha+a-2}*(r+1)^n. In particular, letting a = 2 yields an improvement to the best previous lower bound on L_n (obtained by Hong and Yang) for all but three choices of alpha,r >= 2.
A number which is S.P in base r is a positive integer which is equal to the sum of its base-r digits multiplied by the product of its base-r digits. These numbers have been studied extensively in The Mathematical Gazette. Recently, Shah Ali obtained the first effective bound on the sizes of S.P numbers. Modifying Shah Ali's method, we obtain an improved bound on the number of digits in a base-r S.P number. Our bound is the first sharp bound found for the case r=2.
We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L)+2. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated by their vectors of norms min(L) and min(L)+2.
We extend the results of Ozeki on the configurations of extremal even unimodular lattices. Specifically, we show that if L is such a lattice of rank 56, 72, or 96, then L is generated by its minimal-norm vectors.
Earnest and Khosravani, Iwabuchi, and Kim and Park recently gave a complete classification of the universal binary Hermitian forms. We give a unified proof of the universalities of these Hermitian forms, relying upon Ramanujan's list of universal quadratic forms and the Bhargava-Hanke 290-Theorem. Our methods bypass the ad hoc arguments required in the original classification.
We show that if L is an extremal even unimodular lattice of rank 40r with r=1,2,3 then L is generated by its vectors of norms 4r and 4r+2. Our result is an extension of Ozeki's result for the case r=1.
Shiv Gaglani, Maria Elena De Obaldia, Scott Duke Kominers, Dayan Li and Carol Y. Suh
Do you want to develop useful skills, gain admission to top colleges, win scholarship money, excel at science competitions, and explore career options all while having fun? By reading this book and using the advice within it, you will learn how to formulate a research project idea, find people who can help you complete it, effectively present it to diverse audiences, and participate successfully in research competitions. Whether you are a freshman rookie with a vague interest in science or a senior veteran striving for first place at the Science Talent Search, this guide will help you make the most of your research experience. With its testimonials from high school students whose lives were positively changed by their research experiences, this guide also aims to motivate and empower students who otherwise would not pursue science and research opportunities. In doing so, this book also seeks to encourage more students to pursue science and technology.
We survey the empirical literature on non-practicing entity (NPE) litigation behavior and its consequences. We document both aggregate trends and cross-sectional differences amongst various types of NPEs. Survey evidence illustrates a number of ways in which NPEs can potentially act opportunistically and indicates at least some instances and consequences of observed NPE opportunism. Large-sample empirical work has recently begun corroborating and amplifying the findings from survey evidence. NPEs on average behave as "patent trolls." Indeed, NPEs hold and frequently litigate patents that are likely to be at least partially invalidated; moreover, NPEs target cash irrespective of its relation to alleged infringement. Cash-targeting is neither the main driver of practicing entity (PE) intellectual property (IP) litigation, nor of non-IP litigation against publicly traded firms. The empirical evidence suggests, however, that not all NPEs exhibit trolling behavior—the cash-targeting observed in the data is primarily the behavior of large patent aggregators, rather than small inventors. NPE patent trolling has a real negative impact on targeted firms, without any increase in innovation, technology transfer, or other counterbalancing benefits measured thus far.
We give a new structural development of harmonic polynomials on Hamming space, and harmonic weight enumerators of binary linear codes, that parallels one approach to harmonic polynomials on Euclidean space and weighted theta functions of Euclidean lattices. Namely, we use the finite-dimensional representation theory of sl2sl2 to derive a decomposition theorem for the spaces of discrete homogeneous polynomials in terms of the spaces of discrete harmonic polynomials, and prove a generalized MacWilliams identity for harmonic weight enumerators. We then present several applications of harmonic weight enumerators, corresponding to some uses of weighted theta functions: an equivalent characterization of t-designs, the Assmus–Mattson Theorem in the case of extremal Type II codes, and configuration results for extremal Type II codes of lengths 8, 24, 32, 48, 56, 72, and 96.
In many-to-many matching with contracts, the way in which contracts are specified can affect the set of stable equilibrium outcomes. Consequently, agents may be incentivized to modify the set of contracts upfront. We consider one simple way in which agents may do so: unilateral bundling, in which a single agent links multiple contracts with the same counterparty together. We show that essentially no stable matching mechanism eliminates incentives for unilateral bundling. Moreover, we find that unilateral bundling can sometimes lead to Pareto improvement—and other times produces market power that makes one agent better off at the expense of others.
We show that a mechanism induces an agent to make efficient ex ante investment choices if and only if it rewards that agent with his marginal surplus; additionally, for an ex post efficient mechanism, these properties are equivalent to strategy-proofness for the agent. Our results extend to settings with uncertainty; moreover, they have analogs for mechanisms that are only approximately efficient and approximately incentive compatible. Among other applications, our results imply both that under the worker-optimal stable mechanism, workers are incentivized to make efficient human capital investments before entering the labor market, and that second-price auctions induce efficient bidder participation.
This paper develops a class of equilibrium-independent predictions of competitive equilibrium with indivisibilities. Specifically, we prove an analogue of the “Lone Wolf Theorem” of classical matching theory, showing that when utility is perfectly transferable, any agent who does not participate in trade in one competitive equilibrium must receive her autarky payoff in every competitive equilibrium. Our results extend to approximate equilibria and to settings in which utility is only approximately transferable.
John William Hatfield, Scott Duke Kominers, Richard Lowery and Jordan M. Barry
Many markets, including the markets for IPOs and debt issuances, are syndicated, in that a bidder who wins a contract will often invite competitors to join a syndicate that will fulfill the contract. We model syndicated markets as a repeated extensive form game and show that standard intuitions from industrial organization can be reversed: collusion may become easier as market concentration falls, and market entry may in fact facilitate collusion. In particular, price collusion can be sustained by a strategy in which firms refuse to join the syndicate of any firm that deviates from the collusive price, thereby raising total production costs. Our results can thus rationalize the apparently contradictory empirical facts that the market for IPO underwriting exhibits seemingly collusive pricing despite its low level of market concentration.
Hatfield, John William, Scott Duke Kominers, Richard Lowery, and Jordan M. Barry. "Collusion in Markets with Syndication." Harvard Business School Working Paper, No. 18-009, July 2017. (Revised May 2018.)
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Over 100,000 refugees are permanently resettled from refugee camps to hosting
countries every year. Nevertheless, refugee resettlement processes in most countries
are ad hoc, accounting for neither the priorities of hosting communities nor the preferences of refugees themselves. Building on models from two-sided matching theory, we introduce a new framework for matching with multidimensional constraints that models
refugee families’ needs for multiple units of different services, as well as the service
capacities of local areas. We propose several refugee resettlement mechanisms that can
be used by hosting countries under various institutional and informational constraints.
Our mechanisms can improve match efficiency, incentivize refugees to report where
they would like to settle, and respect priorities of local areas thereby encouraging them to accept more refugees overall. Beyond the refugee resettlement context, our model
has applications ranging from the allocation of daycare slots to the incorporation of
complex diversity constraints in public school assignment.
In this paper, we show that preferences exhibiting some forms of complementarity
in fact have an underlying substitutable structure. Specifically, we show that some
preferences that are not substitutable in the setting of many-to-one matching with
contracts become substitutable when an employer is allowed to sign multiple contracts
with an individual worker. These substitutably completable preferences guarantee the
existence of stable outcomes, even though stable outcomes are not guaranteed, in general,
when complementarities are present. Our results imply the existence of a stable,
strategy-proof mechanism for allocating workers with specialized skillsets; moreover,
our results give new insight into the existing applications of matching with contracts
to cadet–branch matching and the design of affirmative action programs.
We show that increased litigation risk has driven innovators to shield themselves by shifting innovation out of industry and into universities. We show both theoretically and empirically that litigation by Non-Practicing Entities (NPEs) pushes innovation to spaces with reduced litigation threat. Innovation has shifted into universities (and away from public and private firms) in exactly those industries with the most aggressive NPE litigation, precisely following extensive NPE litigation. The extent of innovation shielding is large and significant. An increase of 100 NPE lawsuits in an industry shifts up the university share of innovation by roughly 70% in subsequent years (t=5.34).
We consider the setting of many-to-one matching with contracts, where firms may
demand multiple contracts but each worker desires at most one contract. We introduce
three novel conditions—observable substitutability, observable size monotonicity, and
non-manipulatability—and show that when these conditions are satisfied, the cumulative
offer mechanism is the unique mechanism that is stable and strategy-proof (for workers).
Moreover, when the choice function of some firm fails any of our three conditions, one
can construct unit-demand choice functions for the other firms such that no stable and
strategy-proof mechanism exists. In the final part of the paper, we characterize the
class of choice functions for which the cumulative offer mechanism is guaranteed to
yield a stable outcome.
John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp
We show that in general trading networks with bilateral contracts, a suitably
adapted chain stability concept (Ostrovsky, 2008) is equivalent to stability (Hatfield and
Kominers, 2012; Hatfield et al., 2013) if all agents' preferences are fully substitutable
and satisfy the Laws of Aggregate Supply and Demand. Furthermore, in the special case
of trading networks with transferable utility, an outcome is consistent with competitive
equilibrium if and only if it is not blocked by any chain of contracts.
Human information processing is often modeled as costless Bayesian inference.
However, research in psychology shows that attention is a computationally costly and potentially limited resource. We study a Bayesian individual for whom computing posterior beliefs is costly. Such an agent faces a tradeoff between economizing on attention costs and having more accurate beliefs. We show that even small processing costs can lead to significant departures from the standard costless processing model. There exist situations where beliefs can cycle persistently and never converge. In addition, when updating is costly, agents are more sensitive to signals about rare events than to signals about common events. Thus, these individuals can permanently overestimate the likelihood of rare events (e.g., the probability of a plane crash). There is a commonly held assumption in economics that individuals will converge to correct beliefs/optimal behavior given sufficient experience. Our results contribute to a growing literature in psychology, neuroscience, and behavioral economics suggesting that this assumption is both theoretically and empirically fragile.
We prove configuration results for extremal Type II codes, analogous to the configuration results of Ozeki and of the second author for extremal Type II lattices. Specifically, we show that for n∈{8,24,32,48,56,72,96} every extremal Type II code of length n is generated by its codewords of minimal weight. Where Ozeki and Kominers used spherical harmonics and weighted theta functions, we use discrete harmonic polynomials and harmonic weight enumerators. Along the way we introduce "t12-designs" as a discrete analog of Venkov's spherical designs of the same name.
Dr. Varda Shalev bridges technology and medicine through Maccabitech, a “research and innovation wing” of Israel’s Maccabi Healthcare Services (MHS) that partners with research institutions, pharmaceutical companies, and startups. Shalev hopes to scale Maccabitech's efforts through the creation of a platform that will enable external researchers to access MHS data. Yet it is unclear how best to structure the platform and its policies. How can Maccabitech maximize impact while still creating value for MHS? And what risks does Maccabitech need to manage?
Kominers, Scott Duke, and Carin-Isabel Knoop. "Maccabitech: The Promise of Israel's Healthcare Data." Harvard Business School Case 819-032, February 2019.
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Kominers, Scott Duke, and Allison M. Ciechanover. "GoFundMe: The Giving Layer of the Internet." Harvard Business School Teaching Note 819-090, January 2019.
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This case, set in October 2017, follows Danielle Steer, general counsel for Carbonite, as she defends the company against claims of patent infringement. It provides a broad overview of the U.S. patent system and explores the impact that non-practicing entities (sometimes also called “patent trolls”) can have on companies.
Cohen, Lauren H., Umit G. Gurun, Scott Duke Kominers, and Sarah Mehta. "When Trolls Attack: Carbonite vs. Oasis Research." Harvard Business School Case 219-001, January 2019.
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This case describes how Feeding America, the third-largest nonprofit organization in the U.S., designed a marketplace for allocating donated food across its network of food banks. It considers the promises and pitfalls of using market-based allocation in the context of a centralized artificial currency market and evaluates the importance of different design components in making the marketplace efficient and fair for all participants.
Late in 2017, CEO Ryan Williams and his team debated whether Cadre should become not only a technology-enabled investment manager, but also an online trading exchange providing high levels of liquidity for investors in commercial real estate (CRE) equity. Cadre was a pioneering New York City–based startup, offering investors equity in individual CRE properties that its investment team had sourced and vetted. Traditional private equity (PE) funds required investors in CRE equity to accept an entire portfolio of properties, while imposing high fees and holding periods of up to 10 years. Cadre allowed investors both deal-by-deal selectivity and managed accounts of Cadre properties, at fee levels substantially lower than those charged by PE funds.
Eisenmann, Thomas R., Scott Duke Kominers, and David Lane. "Cadre." Harvard Business School Case 818-058, March 2018. (Revised July 2018.)
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Silkroad—a cross-cultural music collaboration that world-famous cellist Yo-Yo Ma had spearheaded since 1998, was preparing to celebrate its 20th anniversary. In parallel, Ma was stepping back from his role as the organization’s Artistic Director. Silkroad had come of age, gaining international recognition for its uniquely global music, which blended musical traditions from across the world—especially Asia, the Middle East, Europe, and America. The Ensemble had also forged strong partnerships with universities, local governments, and civic groups and developed an array of outreach programs to help people understand and express themselves through music. Ma was confident that there could be no better time to hand over leadership. But the transition was bittersweet: He felt a deep personal connection both to the Ensemble as a whole and to every one of its performers and staff members. And he wondered how reducing his involvement would affect the organization’s sustainability.
Deshpandé, Rohit, Paul A. Gompers, and Scott Duke Kominers. "Yo-Yo Ma and Silkroad." Harvard Business School Case 818-110, March 2018. (Revised May 2018.)
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By 2017, GoFundMe is the world’s largest social fundraising platform. Gross donation volume is growing rapidly, yet the number of monthly campaign starts is relatively flat. The CEO contemplates a variety of growth initiatives.
The U.S. Intellectual Property (IP) Ecosystem is one of the most robust and dynamic in the world—and has been for centuries. The bedrock of this system is the "patent," a legal document that allows its holder exclusive commercialization rights of a part of the "idea space" granted through the patent. Strong legal protection of IP has made the U.S. a destination of great thinkers and innovators worldwide in order to enjoy this legal protection of their valuable insights. A new threat, however, looms. The same legal system that has protected IP has been used to create an organizational form known as a "Patent Troll." Patent Trolls amass patents for the sake of opportunistically extracting rents from firms producing and commercializing products. In this Industry Note, we describe the origin, evolution, costs, benefits, and future outlook for Patent Trolling in the United States.
Cohen, Lauren H., Umit G. Gurun, Scott Duke Kominers, and George Hou. "Patent Trolling." Harvard Business School Background Note 218-085, February 2018.
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Explains how to identify and capitalize on marketplace design opportunities. Defines markets and marketplaces and describes the basic functions of each. Discusses attributes (e.g., heterogeneity of participants' preferences and asymmetry in available information) that determine whether and how marketplaces create value. Explains common causes of market failure and presents a framework for designing marketplaces in response. Discusses tactics for building trust and liquidity when launching new marketplaces as well as challenges encountered as marketplaces mature (e.g., congestion and disintermediation).
Eisenmann, Thomas R., and Scott Duke Kominers. "Making Markets." Harvard Business School Technical Note 818-096, January 2018. (Revised February 2018.)
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To identify design ideas for their own startup, two MBAs compare the different profiling, matching, and monetization approaches employed by five incumbent dating services: Coffee Meets Bagel, OKCupid, Jiayuan, Dating Ring, and HurryDate.
Describes a wallet maker's application of seven Internet marketing technologies: display ads, algorithmic search, sponsored search, social media, interactive content, online distributors, and A/B testing. Provides concise introductions to the key features of each technology, and asks which forms of online marketing the company should prioritize in the future. Discusses similarities and differences between online and off-line marketing, as well as issues of marketing campaign evaluation.
Edelman, Benjamin, and Scott Kominers. "Online Marketing at Big Skinny." Harvard Business School Teaching Note 911-034, February 2011. (Revised June 2014.)
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