Working papers

“Adoption Epidemics and Viral Marketing with Yangbo Song. An earlier version circulated as “Viral Social Learning”. Click for abstract.

An innovation (e.g., new product or idea) spreads like a virus, transmitted by those who have previously adopted it. We characterize equilibrium adoption dynamics and the resulting lifecycle of virally-spread innovations. Herding on adoption can occur but only early in the innovation lifecycle, and adoption eventually ceases for all virally-spread innovations. A producer capable of advertising directly to consumers finds it optimal to wait and allow awareness to grow virally initially after launch. When most innovations would otherwise be mostly high (or low) quality absent any viral spread, running an optimal-length viral campaign decreases (or increases) equilibrium investment in innovation quality.

“The Political Economy of Epidemic Management” with Troy Day. Click for abstract.

During an infectious-disease epidemic, a political leader imposes “stay-at-home orders” (limiting activity) or “go-out orders” (mandating activity) whenever preferred by the majority of the citizenry over the no-intervention status quo. We characterize the resulting equilibrium epidemic trajectory in an economic-epidemiological model that allows for asymptomatic infection and social-economic complementarities of activity, assuming that citizens are myopic optimizers. We find that the qualitative features of equilibrium policy dynamics hinge critically on whether the pathogen is transmitted before or after infected people have developed symptoms. If transmission only occurs symptomatically, then the leader never imposes stay-at-home orders on the healthy but may impose go-out orders during some phases of the epidemic. However, if transmission occurs asymptomatically, then the leader may impose both stay-at-home orders and go-out orders on the healthy during different phases of the epidemic.

“Rational Disagreement and the Fragility of Social Learning: Identification Failures with Noisy Communication” with Matthew Jackson and Suraj Malladi. Click for abstract.

We examine how agents learn when information from original sources only reaches them after noisy relay. In the presence of random mutation of message content and transmission failures, there is a sharp threshold such that a receiver fully learns if and only if they have access to more chains than the threshold number and they perfectly understand the noise process. However, even slight uncertainty over the relative rates of mutations makes learning from long chains impossible, no matter how many distinct sources information emerges from. The identification failure is that an agent cannot distinguish uncertainty about the state from uncertainty about the noise in communication. This result rationalizes long-run disagreement: even agents with a common prior and access to an arbitrary number of primary sources can end up with different beliefs if their network positions place them at different distances relative to primary sources.


“Steady-State Social Distancing and Vaccination” with Christopher Avery and Frederick Chen, American Economic Review: Insights, 6.1 (2024): 1-19 (lead article). Click for abstract.

This paper analyzes an economic-epidemiological model of infectious disease where it is possible to become infected more than once and individual agents make endogenous choices of social distancing and vaccine adoption. Protective actions adopted by any one person reduce future risks to other people. The positive externalities associated with these behaviors provide motivation for vaccine and social-distancing subsidies, but subsidizing one protective action reduces incentives for other protective actions. A vaccine subsidy increases vaccine adoption and reduces steady-state infection prevalence; a social-distancing subsidy can either increase or reduce steady-state infection prevalence.

“Social Connectedness and Information Markets” with Rachel Kranton, American Economic Journal: Microeconomics16.1 (2024): 33-62. Duke Fuqua feature: “Research Finds Having Too Many or Too Few Connections on Social Media Hurts Information Quality”, Sept 13, 2023. Earlier working-paper version with additional extensions of the benchmark model allowing for asymmetric consumers, arbitrary directed graph, and pay-for-actions revenue model. Click for abstract.

This paper investigates information quality in a simple model of socially-connected information markets. Suppliers’ payoffs derive from the fraction of consumers who see their stories. Consumers prefer to share and act only on high-quality information. Quality is endogenous and highest when social connectedness is neither too high nor too low. In highly-connected markets, low-quality stories are widely seen, giving suppliers little incentive to invest in quality. Increasing the volume of misinformation and increasing consumers’ cost of tuning in to suppliers’ broadcasts can each increase equilibrium information quality.

“Equilibrium Social Activity during an Epidemic” with Yangbo Song and Dihan Zou. Journal of Economic Theory 207 (2023): 105591. Click for abstract.

During an infectious-disease epidemic, people make choices that impact transmission, trading off the risk of infection with the social-economic benefits of activity. In this paper, we investigate how the qualitative features of an epidemic’s Nash-equilibrium trajectory depend on the nature of the economic benefits that people get from activity. If such benefits do not depend on how many others are active (“non-social benefits”), as usually modeled, then there is a unique equilibrium trajectory, the epidemic eventually reaches a steady state, and agents born into the steady state have zero lifetime welfare. On the other hand, if the benefit of activity increases as others are more active (“social benefits”) and the disease is sufficiently severe, then there are always multiple equilibrium trajectories, including some that never settle into a steady state and that Pareto dominate any given equilibrium steady state. Moreover, a wider range of diseases can be beneficially eradicated if agents are able to coordinate on an oscillating pattern of collective activity.

“Learning through the grapevine and the impact of the breadth and depth of social networks with Matthew Jackson and Suraj Malladi. Proceedings of the National Academy of Sciences 119.34 (2022): e2205549119. Featured in Duke Daily, CBS17 Raleigh. Virtual Market Design Seminar by co-author Matt Jackson (video).  Click for abstract.

We study how communication platforms can improve social learning without censoring or fact-checking messages, when they have members who deliberately and/or inadvertently distort information. Message fidelity depends on social network depth (how many times information can be relayed) and breadth (the number of others with whom a typical user shares information). We characterize how the expected number of true minus false messages depends on breadth and depth of the network and the noise structure. Message fidelity can be improved by capping depth or, if that is not possible, limiting breadth, e.g., by capping the number of people to whom someone can forward a given message. Although caps reduce total communication, they increase the fraction of received messages that have traveled shorter distances and have had less opportunity to be altered, thereby increasing the signal-to-noise ratio.

The Economics of Managing Evolution with Troy Day (Queens U, math & biology), David A. Kennedy (Penn State, biology), and Andrew F. Read (Penn State, biology & entomology). PLoS Biology 19, no. 11 (2021): e3001409. Press release (by the journal): “Game theory and economics show how to steer evolution in a better direction.” My contribution: I joined this project after an initial draft had already been completed. My contribution was all of the game-theory analysis. My placement as last author indicates that I was the second-most important contributor.

The Blossoming of Economic Epidemiology. Annual Review of Economics, 13 (2021): 539-570. Earlier working-paper version: Economic Epidemiology in the wake of Covid-19, Covid Economics, issue 48, 1-45 (lead article), Sept 5, 2020.Click for abstract.

Infectious diseases, ideas, new products, and other infectants spread in epidemic fashion through social contact. The COVID-19 pandemic, the proliferation of fake news, and the rise of antimicrobial resistance have thrust economic epidemiology into the forefront of public policy debate and reinvigorated the field. Focusing for concreteness on disease-causing pathogens, this review provides a taxonomy of economic-epidemic models, emphasizing both the biology/immunology of the disease and the economics of the social context. An economic epidemic is one whose diffusion through the agent population is generated by agents’ endogenous behavior. I highlight properties of the equilibrium epidemic trajectory and discuss ways in which public health authorities can change the game for the better by (a) imposing restrictions on agent activity to reduce the harm done during a viral outbreak and (b) enabling diagnostic-informed interventions to slow or even reverse the rise of antibiotic resistance.

Adapting environmental surveillance for polio to the need to track antimicrobial resistance with Christine Årdal, Astrid Wester, and Sigrun Møgedal. Bulletin of the World Health Organization, 99, 239-240.Click for summary.

Virtually every country could benefit from increased environmental (sewage) surveillance, but a
logical next step is to multipurpose environmental surveillance in countries already
performing polio environmental surveillance, to detect other pathogens in addition to
poliovirus. Doing so would increase the sustainability of environmental collection efforts,
improving antimicrobial resistance and SARS-CoV-2 surveillance in low-resource settings,
and would strengthen efforts to finally eradicate polio.

Incentivizing wealthy nations to participate in COVID-19 vaccine Global Access Facility (COVAX): A game theory approach, lead author with Kaci Kennedy McDade (Duke Center for Policy Impact in Global Health), Osondu Ogbuoji (CPIGH), Matthew Johnson (Duke Human Vaccine Institute), Siddharth Dixit (CPIGH), and Gavin Yamey (CPIGH). BMJ Global Health 2020;5:e003627. Related press and public-facing effort:

“Nash SIR: An Economic-Epidemiological Model of Strategic Behavior During a Viral Epidemic”, Covid Economics, issue 16, 115-134, May 11, 2020. Click for abstract.

This paper develops a Nash-equilibrium extension of the classic SIR model of infectious-disease epidemiology (“Nash SIR”), endogenizing people’s decisions whether to engage in economic activity during a viral epidemic and allowing for complementarity in social-economic activity. An equilibrium epidemic is one in which Nash equilibrium behavior during the epidemic generates the epidemic. There may be multiple equilibrium epidemics, in which case the epidemic trajectory can be shaped through the coordination of expectations, in addition to other sorts of interventions such as stay-at-home orders and accelerated vaccine development. An algorithm is provided to compute all equilibrium epidemics.

“Antibiotic development—economic, regulatory and societal challenges” by Christine Årdal, Manica Balasegaram, Ramanan Laxminarayan, David McAdams, Kevin Outterson, John H. Rex, and Nithima Sumpradit.  Nature Reviews Microbiology 18, no. 5 (2020): 267-274. My contribution: Christine Årdal invited me to co-author a contribution to this Viewpoint collection, emphasizing insights from McAdams et al (PLoS Biology 2019); see especially our answer to the final question about resistance emergence. Click for abstract.

Antibiotic resistance is undoubtedly one of the greatest challenges to global health, and the emergence of resistance has outpaced the development of new antibiotics. However, investments by the pharmaceutical industry and biotechnology companies for research into and development of new antibiotics are diminishing. The public health implications of a drying antibiotic pipeline are recognized by policymakers, regulators and many companies. In this Viewpoint article, seven experts discuss the challenges that are contributing to the decline in antibiotic drug discovery and development, and the national and international initiatives aimed at incentivizing research and the development of new antibiotics to improve the economic feasibility of antibiotic development.

“Resistance diagnostics as a public health tool to combat antibiotic resistance: A model-based evaluation”, lead author with collaborators from Sam Brown Lab at Georgia Tech Biological Sciences and Marc Lipsitch Lab at Harvard Chan School of Public Health, PLoS Biology 17, no. 5 (2019). My contribution (as explained in bioRxiv version): “DM conceived the project. DM and SB developed the mathematical models. DM analyzed the models. DM and SB wrote the manuscript. DM wrote SI.A-E.” Click for abstract.

Rapid point-of-care resistance diagnostics (POC-RD) are thought to be a key tool in the fight against antibiotic resistance. By tailoring drug choice to infection genotype, doctors can improve treatment efficacy while limiting costs of inappropriate antibiotic prescription. Here we combine epidemiological theory and data to assess the potential of POC-RD innovations in a public health context, as a means to limit or even reverse selection for antibiotic resistance. POC-RD can be used to impose a non-biological fitness cost on resistant strains, by triggering targeted interventions that reduce their opportunities for transmission. We assess this diagnostic-imposed fitness cost in the context of a spectrum of bacterial population biologies and POC-RD conditional strategies, and find that the expected impact varies from selection against resistance for obligate pathogens to marginal public health improvements for opportunistic pathogens with high ‘bystander’ antibiotic exposure during asymptomatic carriage (e.g. the pneumococcus). We close by generalizing the notion of RD-informed strategies to incorporate both POC and carriage surveillance information, and illustrate that coupling transmission control interventions to the discovery of resistant strains in carriage can potentially select against resistance in a broad range of opportunistic pathogens.

Related press and public-facing effort:

“Empirical Work on Auctions of Multiple Objects” with Ali Hortacsu, Journal of Economic Literature, 56, March 2018, 157-184. Click for abstract.

Abstract: Abundant data has led to new opportunities for empirical auctions research in recent years, with much of the newest work on auctions of multiple objects, including: (i) auctions of ranked objects (such as sponsored-search ads), (ii) auctions of identical objects (such as Treasury bonds), and (iii) auctions of dissimilar objects (such as FCC spectrum licenses). This paper surveys recent developments in the empirical analysis of such auctions.

“Supply, Demand, and Uncertainty: Implications for Prelisting Conservation Policy” with Christopher Galik, Ecological Economics, 137, July 2017, 91-98. Click for abstract.

Abstract: The Endangered Species Act (ESA) faces a shortage of incentives to motivate the scale of conservation activities necessary to address and reverse the decline of at-risk species. A recent policy proposal attempts to change this by allowing landowners to generate credits for voluntary prelisting conservation activities. We explore the proposed policy from the perspective of potential participants. We find that uncertainty present in species listing processes complicates the decision to undertake conservation activities, leading to less conservation being supplied than when a listing decision is certain, while also delaying implementation until late in the listing determination process. Incentives created by the prelisting policy may likewise push species status closer to a listing threshold and thus exacerbate uncertainty in the listing process.

“Analysis of the potential for point-of-care test to enable individualised treatment of infections caused by antimicrobial-resistant and susceptible strains of Neisseria gonorrhoeae: a modelling study” with Katy Turner (lead author), Hannah Christensen, Elisabeth Adams, Helen Fifer (Public Health England), Anthony McDonnell (O’Neill Review on Antimicrobial Resistance), and Neil Woodford (Public Health England), BMJ Open, July 2017, 7:e015447. Commissioned by the O’Neill Review on Antimicrobial Resistance (see here) and featured as a supporting document to their final report (“Tackling Drug-Resistant Infections Globally: final report and recommendations”, May 19, 2016. Contribution: “KT, EA and HC developed the models, following initial work by DM and NW.”Click for abstract.

Abstract: Objective. To create a mathematical model to investigate the treatment impact and economic implications of introducing an antimicrobial resistance point-of-care test (AMR POCT) for gonorrhoea as a way of extending the life of current last-line treatments. Conclusions. The introduction of AMR POCT could allow clinicians to discern between the majority of gonorrhoea-positive patients with strains that could be treated with older, previously abandoned first-line treatments, and those requiring our current last-line dual therapy. Such tests could extend the useful life of dual ceftriaxone and azithromycin therapy, thus pushing back the time when gonorrhoea may become untreatable.

“Resistance Diagnosis and the Changing Economics of Antibiotic Discovery,” Antimicrobial Therapeutics Reviews (Annals of New York Academy of Sciences), 1388(1), January 2017, 18-25. Click for abstract.

Abstract: Point-of-care diagnostics that can determine an infection’s antibiotic sensitivity increase the profitability of new antibiotics that enjoy patent protection, even when such diagnostics reduce the quantity of antibiotics sold. Advances in the science and technology underpinning rapid resistance diagnostics can therefore be expected to spur efforts to discover and develop new antibiotics, especially those with a narrow spectrum of activity that would otherwise fail to find a market.

“Resistance Diagnosis and the Changing Epidemiology of Antibiotic Resistance,” Antimicrobial Therapeutics Reviews (Annals of New York Academy of Sciences), 1388(1), 5-17, January 2017, lead article. Click for abstract.

Abstract: Widespread adoption of point-of-care resistance diagnostics (POCRD) reduces ineffective antibiotic use but could increase overall antibiotic use. Indeed, in the context of a standard susceptible-infected epidemiological model with a single antibiotic, POCRD accelerates the rise of resistance in the disease-causing bacterial population. When multiple antibiotics are available, however, POCRD may slow the rise of resistance even as more patients receive antibiotic treatment, belying the conventional wisdom that antibiotics are “exhaustible resources” whose increased use necessarily promotes the rise of resistance.

“On the Benefits of Dynamic Bidding when Participation is Costly”Journal of Economic Theory, May 2015, 959-972. (Previous version titled “Dynamic bidding.”) Click for abstract.

Abstract: Consider a second-price auction with costly bidding in which bidders with i.i.d. private values have multiple opportunities to bid. If bids are observable, the resulting dynamic-bidding game generates greater expected total welfare than if bids were sealed, for any given reserve price. Making early bids observable allows high-value bidders to signal their strength and deter others from entering the auction. Nonetheless, as long as the seller can commit to a reserve price, expected revenue is higher when bids are observable than when they are sealed.

“Identification of First-Price Auction Models with Non-Separable Unobserved Heterogeneity” with Yingyao Hu and Matthew Shum, Journal of Econometrics, June 2013, 186-193. Click for abstract.

Abstract: We propose a novel methodology for identification of first-price auctions, when bidders’ private valuations are independent conditional on one-dimensional unobserved heterogeneity. We extend the existing literature (Li and Vuong (1998), Krasnokutskaya (2011)) by allowing the unobserved heterogeneity to be nonseparable from bidders’ valuations. Our central identifying assumption is that the distribution of bidder values is increasing in the state. When the state-space is finite, such monotonicity implies the completeness conditions needed for identification. When the state-space is continuous, we also provide some new sufficient conditions which ensure that completeness holds. Further, we extend our approach to the conditionally independent private values model of Li, Perrigne, and Vuong (2000), as well as to unobserved heterogeneity settings in which the implicit reserve price or the cost of bidding varies across auctions.

“Strategic Ignorance in the Second-Price Auction”. (This version: September 2011. April 2013 MilgromFest talk (.pdf) Economics Letters, January 2012, 83-85. Click for abstract.

Abstract: Suppose bidders may publicly choose not to learn their values prior to a second-price auction with costly bidding. All equilibria with truthful bidding exhibit bidder ignorance when bidders are sufficiently few. Ignorance considerations also affect the optimal reserve price.

“Performance and Turnover in a Stochastic Partnership”. (This version: July 2010. First submitted version: June 2009.) October 2010 talk (.pdfAmerican Economic Journal: Microeconomics, November 2011, 107-42. Click for abstract.

Abstract: Suppose that players in a stochastic partnership have the option to quit and re-match anonymously. If stage-game payoffs are subject to a persistent initial shock, the (unique) social welfare-maximizing equilibrium induces a “dating” process in which all partners enjoy the full potential equilibrium gains from each match. By contrast, maximizing social welfare in non-stochastic repeated games with re-matching requires that players burn money or otherwise fail to realize all potential equilibrium gains. Comparative statics on welfare and turnover are also provided, consistent with documented patterns of “survivorship bias” and “honeymoon.”

“Carbon Allowance Auction Design: An Assessment of Options for the U.S.” with Giuseppe Lopomo, Leslie Marx, and Brian Murray. Review of Environmental Economics and Policy, Winter 2011, 25-43. Click for abstract.

Abstract: Carbon allowance auctions are a component of existing and proposed regional cap-and-trade programs in the U.S. and are also included in recent bills in the U.S. Congress that would establish a national cap-and-trade program in the U.S. to regulate greenhouse gases (“carbon”).  We discuss and evaluate the two leading candidates for the auction format for carbon allowance auctions: a uniform-price sealed-bid auction and an ascending-bid dynamic auction, either of which could be augmented with a “price collar” to ensure that the price of allowances is neither too high nor too low.  We identify the primary trade-offs between these auction formats as applied to carbon allowance auctions and suggest auction design choices that address potential concerns about efficiency losses from collusion and other factors.  We conclude that a uniform-price sealed-bid auction is more appropriate for the sale of carbon allowances than the other leading choices, in part because it offers increased robustness to collusion without significant sacrifice in terms of price discovery.

“Mechanism Choice and Strategic Bidding in Divisible Good Auctions: An Empirical Analysis of the Turkish Treasury Auction Market” with Ali Hortacsu. Journal of Political Economy, October 2010, 833-865 (lead article). Click for abstract.

Abstract: We propose an estimation method to bound bidders’ marginal valuations in discriminatory auctions using individual bid-level data, and apply the method to data from the Turkish Treasury auction market. Using estimated bounds on marginal values, we compute an upper bound on the inefficiency of realized allocations as well as bounds on how much additional revenue could have been realized in a counterfactual uniform price or Vickrey auction. We conclude that switching from a discriminatory auction to a uniform price or Vickrey auction would not significantly increase revenue. Moreover, such a switch would increase bidder expected surplus by at most 0.02%.

“Partial Identification and Testable Restrictions in Multi-Unit Auctions”Journal of Econometrics, September 2008, 74-85. Spreadsheets with computations verifying the computations in the main Example. Last revision: June 2008. A previous working-paper version has additional results. Click for discussion.

Unlike in single-object auctions, bidder values are not point-identified when multiple identical objects are sold. This paper characterizes the set of value distributions that can generate any given bid distribution in equilibrium, provides tight bounds on inferred bidder values, and allows one to test the joint assumption of non-increasing marginal values and equilibrium bidding. For work that builds on this paper, see “Mechanism Choice and Strategic Bidding in Divisible Good Auctions: An Empirical Analysis of the Turkish Treasury Auction Market” with Ali Hortacsu and “Bounding Best Response Violations in Discriminatory Auctions with Private Values” (currently inactive) and “Bounding Revenue Comparisons across Multi-Unit Auction Formats under epsilon-Best Response”, each with James Chapman and Harry Paarsch.

“On the Failure of Monotonicity in Uniform-Price Auctions”Journal of Economic Theory, November 2007, 137, 729-732. Click for abstract.

Equilibria of the uniform-price auction be may non-monotone when (i) bidders are risk-neutral with affiliated private values or (ii) bidders are risk-averse with independent private values.

“Who Pays When Auction Rules are Bent?” with Michael Schwarz. International Journal of Industrial Organization, October 2007, 25(5), 1144-1157. Click for discussion.

In many negotiations, rules are soft in the sense that the seller and/or buyers may break them at some cost. All such costs (even those paid by buyers) are ultimately passed through to the seller in equilibrium. Examples include hiring shill (fake) bidders and trying to learn others’ bids before making one’s own.

“Uniqueness in Symmetric First-Price Auctions with Affiliation”Journal of Economic Theory, September 2007, 136, 144-166. Click for discussion.

The first uniqueness result when there are more than two bidders with affiliated private information. Uniqueness proven among class of equilibria in monotone pure strategies (without assuming differentiability of player strategies). See “Monotonicity in Asymmetric First-Price Auctions with Affiliation” for a companion paper.

“Perverse Incentives in the Medicare Prescription Drug Benefit” with Michael Schwarz, Inquiry, Summer 2007, 44(2), 157-166. Featured in NBER Bulletin on Aging and Health, Spring 2006, “Incentives in the Medicare Prescription Drug Benefit”. Click for discussion.

Identifies and explores incentives that may shape the future of Medicare Part D.

“Bounding Revenue Comparisons across Multi-Unit Auction Formats under epsilon-Best Response” with James Chapman and Harry Paarsch, American Economic Review, Papers and Proceedings, May 2007, 97(2), 455-458. Click for discussion.

We argue that the Bank of Canada would gain little were it to run its Receiver-General auctions using a Vickrey format rather than the current discriminatory format.

“Adjustable Supply in Uniform Price Auctions: Non-Commitment as a Strategic Tool”Economics Letters, April 2007, 95(1) 48-53. (See a working-paper version for results in a somewhat more general model.) Previous versions circulated under names such as “Adjustable Supply and Collusive-Seeming Equilibria in Uniform Price Auctions”. First draft: Fall 1998. Click for discussion.

Waiting until after the bidding to decide how much to sell has strategic advantages.

“Credible Sales Mechanisms and Intermediaries” with Michael Schwarz. American Economic Review, March 2007, 97(1), 260-276. Web Appendix that accompanies the paper. (A previous version of this paper circulated under the title “Bargaining with and without Intermediaries”.) Click for discussion.

The auction paradigm has dominated the academic analysis of real-world sales mechanisms for over twenty years, despite the fact that buyers and sellers in many transactions conspicuously lack the ability to commit to an orderly sales process. In this paper, we consider a seller who lacks access to an institution to credibly close a sale, i.e. the seller can not resist “haggling” with buyers. A sealed-bid auction arises endogenously when the cost is haggling is very high and an open ascending-price auction arises when this cost is very low, but the seller can suffer significant losses due to delay in the intermediate case. This creates a niche for intermediaries who can help the seller commit to hard rules. See “Who Pays When Auction Rules are Bent?” (also with Schwarz) for work that builds on this paper.

“Monotonicity in Asymmetric First-Price Auctions with Affiliation”International Journal of Game Theory, February 2007, 35(3), pp 427-453. Click for discussion.

Every bidder must bid more given more favorable private information (in any mixed strategy equilibrium). Previously, this was only known for the two-bidder case or for the independent private values case. See “Uniqueness in Symmetric First-Price Auctions with Affiliation” for a companion paper.

“Monotone Equilibrium in Multi-Unit Auctions”Review of Economic Studies, October 2006, 73(4), pp 1039 – 1056. Click for discussion.

Job-market paper (in 2001). Powerful tools from lattice theory vastly simplify the analysis of multi-unit auctions (e.g. procurement and stock IPOs). In particular, when bidders are risk-neutral with independent types, I show that every mixed-strategy equilibrium is “equivalent” to a monotone pure strategy equilibrium. See “On the Failure of Monotonicity in Uniform-Price Auctions” for related work.

“Isotone Equilibrium in Games of Incomplete Information”Econometrica, August 2003, 71(4), pp 1191-1214. Click for discussion.

Some results from the theory of strategic complementarity can still apply when strategic complementarity fails in games having multi-dimensional actions and multi-dimensional private information. For example, the paper sheds light on oligopolistic competition among firms that compete on several dimensions, allowing one to address questions such as, “Should my firm raise or lower its price when others invest more heavily in research?” See “Monotone Equilibrium in Multi-Unit Auctions” for work that builds on this paper.

“Speeding Up the Ascending-Price Auction with Yuzo Fujishima and Yoav Shoham, Proceedings, Int. Journal Conf. in Artificial Intelligence, 1999, pp 554-559. Click for discussion.

How to make internet auctions robust to network communication breakdown.

Inactive working papers

“‘We haven’t got but one more day’: The Cuban missile crisis as a dynamic chicken game” with Avinash Dixit and Susan Skeath. Excel file with numerical details. Click for abstract.

The risk of nuclear war among superpowers seemed to have ended with the old Soviet Union and the Cold War. But Putin’s invasion of Ukraine, and talk of US-China conflict stemming from the “Thucydides trap,” have renewed interest in the theory and practice of brinkmanship. In this paper, we draw lessons and warnings from the past through a game-theoretic case study of the Cuban missile crisis, the most well-known historical example of nuclear brinkmanship. Relative to previous studies of this crisis, our new contribution is to construct a two-sided dynamic-game model of brinkmanship, enriched by recent findings about the course of events, and to solve it using numbers consistent with estimates of key personnel involved in the crisis. This exercise yields useful quantitative estimates of the risks involved, which turn out to be frighteningly high, and insights missed by the traditional (oversimplified) view of brinkmanship in terms of one-sided threats.

“Secrecy in the First-Price Auction”. (This version: January 2012. First version: May 2011.) April 2013 MilgromFest talk (.pdf). Working paper.Click for abstract.

Abstract: This paper endogenizes bidders’ beliefs about their competition in a symmetric first-price auction with independent private values, by allowing bidders to decide whether to participate publicly or secretly. When public participation is more costly, bidders only participate secretly in the unique equilibrium. By contrast, when secret participation is slightly more costly, all symmetric equilibria exhibit a mixture of secret and public participation. In this case, switching to a second-price format increases expected revenue and expected total welfare among all symmetric equilibria.

“Discounts for Qualified Buyers Only”, June 2011. Click for abstract.

The standard monopoly pricing problem is re-considered when the buyer can disclose his type (e.g. age, income, experience) at some cost. In the optimal sales mechanism with costly disclosure, the seller posts a “sticker price” and a schedule of “discounts” available only to disclosing buyers. Unambiguous welfare implications are available in the limiting case when the buyer’s type is fully informative: (i) The buyer is better off and the monopolist worse off when disclosure is more costly. (ii) When discounts are sufficiently rare, social welfare is strictly less than if the seller could not offer discounts.

“Smart Watershed Markets: The Case of the Central Platte Groundwater Exchange in Nebraska” (draft available on request)

Supplementary materials: