I am a game theorist with particular interest in market/mechanism design, industrial organization, and especially strategic interactions between buyers and sellers. See my CV (publications current as of September 2013). For an overview and more discussion of my research, please see the "Overview" section below. For more detail, see my 2012 research statement.
"On the Benefits of Dynamic Bidding when Participation is Costly". (This version: March 2015. Previous version titled "Dynamic bidding.") Conditionally accepted at Journal of Economic Theory.
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.
"Discounts For Qualified Buyers Only". (This version: June 2011. First version: May 2010.) April 2010 talk (.pdf) Working paper.
Abstract: The standard monopoly pricing problem is re-considered when the buyer's type (e.g. age, income, experience) can be credibly disclosed at some cost. In the optimal sales mechanism with costly disclosure, the seller posts a "sticker price" available to any buyer, as well as a schedule of discounts available to those who disclose certain types. 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, total welfare is strictly less than if the seller could not offer discounts.
"Secrecy in the First-Price Auction". (This version: January 2012. First version: May 2011.) Working paper.
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.
"Secrecy in Auctions". Working paper. [Subsumes "Secrecy in the First-Price Auction" with additional results on second-price and English auctions. April 2013 MilgromFest talk (.pdf)]
Note: This paper is part of a new line of research on "pre-auction signaling", including also "Dynamic Bidding," "Anonymity in the Christie's Auction," and  "Strategic Ignorance in the Second-Price Auction".
"Anonymity in the Christie's Auction". Working paper.
Abstract: Auction houses such as Christie's allow bidders to participate in person or by phone, but the strategic implications of this mingling of visible and anonymous bidding are not well-understood. This paper considers the ``Christie's auction," a variation of the standard English auction in which bidders choose whether to bid over the phone or incur travel costs to appear in person, when there is an ``expert" whose personal taste affects others' values. In equilibrium, the expert and all non-experts with sufficiently little interest bid over the phone, while more serious non-experts travel to attend the auction. The resulting expected revenue is higher than in both the English auction and the second-price auction.
1. "Isotone Equilibrium in Games of Incomplete Information". Econometrica, August 2003, 71(4), pp 1191-1214.
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.
2. "Monotone Equilibrium in Multi-Unit Auctions". Review of Economic Studies, October 2006, 73(4), pp 1039 - 1056.
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.
3. "Monotonicity in Asymmetric First-Price Auctions with Affiliation". International Journal of Game Theory, February 2007, 35(3), pp 427-453.
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.
4. (with Michael Schwarz) "Credible Sales Mechanisms and Intermediaries". 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".)
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.
5. "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.
Waiting until after the bidding to decide how much to sell has strategic advantages.
6. (with Michael Schwarz) "Perverse Incentives in the Medicare Prescription Drug Benefit", Inquiry, Summer 2007, 44(2), 157-166. Featured in NBER Bulletin on Aging and Health, Spring 2006, "Incentives in the Medicare Prescription Drug Benefit" (edited by Courtney Coile).
Identifies and explores incentives that may shape the future of Medicare Part D.
7. "Uniqueness in Symmetric First-Price Auctions with Affiliation". Journal of Economic Theory, September 2007, 136, 144-166.
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.
8. (with Michael Schwarz) "Who Pays When Auction Rules are Bent?". International Journal of Industrial Organization, October 2007, 25(5), 1144-1157.
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.
9. "On the Failure of Monotonicity in Uniform-Price Auctions". Journal of Economic Theory, November 2007, 137, 729-732.
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.
10. "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.
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.
11. (with Ali Hortacsu) "Mechanism Choice and Strategic Bidding in Divisible Good Auctions: An Empirical Analysis of the Turkish Treasury Auction Market". Journal of Political Economy, October 2010, 833-865 (lead article).
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%.
12. (with Giuseppe Lopomo, Leslie Marx, and Brian Murray) “Carbon Allowance Auction Design: An Assessment of Options for the U.S.”. Review of Environmental Economics and Policy, Winter 2011, 25-43.
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.
13. "Performance and Turnover in a Stochastic Partnership". (This version: July 2010. First submitted version: June 2009.) October 2010 talk (.pdf) American Economic Journal: Microeconomics, November 2011, 107–42.
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."
14. "Strategic Ignorance in the Second-Price Auction". (This version: September 2011. April 2013 MilgromFest talk (.pdf) ) Economics Letters, January 2012, 83-85.
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.
15. (with Yingyao Hu and Matthew Shum) "Identification of First-Price Auction Models with Non-Separable Unobserved Heterogeneity", Journal of Econometrics, June 2013, 186-193.
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.
16. (with Yuzo Fujishima and Yoav Shoham) "Speeding Up the Ascending-Price Auction, Proceedings, Int. Journal Conf. in Artificial Intelligence, 1999, pp 554-559 .
How to make internet auctions robust to network communication breakdown.
17. (with James Chapman and Harry Paarsch) "Bounding Revenue Comparisons across Multi-Unit Auction Formats under epsilon-Best Response", American Economic Review, Papers and Proceedings, May 2007, 97(2), 455-458.
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.
This section organizes my research by themes, rather than chronologically.
Much of my early research focused on properties of equilibria in well-studied auction models:
Advances in theoretical equilibrium analysis allow for richer empirical identification of real-world auctions. Thus, it is quite natural that I have also contributed to the empirical auctions literature:
Most recently, my auction theory research has focused on relaxing or endogenizing some of the key assumptions of standard auction models:
Separately, supported by NSF grant #SES-0820051 ("Endogenous Exit from a Stochastic Partnership"), I am exploring partnership dynamics in a stochastic environment. This work has a wide variety of potential applications, from macroeconomics and labor to organizational economics.
When the opportunity arises, I enjoy translating the insights of economic theory into more policy-oriented recommendations. My published and consulting work in this vein has focused mostly on issues of market design, in a variety of contexts from electricity and carbon-allowance markets to Medicare Part D exchanges: